User:Jon Awbrey/INQUIRY 2001

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Contents

In My Third Mind

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In My Third Mind ...

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Note 1

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Subj:  Prolegomena To All Future Met Up With Relatives
Date:  Wed, 28 Mar 2001 13:32:44 -0500
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Mary Keeler <mkeeler@u.washington.edu>

Short reply now, as it may be tommorrow before I can
search my CP's -- I still don't have the CD's yet --
but if you do, you might look up what he says about
"continuous relatives" or "continuous relations" --
but in his later use of the terms, as there are
early uses that are red herrings in this regard --
but I remember it sort of like this:

| X is Y.
|
| X has the Property Y.
|
| X is in the Relation of Having to the Property Y.
|
| X is in the Relation of Being the Relate (1st Correlate)
| of the Relation Having whose Correlate (2nd Correlate)
| is the Property Y.

At this point in the series one has arrived
at a "continuous relative", in the sense of
a recurring, not merely transient relative,
that continues to be invoked at each next
stage in the extended hypostasis.

Or something like that ...

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Found it!

I always forget that when I have some really
obscure memory of something I read in Peirce,
and cannot seem to find it in CP, that I ought
to go back to "My Very First Book of Peirce",
which is the Philip Wiener volume, where most
of the time I will find it in what was ever my
favorite readings, the "Letters to Lady Welby".

Under "continuous predicate", pages 396-397.
Will copy out later if on the off-chance
you cannot find yours.

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Note 2

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Subj:  Prolegomena To All Future Met Relations
Date:  Thu, 29 Mar 2001 10:46:48 -0500
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Mary Keeler <mkeeler@u.washington.edu>

JA = Jon Awbrey
MK = Mary Keeler

MK: Jon, but I can't find anything about "continuous relatives" or "cont.
    relations" in the CP.  There is one interesting remark under "map."
    After he explains why it is not a good metaphor for thought, he says,
    a more apt analogy would be "a continuum of maps overlying one another,"
    and the metaphor for each map would be "a projection of the reality,"
    in which any one idea is a section.  At the same time, he insists that
    if the notion of a map is properly understood it is a considerable aid
    in initiating of the introduction of ideas to be clarified in inquiry
    (CP 8.125).  --MK

JA: No, that's the red herring I was talking about --
    though there is a certain logical relationship,
    this is a very distinct sense of "continuous" --
    more like the distinction between transient
    and ultimately periodic among wave forms ...
    Gee, I hope that was the word he used (?)

JA: You must be going thru your mail systematically --
    that'll teach you! -- but the next post from me
    should explain more.  It's in the Lady Welby
    material, in Wiener and elsewhere, & it was
    "continuous predicate" that he used there.
    Let me know if you can't find a copy and
    I will copy it out for you later.

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Note 3

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Subj:  Semes To Be The Truth
Date:  Thu, 29 Mar 2001 12:46:01 -0500
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Stand Up Ontology <standard-upper-ontology@ieee.org>,
       SemioCom <semiocom@listbot.com>
  CC:  John F Sowa <sowa@bestweb.net>,
       Mary Keeler <mkeeler@u.washington.edu>


| The paitrick lo'es the fruitfu fells,
|   The plover lo'es the mountains;
| The woodcock haunts the lonely dells,
|   The soaring hern the fountains:
| Thro lofty groves the cushat roves,
|   The path o man to shun it;
| The hazel bush o'erhangs the thrush,
|   The spreading thorn the linnet.
|
| Robert Burns, "Now Westlin Winds", 1775


| Finally, and in particular,
| we get a Seme of that highest
| of all Universes which is regarded
| as the Object of every true Proposition,
| and which, if we name it at all, we call by
| the somewhat misleading title of "The Truth".
|
| Charles Sanders Peirce, 'Collected Papers', CP 4.539.


John, Mary,

Morning eyes tell me that a number of statements that I made --
sentences I wrote?  paragraphs I wrote?  @@@aaarrrggghhh!!!  --
of late up late are more likely to cause a blur than a sign
with any species of generativity in anybody's mind, so here
is my try at a restatement, a rewrite, a re-whatever.

Mary, I am including you in this because it was the question
that you asked about CP 4.549 that brought the neighboring
passage from CP 4.539 back into my mind.  Let me know if
you found the Lady Welby selections as I will have time
later today to copy them out if you cannot find them.

Obscurity 1

| I would have to say that this propositional expression,
| say, "e", denotes a function e : X -> B, with the type
| of e being left indefinite for the present moment, not
| yet run time, nor even compile time, but only IOU time.
| This semes to suggest that the type of the proposition
| to be e-nunciated is a co-notation that e-fects itself
| not in the mediate but only in the ultimate denotation.
| I belive that Peirce would fairly call that a "symbol".

I am, as usual, back in the saddle of my favorite hobby horse,
pretty near in the "logical equine class" of an old saw horse,
to wit, the one that I illustrate here:

o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o
|  Objective Framework   | Interpretive Framework |
o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o
|                        |                        |
|      Propositions      |      Expressions       |
|           o            |           o            |
|          / \           |          / \           |
|         /   \          |         /   \          |
|        o     o         |        o     o         |
|     Sets     Maps      | Set Names   Map Names  |
|                        |                        |
o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o
|                        |                        |
| 1.  Generic Type       |                        |
|                        |                        |
|     X          X  -> B |                        |
| G c X     g :  X  -> B |      "G"     "g"       |
|                        |                        |
o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o
|                        |                        |
| 2.  Product Type       |                        |
|                        |                        |
|     X =                |                        |
|     Prod<j> X<j> =     |                        |
|     X<1> x ... x X<k>  |                        |
|                        |                        |
|     X          X  -> B |                        |
| G c X     g :  X  -> B |      "G"     "g"       |
|                        |                        |
o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o
|                        |                        |
| 3.  Abstract Type      |                        |
|                        |                        |
|     X = B^k            |                        |
|                        |                        |
|     B^k       B^k -> B |                        |
| G c B^k   g : B^k -> B |      "G"     "g"       |
|                        |                        |
o~~~~~~~~~~~~~~~~~~~~~~~~o~~~~~~~~~~~~~~~~~~~~~~~~o

This means that I take a proposition-name like "g", that names a proposition,
and a proposition-expression like "((p(q))(q(s))((pq(rs))))", that expresses
a proposition, to be just so many species of signs that adumbrate, denote,
express, indicate, name, or whatever, a species of formal object that we
rangers and scouts may all of us call a "proposition", thus conforming
to the "way out here" way of speaking that got imposed on us by those
brutally civilizing folks who settled our accounts when the frontier
that we opened up came to be claimed as their own deepest interior.

By the way, I rather consistently, if just a bit doggedly,
view the proposition-graph of roughly the following shape,
that gets itself construed in dynamic data-structure form
when the above proposition-string gets parsed into memory,
as yet another brand of sign that denotes the proposition:

|    r o   o s     o rs
|      |   |       |
|    p o   o q     o pq
|       \ /        |
|        o---------o
|        |
|        |
|        @

It is, of course, far more efficient to carry out all
of the needed transformations on the pointer-structure
rather than on the text string, so it is convenient for
practical purposes to recognize the resulting parse-graphs,
much like the function of diagrams in mathematical thinking,
as a theoretically respectable species, family, clan of signs.

So, just the way I see things, and was able to teach a computer to do so,
a name like "g", an expression like "((p(q))(q(s))((pq(rs))))", and a graph
like the one shown above are all just as capable, given a suitable interpreter
to bring them to life, of being the signs of this sort of more or less abstract,
formal, ideal, logical, mathematical object that most folks these days insist on
calling a "proposition", but that we could always resort to calling a certain type
of function, if push(down) comes to shove(up).

So far, so good, but not so far, as yet,
into the heart of this primal obscurity.

In the bit that I said about "compile time, run time"
I was trying to be accommodating to your sense of things,
and find some way to make sense of a more refined partition
of what is, for me, the ultimate logical object domain, namely,
the two layer universe of discourse that consists of the points
of type B^k and the functions of type B^k -> B, for suitable k,
that I usually signify as "(B^k, B^k->B)" or even just as "[B^k]".
In this context, I can recognize the fact that this type of typing
is near-maximally abstract, and so I was trying to interpret some
of what you said as a potential reference to the concrete typing
of point spaces and function spaces, say, in which one would be
sensibly justified in distinguishing among various applications
of the "Splendor" of the form "((p(q))(q(s))((pq(rs))))" to
different concrete domains, say, for example, like these:

1.  p = paitrick, q = quail,   r = rooster,   s = sandpiper.
2.  p = particle, q = quantum, r = radiation, s = static.
3.  p = person,   q = quorum,  r = rule,      s = standard.

Thus, the diverse universes of discourse that are severally
compacted under the ccommon name "[p, q, r, s]" each affords
its own distinctive application for the pre-eminent truth of
the abstract proposition of the from ((p(q))(q(s))((pq(rs)))).
Still, it semes to me that the most important thing to know
about this proposition is that it is always true in whatever
universe of discourse, and so the corresponding painting of
the cells is one that paints each cell indifferently, dare I
say "institutionally", the very same color.  But that is just
saying that ((p(q))(q(s))((pq(rs)))) = 1, where one is free to
read this 1 in any one of the following ways, among many others:

a.  1 : B.
b.  1 : B^4 -> B.
b.  1 : {<p, q, r, s>} -> B.

So what I meant by all of that, if I can either remember or make it up afresh,
is that the concrete type that gets associated with a particular application
of a theorem is one of those refined qualities that belongs to the domain of
application and not so much to the theorem itself.  Or something like that.

I was going to move on to the next obscurity,
but I need to take a vitamin before I do.

Obscurity 2

| Imagine that one picks out a finite collection of one's
| favorite propositions for describing an object domain X.
| The propositions are optimally chosen to be "independent"
| of each other, that is, "orthogonal" in a logical sense,
| and are commonly dubbed as one's "basic propositions" or
| singled out by referring to them as "coordinate projections"
| of the form x<j> : X -> B, for j = 1 to k.  I usually picture
| these as the k "circles" of a venn diagram for the universe X.
| If a given system of basic propositions is moderately adequate
| to the demands of describing, more or less approximately, every
| other region of a "relatively arbitrary" shape that one needs to
| cover in the universe X, then one finds it basically convenient
| to "factor" any "arbitrary" proposition f : X -> B through the
| "cartesian power space" B^k, as in the following diagram:
|
|                          f
|                    X o------>o B
|                       \     ^
|  c = <x<1>, ..., x<k>> \   / f'
|                         v /
|                          o
|                         B^k
|
| This says that f(x)  =  f'(c(x))  =  f'(x<1>(x), ..., x<k>(x)), where
| c(x)  =  the "code" of x  =  the bit-list <x<1>(x), ..., x<n>(x)> in B^k
| is the binary coding of the element x in X, and where
| f' is the  "derived mapping" from codes to B.
|
| Given this sort of set-up, we can proceed to work with
| derived propositions f' : B^k -> B, using truth tables
| or something equivalent.
| 
| What's the point, you ask?  Well, I think of the vertex X as being
| the point where the otherwise pure logic gets applied, and this is
| a species of referential meaning that can vary from application to
| application, a "run time parameter", so to speak.  But the logical
| functions themselves, enjoying types like f' : B^k -> B,  I cannot
| see any way to classify these with any more pretense of refinement
| than to sort them into "logical equivalence classes" (LEC's) based
| on, what else, logical equivalence.  And that puts all theorems in
| the same pot, all absurdities in another, and all contingencies to
| gather with birds of variegate and sundry like-continged feathers.

Obscurity 3

| A truth value is just an element of B, treated as a logical value.
| 
| A propositional expression (a sign thing) is the expression of
| a proposition (an abstract or formal object), which by itself
| gets its abstract or formal meaning by being subject to the
| classical laws of logic, or some other axiom system, but
| since I am a concrete-minded person I constantly check
| its putative properties against one or another simple
| sorts of standard models, for example, functions of
| concrete type X -> B, or of abstract type B^k -> B,
| for a suitable X or k, or the corresponding shapes
| of geometric regions in some universe of discourse
| to whose detail within cells we remain indifferent.
| In short, the sentence denotes a proposition that
| can be interpreted as a function of type B^k -> B,
| but the rangey B at the end is not the B all end all,
| and it is certainly not the denotation of the sentence.

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Note 4

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Subject:  Trit
   Date:  Sat, 31 Mar 2001 14:14:28 -0500
   From:  Jon Awbrey <jawbrey@oakland.edu>
     To:  Tom Holroyd <tomh@po.crl.go.jp>
     CC:  Mary Keeler <mkeeler@u.washington.edu>

Tom Holroyd wrote:
> 
> say, just out of my head here, a question i keep asking people,
> that only gets responses during drinking parties,

You are going to the wrong parties ...

> category theory describes dual objects;  mathematical constructs that
> are essentially one idea looked at from two points of view -- not that
> you ever see that one idea clearly exhibited;  indeed, you can't see it
> directly but only as one of two aspects at a time.
> 
> the question is, why two?  are there mathematical objects which have _three_ aspects?
> for example, instead of "dualizing" a theorem to yield another theorem, there would be
> a mechanism that transformed a theorem into first one form, and then another, and then
> back to the original.
> 
> have you ever heard of such a thing?  the only answer i've ever gotten
> to this was that there are such objects but mathematicians don't study
> them because they are too complicated -- but it was at a party and the
> guy in question later denyed saying it ...
> 
> Dr. Tom Holroyd
>
> "I am, as I said, inspired by the biological phenomena in which
>  chemical forces are used in repetitious fashion to produce all
>  kinds of weird effects (one of which is the author)."
>
> -- Richard Feynman, 'There's Plenty of Room at the Bottom'

Tom,

This is pretty weird ...

I was just getting reading to broach the subject of "triality"
to the several lists of my gad-flying acquaintance, and trying
to figure out how, as a question that Peirce scholar Mary Keeler
recently asked me has stirred me from my dualistic slumbers and
reminded me of some work I did in this direction many moons ago.
Contingent on her permission to do so, I will forward you the note
of incitement in question, and include you in future correspondence.

Aside from this issue, that has to with the prospective subject
of "third intentions" in logic, and Peirce's rather mysterious
suggestion that perhaps there might be closure at three but not
before, there is also talk of "trialities" in algebra, especially
group theory and lie algebras, and I think some in geometry, but
I am even more hazy on that.

And you will probably recall that there is an aspect of triadicity
at the very inception of category theory, underlying the notion of
a "natural transformation", that, to define, it became necessary
to define the notion of a "functor, that, in turn, to define,
it became necessary to define the notion of a "category",
with its "arrows" and "objects" trailing along in tao.

Party On, Dude!

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Note 5

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Subj:  Prolegomena
Date:  Wed, 04 Apr 2001 22:06:21 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Tom Holroyd <tomh@PO.CRL.GO.JP>
  CC:  Mary Keeler <mkeeler@u.washington.edu>,
       Jack Park <jackpark@thinkalong.com>

Tom,

Here is what Mary Keeler sent me earlier this week.
I keep trying to get back to this, but I have to be
traveling this weekend and I needed to finish up the
intro to my PERS thread before I lost concentration.
Will try to get back to it early next week.

Thanks to both of you for reminding me of this stuff --
but the work I did before goes back 15-20 years and
there is almost no chance I can find my old notes,
so I may be just a little bit slow warming up
those particular gray cells again.

Mary Keeler wrote:
> 
> Hello Jon,
> 
> I've been working on a manuscript for a book chapter,
> trying to explain P's logic and how it might relate
> to "semantic web" development.  There is one tough
> point I'd like to ask you about.  Have you found
> anything concerning "third intentions," outside
> of the Prolegomena (see paragraph below)?  That
> was 1906, and Peirce just mentions it in passing.
> Do you know what he means by that term, if logic
> (according to tradition) is the study of second
> intentions applied to first intentions?  Is he
> simply making a vague reference to the realm of
> modal logic, still to be developed at that point?
> --MK
> 
> (I particularly like his reference to the Categories
>  as "Predicaments," and think we should observe that
>  change and develop it for better appreciation of his
>  phenomenology?)
> 
> -------------------------------------------------------------------------
>
> | 4.549.  I will now say a few words about what you have called Categories,
> | but for which I prefer the designation Predicaments, and which you have
> | explained as predicates of predicates.  That wonderful operation of
> | hypostatic abstraction by which we seem to create entia rationis
> | that are, nevertheless, sometimes real, furnishes us the means
> | of turning predicates from being signs that we think or think
> | through, into being subjects thought of.  We thus think of the
> | thought-sign itself, making it the object of another thought-sign.
> | Thereupon, we can repeat the operation of hypostatic abstraction,
> | and from these second intentions derive third intentions.  Does this
> | series proceed endlessly? I think not.  What then are the characters
> | of its different members?  My thoughts on this subject are not yet
> | harvested.  I will only say that the subject concerns Logic, but
> | that the divisions so obtained must not be confounded with the
> | different Modes of Being:  Actuality, Possibility, Destiny (or
> | Freedom from Destiny).  On the contrary, the succession of
> | Predicates of Predicates is different in the different
> | Modes of Being.  Meantime, it will be proper that in
> | our system of diagrammatization we should provide for
> | the division, whenever needed, of each of our three
> | Universes of modes of reality into Realms for the
> | different Predicaments.

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Note 6

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Subj:  Continuous Predicates & Hypostatic Abstraction
Date:  Mon, 09 Apr 2001 15:30:30 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>,
       Complexity Group <complexity-l@venus.vcu.edu>,
       Peirce Online Resource Testbed <PORT-L@LISTSERV.IUPUI.EDU>,
       SemioCom <semiocom@listbot.com>,
       Stand Up Ontology <standard-upper-ontology@ieee.org>

This is a quotation that I have been looking for since way last year,
when I thought it would bear on the topic of hypostatic abstraction,
more commonly known as "personification" or "reification", at least,
among the literate, if not yet the literati.  But it fell outside my
presently beaten path, if yet again on the very first path that ever
I walked through these Peircean woods, primeval, and so it was only
with the more recent inquiry of that outside agitator and notorious
Peirce scholar Mary Keeler that I was led to happen on it once again.
To understand this excerpt you will need to know that Peirce uses the
noun form "relate" (with the accent on the first syllable, I guess) to
denominate the first term of a relation, whereas he uses the noun form
"correlate", sometimes specified by an ordinal adjective, to designate
any one of the remaining terms, if any, in that relation.

| When we have analyzed a proposition so as to throw into the subject everything
| that can be removed from the predicate, all that it remains for the predicate to
| represent is the form of connection between the different subjects as expressed in
| the propositional 'form'.  What I mean by "everything that can be removed from the
| predicate" is best explained by giving an example of something not so removable.
| But first take something removable.  "Cain kills Abel."  Here the predicate
| appears as "--- kills ---."  But we can remove killing from the predicate
| and make the latter "--- stands in the relation --- to ---."  Suppose we
| attempt to remove more from the predicate and put the last into the form
| "--- exercises the function of relate of the relation --- to ---" and then
| putting "the function of relate to the relation" into a another subject leave
| as predicate "--- exercises --- in respect to --- to ---."  But this "exercises"
| expresses "exercises the function".  Nay more, it expresses "exercises the function
| of relate", so that we find that though we may put this into a separate subject, it
| continues in the predicate just the same.  Stating this in another form, to say that
| "A is in the relation R to B" is to say that A is in a certain relation to R.  Let
| us separate this out thus:  "A is in the relation R^1 (where R^1 is the relation
| of a relate to the relation of which it is the relate) to R to B".  But A is
| here said to be in a certain relation to the relation R^1.  So that we can
| expresss the same fact by saying, "A is in the relation R^1 to the relation
| R^1 to the relation R to B", and so on 'ad infinitum'.  A predicate which
| can thus be analyzed into parts all homogeneous with the whole I call
| a 'continuous predicate'.  It is very important in logical analysis,
| because a continuous predicate obviously cannot be a 'compound'
| except of continuous predicates, and thus when we have carried
| analysis so far as to leave only a continuous predicate, we
| have carried it to its ultimate elements.  (SW, 396-397). 
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

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Note 7

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Subj:  Why Triadicity Matters
Date:  Mon, 23 Apr 2001 16:40:08 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Christopher Spottiswoode <cms@metaset.co.za>

Christopher Spottiswoode wrote:
> 
> Jon, many thanks for your ever-attentive and - shall we say? -
> lateral-thinking reply of the kind that I imagine I always seek.
> (My delay in answering was merely due to factors beyond my control,
> and has no relationship, anyadic or otherwise, to the value I place
> on this dialog.)
> 
> > > But while I happily skip all the KIF-related stuff I am genuinely
> > > interested in this triadicity question.  As you know, I follow
> > > a binary-relationed approach, but I am ever on the lookout for
> > > fundamental oversimplifications I may be making.
> >
> > I think that the basic problem here is one of automatization --
> > in the sense of "habituation" that psychologists go on about --
> > people seem to have lost the ability to reflect on the depth
> > to which they are utterly swimming in triadic relations with
> > every thought they make or take or even fail to shake (bake?).
> 
> I am in no doubt, I believe, as to the depth and infinite-adicity
> of that in which we live, move and have our being.  The trick is
> to say useful things about it which others can comprehend in ways
> that seem to be relevantly similar to those in which we ourselves
> see them.
> 
> > > As a commercial-application developer for many years
> > > I - like many others - have found binary ER quite adequate, ...
> >
> > What's "ER"? -- over here it always means "Emergency Room" ...
> 
> Yes, I have long rather feared such gybes (= catching the wind as the
> helmsman did not intend).  So I added this little wand-wave to my very
> first web page on this whole subject (as the first paragraph of the
> "Synthesis" section of:
>
> http://jeffsutherland.com/oopsla96/spottisw.html
> 
> | MACK is based on yet another old faithful from The Mainstream:
> | binary entity-relationships spun into a semantic web.  Need that
> | unduly invite oversimplification?  No more so than alphabets or
> | number systems unduly oversimplify the complex realities that we
> | represent with their help!

Okay, it's just been a while since I had the option
to think that way in my "repertoire of choice" (ROC).

> Ever since Chen invented it in 1975, database designers such as
> myself have happily used binary ER in their professional work.

Okay, now I know who to blame for this BER mark-up.

> It is true that many of them express their frustration at not being able
> to take their ER analyses further (I believe that is mostly because they
> get all tangled in too much of it), but I have seen none of my IS/DB
> colleagues believe that the binary aspect is the problem.

I know of people who are frustrated at the notion that Pi =/= 3.

> True, UML is not limited to binary, but there are frequent
> comments that that is one of its unnecessary complications.

UC = 0.1415926535 ...

> > > and my immediate needs in my present far more ambitious
> > > "SUO-like" project seem to be quite adequately met too.
> > > A la Pat Hayes or à la Matthew West I can explicitly
> > > build up any n-arity that is required, yet without
> > > knitting excessive lumps or knots into the fabric.
> >
> > There's this story about "The Peircist & The Pea"
> > that I heard as a child ...
> 
> Methinks [and I can't help but think] the lady doth protest too much.
> Please can you show me that pea?
> 
> > > That is thanks also to some of my key though
> > > presently "trade secret" yet surprisingly
> > > mainstream constructs.
> > >
> > > Like Pat Hayes, and even before he expressed himself that way,
> > > I have been suspecting that the basic Peircean or semiotic triad
> > > may be a factor that leads you insist so on triadicity.  (That was
> > > at least partly what I had in mind in points 3) and 5) of my very
> > > first message to you, of Aug 24 last year.)  If so, then I think
> > > you are at cross-purposes with us conventional binary ERers who
> > > so conventionally and happily reify or create n-propertied
> > > mediating entities.
> >
> > Pat Hayes is apparently under the impression that I began my study
> > of logic with Homer and Lao Tzu and have only recently read up as
> > far as the Nineteenth Century, now and then peeking over the brink
> > of illumination into the realm of that Steam-Fired Locomotive Train
> > of Higher Consciouness known as the "Twentieth Century Limited", but
> > people who know how this sort of thing happens will grok that this
> > Pilgrim's Regress is pretty much exactly in the opposite direction.
> 
> I am sure Pat is wrong if that is what he does believe,  but I don't see
> your answer to his problem, which is that there seems to be no good reason
> why you so insist on triadicity.  That is why I also suspect some confusion
> due to the Peircean triad.

This is all stuff that I learned in my very first college algebra course.
I still have the textbook -- I keep darn near everything! -- and the words
"a binary operation is a ternary relation" live in memory like it was Hamlet.
I have to tell you that I have been rather shocked at the lack of grok on this.

> > > The semiotic triad -- it seems to me (and I think to Hayes too) --
> > > is part of some proto-apparatus for a reflective knowledge-process-
> > > model or model of cognition.  In my (MACK) scheme of things that
> > > aspect is provided for at a much higher level than that of the basic
> > > conceptual model.  Even more cruelly, my present hypothesis is that
> > > your confusion (as I see it, and I suspect it may be Sowa's too)
> > > suffers from some basic Ontological error.
> >
> > I dunno, to me this is just logic and mathematics, whose structures
> > can be used to much good effect to model cognition and computation,
> > but that obey the iron-horse laws of their own internal dynamics.
> 
> I agree with you on the complete respect we must show logic
> and its bearing on things internal to our conceptual models.
> 
> > > Our conceptual models need have no fundamental supposed equivalences
> > > to features of our model of cognition.  They need merely be usefully
> > > manipulable and accurate enough in their application during the
> > > cognition process ...
> 
> > It is possible that I agree with this, but I see logic as normative
> > for thinking, not as something that leans on thinking for its guide.
> 
> No contradiction here either (as in my previous comment just inserted).
> 
> > > That argument or view must come across as crude and/or vague,
> > > but I see it as another clear-enough aspect of my simple-minded
> > > agate model as I set it out here:
> > >
> > > http://jeffsutherland.com/oopsla98/SpottComplexity.html
> > >
> > > The binary ER components are purely for the conceptual stuff
> > > as represented by the crystalline and micro-crystalline interior
> > > of the agate, while the cognition process is represented by the
> > > rough but epistemologically-critical boundary between the fine
> > > agate and its ineffable surrounding matrix.  Those two scenes
> > > are quite different, and I am under the strong impression that
> > > you and maybe John Sowa confuse them.
> 
> > I have a vague impression that this may be related to how I view
> > the tension between the "formative" and the "formalized" context,
> > but I cannot seme to make it any more precise than that right now.
> 
> I can attach some relevant meaning to that distinction,
> if the "formative" aspect refers to the fuzzy relationship
> between our mental constructs and the "deemed-real world"
> (which as you know does not consist of things-in-themselves
> that can be placed, one-to-one, at the end of relationship
> arcs of whatever adicity).

If you are talking aboat "arcs" --
not some fancy brand of hyper-arcs --
then you are talking aboat 2-adic vehicles,
otherwise we are not in the same boat atoll.

> By "fuzzy" I mean here that that relationship (which is part
> of what I referred to as "the cognitive process") cannot be
> modelled in any conclusive way except by means of unpursuable
> metaphors such as my agate or Plato's cave, and I certainly
> mean that the binary/ternary issue just bears no relevance to
> that relationship at all, even though that cognitive process
> model does indeed find that relationship irreducible (as part
> of its ineffable "fuzziness").

Well, I used to call it "casual" or "informal",
but people kept reading "casual" as "causal",
and "informal" had all the disadvantages of
"definition in terms of what a thing is not",
so I have been experimenting with "formative"
just to see how it goes over.  The associations
to "inchoate" (Latin for "all hitched up with no
field to plow" -- I think the "in-" = "ad-" here.)
"incipient", "initial", and "chaotic" come to mind.
Ylem, Ymir, Yggdrasil, I will 4-go writing the 4-gram.

> Jon, I still seek some contradiction to my dismissal
> of your rejection of the validity of binary ER in our
> practical modelling of the real world and our cognitive
> relationships with it.  I still see your problem as
> Ontological rather than ontological, ...

| You try the handle of the road
| It opens do not be afraid
| It's you my friend, you who are the capitalist
| It's you my friend, you who are the Capitalist 

> and I fail to see the relevance to Being or Ontology [BOO!]
> of "ontological" triads that you seem to see.  I cannot help
> but suspect that the Peircean triad lies at or near the root
> of your insistence, and I am more determined than before to
> continue deprecating the use of the lowercase "ontology" word
> in this context, in favour of the plain MACK word "model" (or
> "context" or "perspective", depending on the context).

That's some j'accuse, mon ami!

It's not exactly the "Order Of The Back-Handed Compliment"
that got when Pat Hayes elevated me to that distinguished
company of writers that he does not condescend to read,
but it will have to do, I guess.

> Phew!  I never thought I could work up such a head of steam
> over such a cold and abstract matter.  So:
> 
> Ever seeking contradiction of my potential oversimplifications (and
> noting that I have not yet sought explicit demonstration of my own
> potential overcomplications as an inevitable consequence of my
> binary penchant, and being ever aware that the twin aberrations
> just considered are often betrayed by such mental stews as
> I have just found myself in ... and inflicted upon you!),
> and with many TIA,
>
> Christopher

Look, maybe we should focus on some knitty-grippy
computational questyings out with which to start.

Do you get the bit about "and" invoking a 3-adic relation,
for instance, if you were to call on it each time "as if"
a table look-up, it would be this information structure:

o-----o-----o---------o
|  x  |  y  | z = x&y |
o-----o-----o---------o
|  0  |  0  |    0    |
|  0  |  1  |    0    |
|  1  |  0  |    0    |
|  1  |  1  |    1    |
o-----o-----o---------o

How do you deign to supplant that with a 2-ER replacement?

But No Hurry ...

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 8

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Intentional Orders
Date:  Mon, 23 Apr 2001 23:23:02 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>,
       SemioCom <semiocom@listbot.com>
  CC:  Mary Keeler <mkeeler@u.washington.edu>,
       Tom Holroyd <tomh@PO.CRL.GO.JP>

Mary Keeler wrote:
> 
> Now, Jon, what does Peirce say, along these lines,
> about "third intentions"?  I will eventually get
> my Welby book, just wonder what can be said of
> 3rd intentions with regard to 2nd?  --MK
> 
> On Sat, 31 Mar 2001, Jon Awbrey wrote:
> > 
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > | By 'logical' reflexion, I mean the observation of thoughts in their expressions.
> > | Aquinas remarked that this sort of reflexion is requisite to furnish us with
> > | those ideas which, from lack of contrast, ordinary external experience fails
> > | to bring into prominence.  He called such ideas 'second intentions'.  It is
> > | by means of 'relatives of second intention' that the general method of
> > | logical representation is to find completion.
> > |
> > | Charles Sanders Peirce, 'Collected Papers', CP 3.490.
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Mary, Tom, ...

Here is an old idea of mine that comes to mind in this connection.
I have no idea whether it has anything to do with what Peirce,
much less Aquinas, intended their numerous intentions to mean.

Suppose that you are running through a sequence of thoughts,
when you spontaneously reflect on the circumstance that you
have been thinking in a circle for quite some time running,
and in your mind's eye you form the following image of the
course of your thoughts -- I use a 4-cycle for a circle:

|          o-------->o
|          ^         |
|          |         |
|          |         |
|          |         v
|          o<--------o

But, of course, this image has already been rendered
passé, obsolete, incomplete, and even deceptive to a
degree, in the very moment that you mark by means of
its constellation, and by the very act of reflection
that engenders it, since this reflection constitutes
a novel moment of thought, off the circle of thought
that your former way of thinking traced and retraced,
and so you turn to amending the image to reflect the
perspective that you have gained through this primal
moment of reflection, and this will be a bit like so:

|          o-------->o
|          ^         |
|          |         |
|          |         |
|          |         v
|          o<---o----o
|               |
|               |
|               |
|               v
|               o = "I am being loopy"

This is the result of the first reflection,
what you may well call a retrospective one.

But, of course, the image has already been rendered --
iconoclast that you can now see you are -- a stream
of consciousness under the bridge, as your critical
awareness of being loopy up until now makes you far
less loopy than you had heretofore been, and so you
feel almost compulsively drawn to revise your image
of your self and your thought's own form of conduct,
but this time you have gained a sufficient esthetic
distance from the more habitual rote of the pattern
that you can foresee where the way of things may be
headed, and so you can draw up the new account in a
way that reflects what will be true when it is said
and done.  And this picture will look a bit like so:

|          o-------->o
|          ^         |
|          |         |
|          |         |
|          |         v
|          o<---o----o
|               |
|               |
|               |
|               v
|               o = "I am being loopy"
|               |
|               |
|               |
|               v
|               o = "I will handle it"

This is the outcome of the second reflection,
what you might well call an anticipatory one,
and I think that it enjoys a form of closure.

Hope you enjoyed my little tale,

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 9

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Brouillon Projet, Les Yeux Des Argues, La Laine Des Cartes
Date:  Thu, 03 May 2001 14:34:56 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Jean-Marc Orliaguet <jmo@medialab.chalmers.se>
  CC:  Arisbe <arisbe@stderr.org>,
       SemioCom <semiocom@listbot.com>,
       Standardize Unto Others <standard-upper-ontology@ieee.org>

| Book 1.
| Definitions.
|
| 1.  A 'point' is that which has no part.
|
| 2.  A 'line' is breadthless length.
|
| 3.  The extremities of a line are points.
|
| 4.  A 'straight line' is a line which
|     lies evenly with the points on itself.
|
| 5.  A 'surface' is that which has length and breadth only.
|
| 6.  The extremities of a surface are lines.
|
| 7.  A 'plane surface' is a surface which
|     lies evenly with the straight lines on itself.
|
| [It Continues ...]
|
| "Euclid",
| 'The Thirteen Books of Euclid's "Elements"', Second Edition,
| Translated from the Text of Heiberg, With an Introduction and
| Commentary by Sir Thomas L. Heath, Dover, New York, NY, 1956.
| Volume 1, page 153.

Jean-Marc,

I am going to recoup one of my earlier essays on this subject --
there were so many clever things that I blurted out within it,
as the initial incitements of the topic struck me on my first
impression, that my elastic, all too elastic stores of memory
are already beginning to blur into obliviscence, that form of
resilience in impressionability that I suspect you share, too.
Besides which concern I am for the moment earnestly of a mind
and a mettle to keep on broadening out this malleable subject
to take in some aspects of what we mean by definition, in the
first place, if that is indeed the only place for definitions
to make a place for themselves, which I occasionally question.

JM:  A mon avis dans l'extrait que vous citez (1.551) le terme "ground"
     est pris dans un sens beaucoup plus large que implement le ground
     d'un signe, puisque Peirce écrit (New List ... ): 

     | Moreover, the conception of a pure abstraction is indispensable,
     | because we cannot comprehend an agreement of two things, except
     | as an agreement in some respect, and this respect is such a pure
     | abstraction as blackness.  Such a pure abstraction, reference to
     | which constitutes a quality or general attribute, may be termed
     | a ground.
     |
     | The conception of second differs from that of other,
     | in implying the possibility of a third.  In the same way,
     | the conception of self implies the possibility of an other.
     | The Ground is the self abstracted from the concreteness which
     | implies the possibility of an other.

JM:  Since no one of the categories can be prescinded from those
     above it, the list of supposable objects which they afford is,

     What is:

     Quale         -- that which refers to a ground,

     Relate        -- that which refers to ground
                      and correlate,

     Representamen -- that which refers to ground,
                      correlate, and interpretant.

JM:  C'est à dire qu'on peut penser le ground sans le signe
     mais pas l'inverse.  Donc il ne s'agit pas seulement du
     ground du signe, mais du ground de manière beaucoup plus
     générale, puisque "le ground est abstrait d'un être concrêt
     (après coup identifié comme le representamen/signe) et implique
     la possibilité d'un autre être (après coup identifié comme l'objet
     du signe)".  Donc définir le ground à partir de la notion est signe,
     interprétant ... c'est mettre la charrue avant les boeufs. 

JA:  Arisbeans, SemioCompères, ...

JA:  This is my first essay at making some remarks,
     all of which have been accumulating in my mind
     for quite some time, about the uses that people
     frequently make of Peirce's Categories, but that
     I think, in my arrogance, go against the grain of
     his thought overall.  This is a difficult subject
     to get a handle on, and so I am likely to fail on
     the first few tries, at best, if not perpetually.

JA:  What I want to say, first and foremost, is that
     Peirce was a relational thinker, one of the first,
     one of the best, and, I am beginning to fear, one
     of the last thoroughly relational thinkers that we
     will ever see throughout our intellectual history.
     I have had my own struggles in trying to transform
     my thinking in this way, and, after a long time,
     I can still see many absolutist and essentialist
     habits that were ingrained in me by the standard
     experiences and impressions of my rote education.
     But that is another story.  What is pertinent here
     is the observation that Peirce's unique daimon as
     a relational spirit means that we cannot interpret
     his ostensible Categories in the same absolutist
     and essentialist ways that we have been accustomed
     to regard Aristotle's, Kant's, Hegel's, and so on.
     Another time I will argue whether it was right to
     interpret even Aristotle in so extreme a manner,
     but another time.  In particular, I think that it
     would be a mistake for us to seek out in Peirce's
     work, or to foist upon it, a new fundamentalism
     that seeks to base itself on the idea of "ground".

JA:  And so, just to 'cut to the chase', and to tell you the way
     that I have personally worked out to negotiate a compromise
     between this ordinarily so unrelational a term as "Category"
     and what is evidently a thoroughly relational way of thinking,
     let me suggest this interpretation of 1-ness, 2-ness, 3-ness,
     insofar as they apply to the subject matter of sign relations.

JA:  1-ness has to do with the 1-dim projections of sign relations.
     2-ness has to do with the 2-dim projections of sign relations.
     3-ness has to do with the 3-dim projections of sign relations.

JA:  In the 1st category we find the relations of O to O, S to S, I to I.
     In the 2nd category we find the relations of O to S, O to I, S to I.
     In the 3rd category we find the relations of O, S, I, in 3-foldness.

JA:  Similar studies can be outlined for any other type of k-adic relation.
     But we simply must begin to lift our eyes above the level of one tuple
     at a time if we wish to understand what 3-adic or k-adic relations are.

JM:  Isn't the ground of the nature of a "form"
     or a relational structure?  What else could
     it be like?

JA:  I am tempted to agree, and I probably would if I could use the
     words "form" and "relational structure" in the ways that I am
     already used to, but I cannot be sure yet of the way that you
     may intend them, so I must hesitate until I know your meaning.

JM:  [Quotes JA:]

     | And so, just to 'cut to the chase', ...
     | 
     | In the 1st category we find the relations of O to O, S to S, I to I.
     | In the 2nd category we find the relations of O to S, O to I, S to I.
     | In the 3rd category we find the relations of O, S, I, in 3-foldness.

JM:  There you have a circular definition.

JA:  I pretend no definition.

JA:  I am presenting the relations among primitive notions,
     undefined in themselves and yet aphorized in relation
     to one another.  This is in practice a very common way,
     at least among non-fundamentalists, for setting out the
     underpinnings of a conceptual framework, as if to raise
     the geodesic domes of our thought by gradually allowing
     the 'tensegrity' of the whole structure to raise itself
     in the very process of hanging together.  It goes back to
     Euclid, of course, where points and lines remain undefined,
     but bear their mutually supportive relationship to each other.

JM:  If the definition of the 1st category
     is derived from the idea of S, O, and I,
     as elements of a genuine triad ("1-ness
     has to do with the 1-dim projections of
     sign relations"), then the first category
     presupposes the 3rd category.  (???)

JM:  Idem with the 2nd category

JA:  Let me express the general principle in the words of Noam Chomsky:

     | In linguistic theory, we face the problem of constructing
     | this system of levels in an abstract manner, in such a way
     | that a simple grammar will result when this complex of abstract
     | structures is given an interpretation in actual linguistic material.
     |
     | Since higher levels are not literally constructed out of lower ones,
     | in this view, we are quite free to construct levels of a high degree
     | interdependence, i.e., with heavy conditions of compatibility between
     | them, without the fear of circularity that has been so widely stressed
     | in recent theoretical work in lingustics.  (Chomsky, LSOLT, page 100).
     |
     | Noam Chomsky, 'The Logical Structure of Linguistic Theory',
     | Based on a widely circulated manuscript dated 1955.
     | University of Chicago Press, Chicago, IL, 1975.

JA:  And, of course, everyone has heard of the "hermeneutic circle".

JA:  Without understanding the power of these potentials,
     I fear that semiotics will never get off the ground.

To the present:

JM:  Isn't the ground of the nature of a "form"
     or a relational structure?  What else could
     it be like?

JA:  I am tempted to agree, and I probably would if I could use the
     words "form" and "relational structure" in the ways that I am
     already used to, but I cannot be sure yet of the way that you
     may intend them, so I must hesitate until I know your meaning.

JM:  my meaning would be, a collection of points and relations
     between these points so that no point is left alone.

     | "... the phaneron is made up entirely of qualities of
     |  feeling as truly as Space is entirely made up of points. ...
     |  no collection of points ... without the idea of the objects
     |  being brought together can in itself constitute space."

JM:  What is yours?

JA:  Form.  From Latin "forma" = "beauty".
     There's more to say, of course, but
     that is all you really need to know.

JA:  Relational Structure.  Any relation
     viewed with an eye to its form, q.v.

JA:  Relation.  Here I see two cases:

     1.  Relation in Extension = a set of tuples.
         Tuple = finite sequence of elements from
         a predesignated set or collection of sets.
         If the tuples all have the same cardinality k,
         then they are called k-tuples and the relation
         is said to have "arity", "adicity", "valence" k.

     2.  Relation in Intension = a property ("intension")
         that is common to all of the elements in a set.
         Nota bene:  Saying that a property is shared by
         all of the elements in a set is different from
         saying that the property is a property of a set.
         The elements of a relation in intension are known
         as "elementary relations".  These are the analogues,
         in intension, of the tuples in extension.

JA:  For the past many years, all against my first inclinations,
     I have been working to develop the extensional side of the
     theory of sign relations, simply because this area is less
     crowded, because far less work has been done on this face
     of the mountain, and because this is the side of things
     that makes a connection with empirical efforts, say,
     in databases, ethology, and qualitative research.

JA:  In the 1st category we find the relations of O to O, S to S, I to I.
     In the 2nd category we find the relations of O to S, O to I, S to I.
     In the 3rd category we find the relations of O, S, I, in 3-foldness.

JM:  These would be the degenerate categories of thirdness.
     I believe that it is better to build the categories so
     that they are hierachized but still be independent of
     each other.  How do you express the fact that genuine
     secondness is independent of genuine thirdness?

JA:  I have the feeling that "independent" may be another one of
     those words that we use in different ways from one another.

JM:  Genuine thirdness requires an independent secondness
     and an independent firstness, i.e. a genuine secondness
     that exists independently of genuine thirdness, but all
     genuine secondness is not necessarily independent of all
     thirdness (ex: degenerate thirdness in the first degree).

     | Thirdness it is true involves Secondness and Firstness, in a sense.
     | That is to say, if you have the idea of Thirdness you must have had
     | the ideas of Secondness and Firstness to build upon.  But what is
     | required for the idea of a genuine Thirdness is an independent
     | solid Secondness and not a Secondness that is a mere corollary
     | of an unfounded and inconceivable Thirdness.  (CSP, EP2, p.177).

You have given me examples of citations, in your own words
and in those of Peirce, where the word "independent" is
employed in context, and this is helpful up to a point,
but does it really tell us what anybody means by it?

JA:  But I may need to repeat that I am not trying to define
     the Categories of 1-ness, 2-ness, 3-ness, as I consider
     them to be primeval, primitive, undefined terms, and so,
     in a peculiar sense, already independent "in terms of"
     each other.  Here, I am merely seeking to illustrate
     how I understand their application to sign-theoretic
     subject matter.  It may help if I quote Chomsky again:

JA:  [Quotes Chomsky, LSOLT, p. 100, again.]

JM:  Chomsky says "Since higher levels are not literally constructed out of
     lower ones, we don't need to fear circularity".  But would you say that
     thirdness (seen as a "level" ) is not constructed out of lower levels
     (secondness, firstness)?  The categories are hierachized, aren't they?

Points, lines, planes -- they are customarily regarded as falling
into a hierarchy, are they not?  But consider the "definitions"
of the eponymous Euclid.  Were these ever actually regarded as
strict definitions, or merely intended as assists, helpful to
an extent, if taken with a grain of sapience, distracting in
the extreme, if read with eyes too near their gradgrindstone,
almost being completely dispensable, except for gratuitously
having in joint kilter much news of points, and all the rest?
I cannot say.  But I know how these elements, points, lines,
planes, and so on up the scale, if up it be, are generally
regarded today, as undefined primitives held in relation
to each other by the whole panoply of tales that can be,
up to the limits of logical consistency, told of them.

JA:  It did not occur to me that anyone would take what I said
     as a strict definition of anything, since it was intended
     more as a way of building relations among constructs that
     are either primitive or else already sufficiently defined.
     First of all, we already have a good enough definition of
     the sign relation -- I personally consider the one in L75
     to be the most clear, detailed, explicit, and formalized
     of them all -- and this defines all of the roles O, S, I
     simultaneously in relation to each other.  Moreover, the
     definition of the cartesian product, that comes into the
     game as soon as we start to develop the theory of signs
     along extensional lines, and which is almost inevitable
     if we want to use sign relations as models of empirical
     activities and natural forms of conduct, already brings
     us the utilities of the various dimensional projections.
     So my purpose here was more to elucidate or rationalize
     the Categories as aspects or facets of 3-adic relations
     than it was to define them on any particular foundation.

JM:  [Quotes L75:]

     | [I define a sign as] something, A, which brings something, B,
     | its interpretant sign determined or created by it, into the
     | same sort of correspondence with something, C, its object,
     | as that in which itself stands to C.  [Peirce, NEM 4, L75].

JA:  More fully:

     | On the Definition of Logic [Version 1]
     |
     | Logic will here be defined as 'formal semiotic'.
     | A definition of a sign will be given which no more
     | refers to human thought than does the definition
     | of a line as the place which a particle occupies,
     | part by part, during a lapse of time.  Namely,
     | a sign is something, 'A', which brings something,
     | 'B', its 'interpretant' sign determined or created
     | by it, into the same sort of correspondence with
     | something, 'C', its 'object', as that in which it
     | itself stands to 'C'.  It is from this definition,
     | together with a definition of "formal", that I
     | deduce mathematically the principles of logic.
     | I also make a historical review of all the
     | definitions and conceptions of logic, and show,
     | not merely that my definition is no novelty, but
     | that my non-psychological conception of logic has
     | 'virtually' been quite generally held, though not
     | generally recognized.  (CSP, NEM 4, 20-21).
     |
     | On the Definition of Logic [Version 2]
     |
     | Logic is 'formal semiotic'.  A sign is something,
     | 'A', which brings something, 'B', its 'interpretant'
     | sign, determined or created by it, into the same
     | sort of correspondence (or a lower implied sort)
     | with something, 'C', its 'object', as that in
     | which itself stands to 'C'.  This definition no
     | more involves any reference to human thought than
     | does the definition of a line as the place within
     | which a particle lies during a lapse of time.
     | It is from this definition that I deduce the
     | principles of logic by mathematical reasoning,
     | and by mathematical reasoning that, I aver, will
     | support criticism of Weierstrassian severity, and
     | that is perfectly evident.  The word "formal" in
     | the definition is also defined.  (CSP, NEM 4, 54).
     |
     | Charles Sanders Peirce,
     |'The New Elements of Mathematics', Volume 4,
     | Edited by Carolyn Eisele, Mouton, The Hague, 1976.
     |
     | Available at the Arisbe website:
     |
     | http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm

JM:  The problem is that the definition only says
     that the sign determines the interpretant.
     It says nothing about the relation between
     the object and the sign, i.e., that
     the object determines the sign.

JA:  Are you under the impression that objects determine signs?
     I will have to think about that.  As you know, the proper
     reading of the definition, if ever we arrive at it, will
     depend on using the author's meanings for "correspondence"
     and for "determination", which CSP gives in full, and at
     length, needless to say, in many other prominent places.
     But I still read this definition as defining a relation
     among three roles of players or domains of components,
     and so defining all of them in relation to each other.

JM:  Definition L.75 says:
     A (sign) determines B (interpretant).
     A (sign) puts B (interpretant) in correspondence
     with C (object) so that the correspondence between
     C and B is of the same sort of as that between C and A.

JM:  i.e. the sign determines the interpretant,
     which as a sign determines other interpretants ...

JM:  But to say that the correspondence between C and B
     is of the same sort as that between C and A doesn't
     imply that there should be a determination at all.
     If there is a determination of the sign by its object,
     there will be a determination of the Interpretant
     by the object, which is consistent with Peirce's
     later definitions where the object clearly
     determines the sign:

JM:  You write:  "Are you under the impression that objects determine signs?"

JM:  Jon, this is not just an impression ...

     | http://www.door.net/arisbe/menu/LIBRARY/rsources/76defs/76defs.htm
     |
     | 32 - v. 1905 - MS 283.  p.125, 129, 131.  "The Basis of Pragmaticism":
     |
     | A Sign, on the other hand, just in so far as it fulfills
     | the function of a sign, and none other, perfectly conforms
     | to the definition of a medium of communication.  It is
     | determined by the object, but in no other respect than
     | goes to enable it to act upon the interpreting quasi mind;
     |  and the more perfectly it fulfill its function as a sign,
     | the less effect it has upon that quasi-mind other than that
     | of determining it as if the object itself had acted upon it.
     |
     | 33 - 1906 - S.S. 196 - Letter to Lady Welby (Draft) dated "1906 March 9":
     |
     | I use the word "Sign" in the widest sense for any medium
     | for the communication or extension of a Form (or feature).
     | Being medium, it is determined by something, called its Object,
     | and determines something, called its Interpretant or Interpretand.
     |
     | 34 - 1906 - C.P. 4-531 - "Apology for Pragmaticism":
     |
     | First, an analysis of the essence of a sign, (stretching that word
     | to its widest limits, as anything witch, being determined by an object,
     | determines an interpretation to determination, through it, by the same
     | object), leads to a proof that every sign is determined by its object, ...
     |
     | 35 - v, 1906 - C.P. 5-473 - "Pragmatism":
     |
     | [...]  That thing which causes a sign as such is called the object
     | (according to the usage of speech, the "real", but more accurately,
     | the existent object) represented by the sign:  the sign is determined
     | to some species of correspondence with that object.  [...]
     |
     | 36 - v. 1906 - MS 292.  "Prolegomena to an Apology for Pragmaticism":
     |
     | A sign may be defined as something (not necessarily existent)
     | which is so determined by a second something called its Object
     | that it will tend in its turn to determine a third something
     | called its Interpretant ...

So it's true, you are of the impression that a sign is determined by its object?

JM:  If you find a sign not determined by its object,
     it will be a sign only according to Peirce's earlier definitions of a sign,
     and it will not be a sign according to Peirce's later definitions.

JM:  So carefully choose your definitions.

Moi?  Peircenally speaking, I am learning to go with my first impressions.

JM:  Now you say that the sign relation is a cartesian product <O,S,I>?

JA:  No, I say that a sign relation L
     is a subset of a cartesian product OxSxI.
     At least, that is what I say on extensional days,
     which is most days of late.

JM:  OK, that is what I meant, then,
     by asking what is S, O, and I.
     So the question is: how do you choose them,
     since you are taking an extensional approach?
     Do you list all possible signs?   And once
     you have selected either O, S, or I, how do
     you express the idea that there are three
     determinations (O -> S, S -> I, O -> I)?

I have some stuff that I wrote back in the first eleven or twelve drafts
of my dissertation proposal that may fit in about here.   I will find it.

JM:  Take for example a photograph with your picture on.
     The picture on the photograph represents you, but
     you do not represent the picture on the photograph.
     How do you express that mathematically?

JM:  so you have three sets: O, S, and I and the cartesian product
     is O x S x I = {(o, s, i) | o is in O, s is in S, i is in I}, i.e.
     all possible combinations of elements from each set, corresponding
     to "points in space" with coordinates (o,s,i) or ordered triplets,
     which you project on lines, planes --?

JA:  Yes, that is a good description of the full product space OxSxI.
     A sign relation L, then, is a subset L c OxSxI.

JM:  But I believe that it is only begging the question:
     what are S, O, and I?  what are they sets of?
     and why should it matter at all?

JA:  I do not understand.  It is a form of description, no more.
     It is not meant to tell you why you should care about this
     or that sign relation.  That is a matter for you to choose.

JM:  see above

JA:  Where?

JM:  Why not simply say as Peirce that when you have a triplet
     you have three pairs, and when you have a pair you have
     two units, no matter what the triplet is made of?
     Why does the relation have to be a sign relation?
     and how do you translate into the cartesian product
     that idea that O determines S, S determines I,
     and O determines I?

JA:  Again, this is just a form of description.  As it happens,
     and this is a very common tactic in mathematical practice,
     it is very useful to begin by weakening it, and simply to
     incorporate all subsets of such a space under a "nominal"
     title of sign relations, only coming back at the second
     or third pass to note that some of them qualify only in
     a "trivial" way.  The properties that they have are the
     properties that they have.  It is our job but to notice,
     to describe, and to articulate them, species by species,
     genus by genus, an so on.  It is all very straightforward,
     well, in principle, at least.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Sop To Cerberus: What In Hades Was CSP Talking About?
Date:  Mon, 21 May 2001 15:33:30 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>,
       SemioCom <semiocom@listbot.com>,
       Standardize Unto Others <standard-upper-ontology@ieee.org>
  CC:  Jean-Marc Orliaguet <jmo@medialab.chalmers.se>,
       Josiane Caron-Pargue <Josiane.Caron@mshs.univ-poitiers.fr>,
       Joseph Ransdell <ransdell@door.net>

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

I trust that will be the end of that -- hah!

Incidental Musements:

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 10

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Three Sections of "Mapping the Conduct of Inquiry"
Date:  Thu, 24 May 2001 22:38:45 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Mary Keeler <mkeeler@u.washington.edu>
  CC:  Tom Holroyd <tomh@po.crl.go.jp>

Mary,

I can't believe I have lost another month
of my life in the Land of the Lotus Eaters!
Created a plain text of this for commentary,
but then ran out of time after only one remark,
at the marker below.  Will send anyway and try
to get more time tomorrow -- have actually been
working on my disertation a little!

> Mapping the Conduct of Inquiry
>  
> * No Map Is the Territory
> * Many Maps for the Same Territory
> * What Sort of Map Does the Conduct of Inquiry Need?
> * What Sort of Territory Do We Want to Map?
> * Who Needs What Map, For What Purpose?
> 
> No Map Is the Territory
>  
> In Jonathan Swift's story Gulliver's Travels, the author-adventurer finds a fictional land where 
> there is a man who carries everything he wants to refer to around on his back.  Those of us who 
> trust language and other forms of representation to "carry the burden of reference" for us do not 
> have the physical burden of weight, but we have another (perhaps more difficult) burden of having 
> to remember that any medium we use in communication cannot completely re-present what we 
> may want to refer to.  What we give up in accuracy of reference to perceivable objects of 
> experience, however, we gain in power to express our feelings, thoughts, and judgments about 
> this experience.  In other words we gain human communication. 
> 
> The essential nature and purpose —- and virtue -— of communication is not simply to transmit messages 
> accurately, which is what information theory was conceived to predict, but to grow new ideas about 
> our experience of objects —- no matter how abstract or generalized our representations may become.  
> Many of the recognizable objects of our experience have been created as symbols, entirely for the 
> purpose of advancing the growth of meaning, which might otherwise be conceived as the haphazard 
> increase in information.  On the one hand, if symbols were purely and accurately referential, they 
> would be no use to us in learning more;  on the other, if symbols had no referential capability, they 
> would give us no hope of learning more than the rhetorical games they let us play with language.  
> From weather forecasts and advertising to political pronouncements, logically meaningless forms of 
> expression probably dominate our daily experience.  
> 
> In communication, we keep ideas growing and responding to our collective experience of the 
> conditions that confront us —- whether these conditions are presented by natural phenomena or by our 
> own creative expressions, and whether or not they refer to anything of apparent pragmatic value.  
> That consequence always remains to be discovered in the future.  Uncertainty about the future tends 
> to draw us out of the certainty of the past.  Notions of probability and chance (as tendencies) would 
> have no meaning without our awareness of time.  In that awareness, we gain our sense of purpose.  
> A theory of human inquiry must explain how this continuity of experience operates through thought 
> and expression.
>       
> Expressions we construct in culturally-derived systems and forms of media have virtual reference for 
> us as we communicate with ourselves and with others.  Although these "maps" do not re-present the 
> collections of objects we would otherwise have to carry around, they have some of the efficiency of 
> doing so, provided we have learned how to interpret them and understand that the "territory" is 
> always more than what any "map" can exhibit to us.  From any human point of view (which is 
> necessarily limited), the meaning of any expression cannot be simply a matter of probability (or 
> some established conventional response) but must include possibility (or an individual's unique 
> experience in which the interpretation of meaning occurs), which cannot help but contribute to its 
> growth.  A simplistic theory that construes a "sender" as omniscient and a "receiver" as robotic, can 
> only attribute some effect (response of receiver) to a particular cause (intention of sender) through a 
> sort of "transparent window" as the medium of communication.  A theory of "coded behavior" will 
> never explain the creative productivity (that is, account for the unpredictable diversity) that 
> particularly characterizes human thought in communication, through many media of expression.
> 
> Gulliver's burden-carrier parodies a hypothetical human predicament:  what if we could not rely on 
> symbolic representation?  Not only would the objects we could refer to be limited to what is at hand, 
> but even if we named those objects, the names by themselves would tell us nothing beyond what the 
> objects themselves tell us, simply that they are there as we each perceive them.  That reification 
> gives us no means of understanding how those objects might be useful to us, according to how each 
> of us will perceive them under different circumstances.  The names give us some sort of "view" of 
> the objects in our imagination when we cannot directly view them, but they tell us nothing about how 
> the objects might be purposefully related.  We can only associate the name with the object, not relate 
> the objects to each other.  Symbolic expression makes associations possible that allow us to create 
> hypothetical relations among objects as concepts.  When the names of objects can be related with 
> one another by some convention such as language, human expression can be used to refer virtually to 
> experienced objects, so that we can examine and discuss how they might be related and relatable.  
> These hypothetical relations are the concepts by which we reason in thought, to classify objects and 
> predict their behavior, and to experiment with these conceived relationships, which we call facts if 
> they prove to be reliable enough.  The "window of named things" then becomes a sort of map of 
> what we have named and related as language re-constructs "the territory" of our previous experience 
> through our current experience of the map.  No ones map gives us perfect re-construction, or a 
> God's-eye view, and no language or symbol system can perfectly re-construct our experience.  In 
> fact, how languages interact with and determine the "structure of our experience" remains our most 
> significant theoretical and pragmatic concern in human inquiry.  Twentieth century developments in 
> logic began to respond to that concern.
> 
> Certainly, in our multi-cultural world, we should be aware that the more than a dozen different 
> language families differ radically in how they shape their speakers' thinking.  Even among the 
> Indo-European group, only English has numerous distinctive common nouns.  In languages that 
> have a verb meaning "is a man," the noun "man" becomes a superfluity.  And since, as the 
> Gulliver example shows, a noun or even combination of nouns by itself says nothing explicitly 
> about objects, they give us no basis for interpretation or relating things, except as syntactical 
> place-holders in symbolic formulations.  When simply linked in hypertext, they are merely 
> connected, not meaningfully related in the logical sense to be explained in this chapter.
> Linguists find that the roots of inference are in verbs, even unspoken ones, and in the
> unassuming prepositions, which transparently make common nouns operate as unexpressed
> assertions in any language.  An English speaker who sees "Glass" written on a package
> will infer that there is glass inside.
> 
> In defining terms (especially common nouns), we strive to make their relatedness explicit and their 
> relationships reliable within the context of a language or system of symbols, as a standard for their 
> use by which meaning can be grounded, or stabilized.  These terms have no meaning without those 
> semantic webs we create that conventionally relate words to one another, and which can be used to 
> validate or standardize the application of those terms in specific linguistic contexts of application.

This is not the way I personally would use the word "semantics", which I would reserve
for the referential (sign to object) aspect of the 3-adic sign relation.  I realize that
you are bowing to popular use, but the popular use represents a misunderstanding of what
even Frege was talking about, not to mention Peirce.  I suppose there is no hope for it,
though, not until the "decline in logical literacy" (DILL) that was the 20th Century and
the overall "degeneration of logically operative realism" (DOLOR) have come to be healed,
if ever they can be at this late stage.  For Peirce, of course, the "webs we create that
conventionally relate words to one another" are "semiotic webs", that is, connotative or
interpretive entanglements.

> These semantic relations, not the terms by themselves but the sentences, propositions, assertions, and 
> even arguments they imply, are concepts or the complex representations by which we assume or 
> infer the objects of our experience to be related meaningfully.  In further inference, we use them to 
> establish judgments based on how we experience the relatedness of the objects we recognize in the 
> world.  The power of inference both underlies and yet relies on this symbolic "glass" of linguistic or 
> symbolic structure by which meaning and knowledge inevitably grow, even without our notice.  
> Logic, in its modern form, has become an instrument for analyzing the intricacies of how inference 
> works to establish symbolic reference from experience.  The theory behind that instrument considers 
> names, definitions, concepts and other features of semantic relations to be an elaborate set of 
> hypotheses that are continually tested and improved through human experience and communication.
> 
> Saint Thomas Aquinas defined logic as the science of second intentions applied to first intentions, 
> a definition that begins to clarify the purpose of logical analysis.  First intentions are concepts 
> derived from comparing percepts (as concepts of classes, relations, etc.); second intentions are 
> concepts formed by observing and comparing first intentions.  Classifying objects of experience is 
> a conscious mode of conduct only to the extent that we can take notice of that conduct and 
> conceive it as classification.  We can only distinguish figments from realities and meaningless 
> terms from meaningful ones by our ability to relate second intentions in such concepts as identity, 
> otherness, and co-existence, such as when we consciously identify some trait as human or as a 
> trait of some other animal.  Although it is not a technical term in logic, logicians have generally 
> defined meaning in terms of breadth and depth: a sign stands for, its denoted breadth," and it 
> signifies, its connoted depth.  Depth or signification is considered intrinsic and breadth extrinsic.  
> Charles S. Peirce's logical theory introduces a third kind of meaning:  when we define an idea as a 
> state of mind which consciously means something, we consider that it means something in the 
> sense of intending or purposing something.  "Now a purposive state of mind is one that signifies 
> something by virtue of intending to be interpreted in a deed.  Therefore, although an idea certainly 
> has its internal and its external meaning, yet its principal meaning is of a different kind from either 
> of those" [8.119].
> 
> Since meaning is attributed to representations not to objects they refer to, as Gulliver's tale 
> indicates, and the only representation that has a definite professed purpose is an argument (its 
> purpose is to determine an acceptance of its conclusion), and since to call the conclusion of an 
> argument its meaning quite well accords with general usage, Peirce designates the word 
> "meaning" to denote the intended idea of a symbol [CP, 5.175].  He then further clarifies the 
> current focus and terminology of logical analysis.  If second intentions are the objects in our 
> understanding represented in symbols such as language, and the first intentions to which they in 
> turn apply are the objects of those representations as we perceive or conceive them, then we can 
> derive third intentions as representations of second intention symbols when viewed themselves as 
> objects or forms of argument [see CP, 4.549].  In these self-conscious steps of abstraction, we 
> turn the predicates by which we think into subjects of our thought [see CP 1.559].  Logic finds its 
> proper phenomena of study at that third stage of hypostatic abstraction, in using forms of 
> symbolic notation to represent and analyze the conventional symbolic forms of languages, which 
> express thoughts about the conceived objects of perceptual experience.  We can say that an 
> argument distinctly represents its idea as the conclusion, a proposition distinctly indicates the 
> object which it denotes as its subject but leaves the interpreted idea (or meaning) to be whatever 
> someone might interpret, and a term distinctly indicates only the object it denotes (it names only a 
> particular, Gulliverian, object).  Take away the subject of a proposition and you have a term 
> called its predicate; take away the conclusion of an argument and you have a proposition called 
> its premise (usually there is more than one) [see CP, 2.95].  If arguments are the only forms of 
> expression which truly relate our episodes of experience meaningfully, as hypothesized in Peirce's 
> theory of logic, then any fully functioning symbols must be arguments, in some form.
> 
> Somehow, hidden within any expressions of human communication are the logical forms of 
> argument.  When we communicate informally, what is hidden is well-enough understood, but 
> without our notice can be manipulated in rhetorical style.  But formal communication progresses by 
> explicit arguments that can be efficiently validated by a communicating group.  To explicate and 
> analyze those argument forms, Peirce proposed that a modern logic be developed as a genuine 
> science of reasoning or inquiry with three necessarily related stages or forms of argument 
> (abduction, deduction, and induction) to explain how meaning can evolve in experience.  He argued 
> that even in proposing a hypothesis to account for some facts (in abduction), a scientist must furnish 
> reasons (to be argued and judged good or bad) as to why it is worthy of testing.  It is the work of the 
> logician to analyze these reasons and to discover an ideal method of investigation for pursuing the 
> truth—understood as the hypothetical result of indefinite inquiry that encourages us to persist in the 
> conduct of inquiry at all.
> 
> Many Maps for the Same Territory
> 
> Alzheimer's researchers tell us that as victims lose memory they also lose a sense of the future, 
> and so the ability to compare past to present and to conjecture about possible consequences.  They 
> lose the sense of need for principle, planning, and strategy—the ability to make cause and effect 
> or conditional judgments.  These hypothetical inferences, of the form "Y would happen, if I do X" 
> are a rudimentary facility in human reasoning and self-controlled conduct based on our sense of 
> past, present, and future.  As does any conduct in life, intellectual conduct in the life of thought 
> resides in its forms and patterns, although these norms are more self-consciously adopted in 
> methods, procedures, and conventions which must be explicitly learned.  Logic studies those 
> forms in representation: classifies them, manipulates them, and observes how they can grow much 
> as scientists do first intentional phenomena of nature.  Second intentional phenomena of language 
> and symbols are the objects of the understanding considered as representations or signs, and the 
> first intentions to which they apply are the perceived objects to which those representations refer.
> 
> In the nineteenth century, logic was re-developed in response to the insufficiency of Aristotle's 
> syllogistic forms in analyzing the nature of representation, to serve as instrument powerful enough 
> to scrutinize the minute structural relations of symbolic expression used in the context of any 
> formal reasoning procedure, not limited to human.  C.S. Peirce, a scientist for the U.S. Coast and 
> Geodetic Survey (now NOAA) was the American leader of this development, which took place 
> primarily in Europe.  For Peirce (who was also a mathematician, philosopher, computer, and 
> cartographer), a modern logic of relations was to serve as the "lens" for his pragmatic method in 
> guiding the conduct of scientific inquiry.  Toward the end of his life, in 1902, he foresees a logic 
> of the future based on his 50-year effort to render it as an analytical tool.
> 
> I took it and melted it down, reduced it to a fluid condition. I filtered it till it was clear. I cast 
> it in the true mold; and when it had become solid, I spared no elbow-grease in polishing it. It 
> is now a comparatively brilliant lens, showing much that was not discernible before. I believe 
> that it will only remain to those who come after me to perfect the processes. I am as confident 
> as I am of death that Logic will hereafter be infinitely superior to what it is as I leave it; but 
> my labors will have done good work toward its improvement. [CP, 2.198]
> 
> In his teaching at Johns Hopkins University (1879-1884), Peirce explained logic as the art of 
> devising methods of research, "the method of methods" [CP 7.59].  His pragmatic theory of logic 
> differs significantly from traditional views, which generally consider it to be "the art of 
> reasoning."  Logic is not a human invention, but is simply a refinement of human reasoning in 
> practice [see Ransdell, 7: 100].  To accomplish that refinement, logic must consider "what 
> reasoning ought to be" [CP 2.7], not "how we do think [which is psychology]; nor how we ought 
> to think in conformity with usage, but how we ought to think in order to think what is true" [CP 
> 2.52].  And truth is what we must hypothesize as the theoretical limit or end of inquiry, giving us 
> the hope we need to continue investigation.  We are responsible for our reasonings just as we are 
> responsible for our conduct.  His theory of logic is a theory of normative science necessary to 
> explain the directedness or tendency of experience to grow as meaning.  "Nothing can be either 
> logically true or morally good without a purpose to be so.  For the conclusion of an 
> argument which is only accidentally true is not logical" [CP 1.575].  Peirce's logic studies 
> the means of attaining the end of thought; ethics and aesthetics determine what should be 
> our ultimate aim; together, these are the normative sciences yet to be developed [see CP 
> 1.191].  In Peirce's view, reasoning is a species of conduct that is subject to criticism:
> "A mental operation which is similar to reasoning in every other respect except that it is
> performed unconsciously cannot be called 'reasoning'," because "it is idle to criticize as
> good or bad that which cannot be controlled" [CP 2.182,CP 5.108].  
>       Because much of Peirce's theory of logic is effectively inaccessible in some 80,000 pages 
> of manuscript in the Houghton Library at Harvard, modern scholars and researchers have 
> benefited from his comprehensive advancements only in piecemeal (and often distorted) 
> respects—if at all.  For example, in his book Things That Make Us Smart: Defending Human 
> Attributes in the Age of the Machine, Donald Norman recounts a view of traditional logic: "From 
> the seventeenth-century views of Descartes through today, the human mind has been thought of as 
> a computational device, usually rigid, . . . based on clockwork or simple logic.  Almost every 
> advance in the science and technology of computation, control, and communication has also been 
> described as an advance in the science of thought processes, usually without any evidence, usually 
> by people who had never studied people" [8: 228].  From these historical circumstances, he 
> concludes:
> 
> Logic is most definitely not a good model of human cognition.  Humans take into account 
> both the content and the context of the problem, whereas the strength of logic and formal 
> symbolic representation is that the content and context are irrelevant.  Taking the content into 
> account means interpreting the problem in concrete terms, mapping it back onto the known 
> world or real actions and interactions.  The point is not simply that people make internal 
> mental models, stories, or scenarios of the problems they are attempting to solve . . . People 
> map problems back onto their own personal knowledge and experiences. [8: 228]
> 
> Unlike the language of logic, he insists, "Human language takes into account the point of the 
> encounter, which is to communicate" [8: 229].
>
>       Peirce's advanced theory of logic (called "semiotic" —- not "semiotics" -— from Greek 
> origins) explains the capability of intelligent behavior, so fundamentally human and so easily 
> taken for granted, that we are barely aware of its routine and pervasive operation: How we can 
> learn by experience.  Based on that understanding, we might hope to learn by experience more 
> effectively; that is, find out how the procedure of learning by experience might be improved.
> And finally, we might learn how to create knowledge in learning by collective experience, by 
> improving communication media.  Peirce formulated his pragmatic method of logic for refining 
> learning procedures, and he even created a graphical notation tool (called Existential Graphs),
> as a "topology of logic" for observing and demonstrating how that improvement can occur through
> the process of communicating.  If we hope to bring a human perspective to the encounter of using 
> technology for improving inquiry, Peirce's logic offers valuable guidance.  Based on his experience
> as a practising scientist, he concluded that the essence of successful inquiry of any sort is due
> not primarily to the sophistication of its measuring instruments or its investigational techniques,
> although those are essential.  Careful observation and ingenious conceptualization generate knowledge
> only to the extent that they are collaboratively validated by those engaged in the conduct of inquiry.
> 
> His pragmatism identifies self-critical, collective reasoning through dialogue as the scientific 
> method—and science is not a body of certified truths or systematized knowledge.  Peirce even 
> suggested that knowledge is not the point of science at all, since knowledge though systematized 
> may be dead memory (the hide-bound habits of thought).  The scientist is a member of a 
> community of inquirers who impartially pursue the truth (or "real meaning"), which none can 
> know as a matter of fact and which must be conceived as an ideal or limit.  The pursuit advances 
> and is successful to the extent that we can produce testable representations as hypotheses of what 
> each of us observes and interprets.  Our power to contemplate and converse about these beliefs 
> makes it possible for us to "know," or to gain some control of what happens in our experience by 
> imagining and anticipating consequences in the long run.  Knowing, then, is the tendency for the 
> meaning of our representations to grow reliably.  "Does not electricity mean more now than it did 
> in the days of Franklin? . . . men and words reciprocally educate each other; each increase of a 
> man's information involves and is involved by, a corresponding increase of a word's information" 
> [CP: 5.313].  Although the ideal of scientific terminology is that each term should have a single 
> exact meaning, Peirce explains,
> 
> | this requisite might be understood in a sense which would make it utterly impossible.
> | For every symbol is a living thing, in a very strict sense that is no mere figure of
> | speech.  The body of the symbol changes slowly, but its meaning inevitably grows,
> | incorporates new elements and throws off old ones.  But the effort of all should
> | be to keep the essence of every scientific term unchanged and exact;  although
> | absolute exactitude is not so much as conceivable.  Every symbol is, in its origin,
> | either an image of the idea signified, or a reminiscence of some individual occurrence,
> | person or thing, connected with its meaning, or is a metaphor.  [CP 2.222].
> 
> The semiotic view of communication confirms the relativity of meaning, and our ultimate 
> uncertainty as to what we actually know for sure.  These are the conditions of representation that 
> confront us: none of us will ever have "the map that can fully capture the territory of our 
> experience" (which, in any case, continues to grow as we are constructing our "maps"); and after 
> all, each of us can have only mortal (time-and-space-limited) experience of whatever exists as 
> "the territory."  But pragmatism gives us the methodological hope that the more we can 
> effectively "construct the maps based on collected individual experiences," which through 
> communication extends individual experience indefinitely, the closer we can hope to come in 
> knowing what really is the territory (that is, what might really exist, or be true).  We must 
> suppose that this semiotic process will continue indefinitely because since we are part of "the 
> creative evolution of the territory" it remains beyond our reach, as our interpretations continue to 
> contribute to its creation.  Semiotic logic tells us that our representations can never establish 
> complete truth, but only indicate what is possible evidence to test in further experience.  
> Pragmatism says: Truth is what would be the result of indefinite inquiry.
> 
> To the extent that we, unself-consciously, believe that we can capture the truth in representational 
> structures (of any kind), we are fooling ourselves that we have the only possible view of what 
> truly is.  We forget that our necessarily hypothetical view of what happens can never tell us what 
> has, does, or will happen, which is independent of what any person or group of persons thinks 
> about it.  In conscious hypothesizing, we find some surprising fact that could be explained by 
> supposing it was a case of a certain general rule, and then assume that supposition on probation.  
> The difficulty is: each of us must believe something in order to make judgments, in order to direct 
> our conduct with respect to whatever happens—to make our actions more than simple physical 
> reactions (that is, to mediate our actions by means of inferences about what appears to be true).  
> The urge to reach conclusions, to take our "maps" to be the truth, is a necessary part of effective 
> "pragmatic conduct," but we don't want to exchange the Gulliverian burden of reference for the 
> burden of habit-bound thought in beliefs that cannot evolve through experience.  According to 
> Peirce's pragmatic logic, we can consciously maintain a provisional view by self-critically 
> examining the outcomes of our conduct in thought, by as many means as we can create to do so.  
> These include special skills of observation, multiple powers of expression and comparison of 
> these observations, and elaborate technological augmentations of these skills and powers through 
> media.
> 
> A recent American Academy of Sciences report [AP story/3/6/01] concludes that those who have 
> no intellectually challenging hobby, such as chess-playing or puzzle-solving, throughout life are 
> more than twice as likely to succumb to Alzheimer's disease.  Inquiry, like strategic game-
> playing, exercises our capability to formulate hypotheses, which does not commit us to do 
> anything that has consequences beyond the conjectures as to what would be the consequences of 
> doing what we conceive.  The more experience we have, the more likely to be true those guesses 
> will be.  Peirce insists that such "refined guessing" cannot be explained by psychological, 
> sociological, or historical investigations alone.  Investigation of this essence of human thought 
> requires full logical analysis of the reasoning process in making conjectures, selecting and testing 
> them.  A theory of inquiry should explain the evolution of intellect from instinct, Peirce maintains, 
> because: "All Human knowledge, up to the highest flight of science, is but the development of our 
> inborn animal instincts" [CP 2.754, 6.604].  And yet, no creature can have instincts for every 
> possible circumstance and, "When ones purpose lies in the line of novelty, invention, 
> generalization, theory—in a word, improvement of the situation . . . instinct and the rule of thumb 
> manifestly cease to be applicable" [CP 2.178].  How then can we use logic to augment our 
> "instinctive reasoning"?
> 
> What Sort of Map Does the Conduct of Inquiry Need?
> 
> "We simply didn't evolve senses capable of detecting some of the most serious problems unaided.  
> Knowledge of that suggests directions in which solutions might be found," observes Paul Ehrlich 
> in his latest assessment of our current circumstances, Human Natures: Genes, Culture, and the 
> Human prospect, in which he concludes: "An answer to environmental misconceptions, if 
> humanity could manage it, would be to create a conscious evolutionary process" [xi, 328].
> 
> What sort of "detecting aid" for inquiry could give us the power to create "a conscious 
> evolutionary process," augmenting our self-conscious capability to observe and analyze the 
> possible consequences of the beliefs which drive our conduct?  If none of us can have a God's-eye 
> view, and since we must effectively collaborate if we hope to create any sort of "map of the 
> territory" for any realm of inquiry, we need the "third-intentions lens" that logic has developed and 
> refined since Aristotle.  From that logical perspective, if first intentions are concepts that compare 
> or relate percepts, and second intentions are concepts that relate first intention concepts, then third 
> intentions are concepts that relate second intention concepts (not forgetting that these relate 
> concepts that relate percepts).  When representations are considered under this "microscope," that 
> is as representations, they are viewed as symbolic structures, the forms or patterns in any natural 
> language.  Logicians can then "observe" these forms as phenomenal objects (called signs), analyze 
> their genetic relatedness, and study how they replicate and grow.
> 
> From this analytical perspective, we first notice that signs exist only in replica.
> They differ from first intentional objects in that essential respect;  no first
> intentional object is an exact replica, in fact we define nature by its infinite
> variations.  Symbols function reliably for us in communication to the extent that
> they are exact replicas; take the word "man" printed on any page, it is the same 
> word in all its occurrences.  A common noun is a symbol we use to associate
> a conceived collection of objects, and using its replicas tends to produce
> the habit of thought (as a belief or conception) that these objects are in
> fact related somehow, so that each replica can be interpreted as referring
> to an object that is an instance of that conceived collection.  When we use
> the noun, we take that association for granted, along with whatever basis
> there may be for relating the objects in the collection.  In learning
> a language, we come to believe that the objects named are related in
> some way, and use the noun to stand for that believed relationship.
> Could we map the structure of beliefs based on logically-defined
> conceptual relations, by which we could locate detailed assumptions
> in reasoning which are not noticed without that map-perspective, giving
> us the power to experiment with alternative courses of thought explicitly?
> Could we observe hypothetical consequences to which our conceptualized beliefs
> might lead?  Such a map would diagram the form of the relations of the symbols
> we use in thought, regardless of their significance or signification, which is
> what deductive logic was designed to do centuries ago.
> 
> As Donald Norman assumes, most logicians study only necessary reasoning (called deduction), 
> and so confine their theories about reasoning to its "correctness" or our absolute inability to doubt 
> the truth of the conclusion if the premises can be assumed to be true, which they explicate 
> mathematically in two values, true and false.  Peirce makes use of that view but extends it: "we 
> shall do well to understand necessary reasoning as mathematics . . .in order to fix our ideas as to 
> what we shall understand by the meaning of a term" [CP, 5.176].  His theory of logic conceives 
> the conduct of inquiry—or the creating, validating, and testing of representations—in three steps 
> or stages of inquiry: retroduction (sometimes called abduction), deduction, and induction [see CP: 
> 1.65].  Jay Zeman explains how these steps relate in inquiry.
> 
> Retroduction is educated hypothesis-formation which proposes initial organizations of figure 
> in the problematic field.  Deduction enters in a mediating way, drawing out the consequences 
> of the abductive hypotheses.  And induction consists in the return to experience which aims at 
> confirming or refuting those hypotheses by seeing whether the deduced consequences hold or 
> not see. [Zeman 1986, p. 12; see CP: 2.269]
> 
> Under close logical examination, Peirce finds that deduction is the critical link between the other 
> two steps [see CP: 5.193].  Retroduction essentially postulates a vaguely formulated deductive 
> argument that can explain the facts and is capable of experimental verification (by induction).  
> Induction and retroduction refer to the context and aim of inquiry, while deduction is its engine.  
> In hypothetical inference we compose imaginary experiments and suppose their results: "If X 
> happens, Y would result."  Deduction only fills in the assumed (not explicitly expressed) parts of 
> the inference by critical examination and explication of its formal, symbolically expressed, details.  
> Peirce explains that the critical operations of deduction are performed by observing an argument 
> as a diagram of formal relations [see CP, 5.581], as mathematicians use formulas, but with the 
> objective of understanding the nature of the process by which the conclusion is reached.  "The 
> mathematician seeks the speediest and most abridged of secure methods; the logician wishes to 
> make each smallest step of the process stand out distinctly, so that its nature may be understood. 
> He wants his diagram to be, above all, as analytical as possible" [CP, 4.533].
> 
> Even in its algebraic form, deduction involves constructing a diagram (which appears as a 
> formula) of what we suppose is the hypothetical state of things, and in observing it we suspect 
> that something is true, whether or not we can formulate the hypothetical inference for it with 
> precision.  In proceeding to inquire whether it is true or not, the most difficult part of the 
> operation is to form a plan of investigation.  Not only do we have to select the features of the 
> diagram which are pertinent to pay attention to, but we must return to it repeatedly to check and 
> modify certain features, based on our inevitably growing experience of what it refers to.  Without 
> that process of improving the details of the diagram, although our conclusions may be correct (or 
> have a valid form), they will not be the particular conclusions relevant to our purposes.  Rule-
> driven deductions may even drive us to lose track of our purposes, as can any mechanism.  
> Logical procedure, driven by deduction, under our conscious control, gives inquiry its vital power 
> of self-correction, as Peirce describes:
> 
> one can make exact experiments upon uniform diagrams; and when one does so, one must 
> keep a bright lookout for unintended and unexpected changes thereby brought about in the 
> relations of different significant parts of the diagram to one another. Such operations upon 
> diagrams, whether external or imaginary, take the place of the experiments upon real things 
> that one performs in chemical and physical research. Chemists have ere now, I need not say, 
> described experimentation as the putting of questions to Nature. Just so, experiments upon 
> diagrams are questions put to the Nature of the relations concerned. [CP, 4.530] 
> 
> Deductive or necessary reasoning only explicates the meanings of the terms of the premises of an 
> argument to aid us in keeping track of the evolution of the meaning of those terms.  The 
> "necessary reasoning" of deduction is not infallible, but the conclusion necessarily follows from 
> the form of the relations set forth in the premise(s).  Retroduction furnishes any possible 
> explanations as hypotheses to test, but these are mere conjectures with no measure of certainty.  
> Deduction is certain but only of its idealize forms or diagrams representing the explanations.  
> Induction gives us the only approach to certainty concerning what we experience but has nothing 
> definite to test without the previous steps [see CP, 8.209].  Peirce extends logic to account for the 
> aim and context of inquiry, from hypothesis to experimentation.  Non-relative logic gives the 
> impression that deductive inference is simply following a rigid rule, no more than machines can 
> do, Peirce explains.  "People commonly talk of the conclusion from a pair of premises, as if there 
> were but one inference to be drawn. But relative logic shows that from any proposition whatever, 
> without a second, an endless series of necessary consequences can be deduced; and it very 
> frequently happens that a number of distinct lines of inference may be taken, none leading into 
> another" [CP, 3.641].  Deduction has no way to select a possible inference "map" without 
> abduction and induction to specify what is our aim in the search of what "territory" of inquiry.  
> "Abduction seeks a theory. Induction seeks for facts. In abduction the consideration of the facts 
> suggests the hypothesis. In induction the study of the hypothesis suggests the experiments which 
> bring to light the very facts to which the hypothesis had pointed" [CP, 7.218].
> 
> On Peirce's account, the process of inquiry is an iterative procedure in which the related forms of 
> the symbol-replicas we use must function to stabilize the evolution of meaning with reference to 
> what we experience, giving us the sense of continuity in thought and making what we call 
> knowledge possible.  Meaning, then, is a continuing inferential process of relating, not permanent 
> dyadic or arbitrary relations between sign and signified.  "[N]o present actual thought (which is a 
> mere feeling) has any meaning, any intellectual value; for this lies not in what is actually thought, 
> but in what this thought may be connected with in representation by subsequent thoughts; so that 
> the meaning of a thought is altogether something virtual. . . . At no one instant in my state of mind 
> is there cognition or representation, but in the relation of my states of mind at different instants 
> there is" [CP: 5.289].  
> 
> Peirce invented a graphical notation, called Existential Graphs, to "put before us moving pictures 
> of thought, I mean of thought in its essence free from physiological and other accidents" [CP: 
> 4.8].  These graphs map the relational evidence of inquiry in its progression [see CP: 4.512, 
> 513], to make possible the same sort of critical control that sophisticated instruments and 
> techniques give physical investigation in examining empirical evidence [see MS 291 (1905)]).  
> Deductive thought need not be the rigid rule-driven (algorithmic) procedure that traditional logic 
> conveniently assumes, if we realize its proper role in making explicit the evolution of meaning.  
> His Graphs serve as a logical instrument for observing deductive inference minutely enough in the 
> critical testing of ideas, that we can make meaning tend to become more and more reliable in 
> reference, by an iterative procedure which makes logical validity entail that reliability.  "Thus the 
> system of existential graphs is a rough and generalized diagram of the Mind, and it gives a better 
> idea of what the mind is, from the point of view of logic, than could be conveyed by any abstract 
> account of it" [CP: 4.582].  
> 
> Peirce makes clear that his graphs were not intended as a calculus for "thinking machines" [see 
> CP: 4.581].  Calculus seeks a solution, and by the most direct reasoning to be found; while the 
> logic must examine the possible paths reasoning can take, and any conclusion must be merely a 
> new premise in a possible continuing argument.  Mathematical treatment in measuring involves 
> the concept of number but also idea of continuous quantity. "Number, after all, only serves to pin 
> us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty 
> conceptions, and frequently descends to pettiness" [CP, 2.646].  But the conception of continuous 
> quantity, aside from its attempt at precision, gives us the power to generalize.  A biologist studies 
> a species, beginning with a collection of specimens more or less similar in form.  Observing that 
> they are more or less alike in particular respects, the scientist defines features of resemblance that 
> are not precisely the same, but lead to the belief that intermediate forms could be found between 
> any two observed.  When other forms found are quite dissimilar, the question is whether 
> intermediate forms can still be found that connect these with the first forms recognized.  Even 
> though at first it often seems impossible, scientists frequently succeed in finding intermediate 
> forms to build up from the observations of nature a general conception relating the specimens.  
> Eventually, the greatest differences are resolved into differences of degree, and with repeated 
> efforts conceptions are broadened and knowledge grows.  The deductive engine of relational logic 
> is the essence of that method of classification. "[Logic's] engine and distinction is accurate 
> analysis. But absolute completeness of logical analysis is no less unattainable [than] is 
> omniscience. Carry it as far as you please, and something will always remain unanalyzed" [CP, 
> 2.646, FN].
> 
> Logic will not tell us what data to select or what experiments to conduct, but it will tell us how to 
> formulate a plan or procedure for learning by experiment.  Deductive logic machines differ from 
> other machines only in working by excessively simple principles operating in complex ways, 
> instead of complex principles operating a monotonous ways.  A result from the logic machine has 
> a relation to the data fed in, that relation determines whether the result could be false so long as 
> the data are true.  Peirce reminds us that we often perform as a machine, turning out a written 
> sentence expressing a conclusion, having been fed with a written statement of fact, as premise, a 
> performance essentially no different from what a machine can do [see CP, 2.59].  To the extent 
> that we conduct our inquiry in that manner, we are subject to the same sort of logical criticism as 
> the procedure of a machine.  Peirce stresses this point, saying, "no other in all logic, although it is 
> a science of subtleties, is so hard to see.  The confusion is embedded in language, leaving no 
> words available to epigrammatize the error."  Numerical computation is certainly reasoning, and 
> though not all reasoning is computation, any instrument that performs inferences is subject to 
> logical criticism to determine if from true premises they always yield true conclusions.  Even if 
> we decide that machines can think, we must be able to examine the logical correctness of their 
> operations, "which we should still have to assure ourselves of in the same way we do now" [CP, 
> 2.56].  Only our critical examination of it could give us that assurance and, consequently it would 
> not strictly be a reasoning machine.  
> 
> Logic can help us build maps of formal conceptual structures as abstract representations of our 
> beliefs, ideas, and judgments, but it will not tell us how to use them reliably.  Peirce designed his 
> graphical instrument for observing the deductive progress of thought.  He insisted that when we 
> think, we are "conversing with another self that is just coming into life in the flow of time."  He 
> explains, "When one reasons, it is that critical self that one is trying to persuade . . . The second 
> thing to remember is that the man's circle of society (however widely or narrowly this phrase may 
> be understood), is a sort of loosely compacted person, in some respects of higher rank than the 
> person of an individual organism" [CP: 5.421].  For Peirce, thought is communication, in the 
> most general theoretical terms.  And if all thought is relative to our limited points of view, then 
> communication is required in order for knowledge (or whatever we can agree, tentatively, is true) 
> to refer increasingly reliably to the world of our experience, making it possible for us to establish 
> successful conduct in that world as our symbol systems evolve as part of it.  Knowledge in a 
> particular field will continue to progress effectively, depending on how well the communication 
> procedure works for validating individual interpretive contributions, providing that we never 
> forget that the "valid judgment" established by any group of inquirers is never final and infallible 
> with respect to the evidence.  Increasing validity entails improving reliability.
> 
> Erhlich emphasizes that to make much sense of human biology we must consider the context of 
> culture, and that history is now how we refer to the evolutionary process of cultural change [see 
> x.].  He cautions: "If Homo Sapiens is to improve its lot by manipulating human evolution, clearly 
> it must do so by attempting to influence the course of human cultural evolution—and doing that 
> with great care to avoid the abuses that could so easily occur and to preserve the diversity of 
> natures that is such an important human resource" [330].  In converting social movements into 
> conscious evolution, he says we require "a systematic, interdisciplinary consideration of the issues 
> involved" by a process that is "transparent to all participants" [329].  The languages and symbol 
> systems of inquiry operate by effecting a sort of transparency, the nature of which a logic-based 
> map would reveal.

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Note 11

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Language is but one possible formal system
Date:  Wed, 20 Jun 2001 21:16:35 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  VCU Complexity Research Group <COMPLEXITY-L@VENUS.VCU.EDU>
  CC:  Arisbe <arisbe@stderr.org>,
       SemioCom <semiocom@listbot.com>

Gary Richmond wrote:
> 
> Charles,
> 
> I do not see any real connection between the triad:
> object-sign-interpretation--better, interpretant,
> or interpretant sign -- and Aristotle's four causes
> (a search of the electronic Collected Edition confirmed
> this, though that is far from a complete resource)
> 
> But as a foil to Jon's analysis I'll offer this Peirce quotation:
> 
> 347. . . . Suffice it to say that a sign endeavours to represent,
> in part at least, an Object, which is therefore in a sense the
> cause, or determinant, of the sign even if the sign represents
> its object falsely.  But to say that it represents its Object
> implies that it affects a mind, and so affects it as, in some
> respect, to determine in that mind something that is mediately
> due to the Object.  That determination of which the immediate
> cause, or determinant, is the Sign, and of which the mediate
> cause is the Object may be termed the Interpretant. . .

Gary,

And you already know the obligatory parry:

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj:  SUO: Sop To Cerberus: What In Hades Was CSP Talking About? 
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>, SemioCom <semiocom@listbot.com>,
       Standardize Unto Others <standard-upper-ontology@ieee.org>  
Date:  Mon, 21 May 2001 15:33:30 -0400 

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

I trust that will be the end of that -- hah!

Jon Awbrey

Incidental Musements:

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

o~~~~~~~~~o~~~~~~~~~o~EVIHCRA~o~~~~~~~~~o~~~~~~~~~o

The fact that Peirce maintained what he himself called
a "non-psychological" view of signs and logic is pretty
much beyond dispute.  What that means, of course, takes
a bit more reading to get clear about.  All in all, it
seems to me that the contrasts between these sorts of
passages illustrates a number of issues:

1.  In reading a complex thinker, say Peirce, Dickinson, Melville,
    Einstein, Bohr, Heisenberg, Rosen, to name a few, who happens
    to write for several different audiences, and whose manner of
    expression, if not always whose Big Idea, happens to develop
    over time, it is crucial to sort out the illustrative cases
    from the generic examples of what is overall being conveyed.

2.  For all the same reasons, in the case of such a thinker,
    it is critical to make an unbiased and wide selection
    from the diversity of their writings in order to get
    even a glimmer of what is primary and what is not.

3.  It is a curious property of the English language that
    the "or" construction, for instance, as used above in
    the phrase "cause, or determinant" can be employed to
    convey any one of the following logical operations:

    a.  inclusive disjunction
    b.  exclusive disjunction
    c.  equivalence ("id est")
    d.  exemplification ("for example")
    e.  generalization ("more broadly")
    f.  retraction of an over-generalization

    Consequently, one is forced to read what Peirce says
    in many other places in order to get at how he groks
    the relationship between "cause" and "determination".
    Anybody who desires to do this might well begin here:

    http://suo.ieee.org/email/msg04784.html
    http://suo.ieee.org/email/msg04785.html
    http://suo.ieee.org/email/msg04786.html
    http://suo.ieee.org/email/msg04787.html
    http://suo.ieee.org/email/msg04791.html
    http://suo.ieee.org/email/msg04794.html
    http://suo.ieee.org/email/msg04795.html
    http://suo.ieee.org/email/msg04796.html
    http://suo.ieee.org/email/msg04797.html
    http://suo.ieee.org/email/msg04798.html
    http://suo.ieee.org/email/msg04802.html
    http://suo.ieee.org/email/msg04814.html
    http://suo.ieee.org/email/msg04956.html
    http://suo.ieee.org/email/msg04958.html
    http://suo.ieee.org/email/msg04962.html
    http://suo.ieee.org/email/msg05000.html
    http://suo.ieee.org/email/msg05056.html
    http://suo.ieee.org/email/msg05078.html
    http://suo.ieee.org/email/msg05111.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 12

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Bridge Over Semiotic Waters
Date:  Wed, 27 Jun 2001 11:04:27 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Standardize Unto Others <standard-upper-ontology@ieee.org>
  CC:  Arisbe <arisbe@stderr.org>,
       SemioCom <semiocom@listbot.com>

There a couple of critical passages in Peirce's work
that bear on the relations of the interpretive agent
to the interpretant sign, and thus of an interpreter
to the whole sign relation being sampled at a moment.
I am beginning to consider these passages as forming
the "pons asinorum" to the entire realm of semiotics.

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj:  SUO: Sop To Cerberus: What In Hades Was CSP Talking About?
Date:  Mon, 21 May 2001 15:33:30 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>, SemioCom <semiocom@listbot.com>,
       Standardize Unto Others <standard-upper-ontology@ieee.org>

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

I trust that will be the end of that -- hah!

Incidental Musements:

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

The fact that Peirce maintained what he himself called
a "non-psychological" view of signs and logic is pretty
much beyond dispute.  What that means, of course, takes
a bit more reading to get clear about.  All in all, it
seems to me that the contrasts between these sorts of
passages illustrates a number of issues:

1.  In reading a complex thinker, say Peirce, Dickinson, Melville,
    Einstein, Bohr, Heisenberg, Rosen, to name a few, who happens
    to write for several different audiences, and whose manner of
    expression, if not always whose Big Idea, happens to develop
    over time, it is crucial to sort out the illustrative cases
    from the generic examples of what is overall being conveyed.

2.  For all the same reasons, in the case of such a thinker,
    it is critical to make an unbiased and wide selection
    from the diversity of their writings in order to get
    even a glimmer of what is primary and what is not.

3.  It is a curious property of the English language that
    the "or" construction, for instance, as used above in
    the phrase "cause, or determinant" can be employed to
    convey any one of the following logical operations:

    a.  inclusive disjunction
    b.  exclusive disjunction
    c.  equivalence ("id est")
    d.  exemplification ("for example")
    e.  generalization ("more broadly")
    f.  retraction of an over-generalization

    Consequently, one is forced to read what Peirce says
    in many other places in order to get at how he groks
    the relationship between "cause" and "determination".
    Anybody who desires to do this might well begin here:

    http://suo.ieee.org/email/msg04784.html
    http://suo.ieee.org/email/msg04785.html
    http://suo.ieee.org/email/msg04786.html
    http://suo.ieee.org/email/msg04787.html
    http://suo.ieee.org/email/msg04791.html
    http://suo.ieee.org/email/msg04794.html
    http://suo.ieee.org/email/msg04795.html
    http://suo.ieee.org/email/msg04796.html
    http://suo.ieee.org/email/msg04797.html
    http://suo.ieee.org/email/msg04798.html
    http://suo.ieee.org/email/msg04802.html
    http://suo.ieee.org/email/msg04814.html
    http://suo.ieee.org/email/msg04956.html
    http://suo.ieee.org/email/msg04958.html
    http://suo.ieee.org/email/msg04962.html
    http://suo.ieee.org/email/msg05000.html
    http://suo.ieee.org/email/msg05056.html
    http://suo.ieee.org/email/msg05078.html
    http://suo.ieee.org/email/msg05111.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Semiotics Formalization
Date:  Sat, 23 Sep 2000 20:01:59 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Stand Up Ontology <standard-upper-ontology@ieee.org>

Semiotic SIG,

Here is a passage from Peirce that is decisive in clearing up
the relationship between the interpreter and the interpretant,
and, not by coincidence, has some bearing on the placement of
concepts as symbols, as their principal aspects are refracted
across the spectrum of sign modalities.

| I think we need to reflect upon the circumstance that every word
| implies some proposition or, what is the same thing, every word,
| concept, symbol has an equivalent term -- or one which has become
| identified with it, -- in short, has an 'interpretant'.
|
| Consider, what a word or symbol is;  it is a sort of representation.
| Now a representation is something which stands for something.  ...
| A thing cannot stand for something without standing 'to' something
| 'for' that something.  Now, what is this that a word stands 'to'?
| Is it a person?  We usually say that the word 'homme' stands to
| a Frenchman for 'man'.  It would be a little more precise to say
| that it stands to the Frenchman's mind -- to his memory.  It is
| still more accurate to say that it addresses a particular remembrance
| or image in that memory.  And what 'image', what remembrance?  Plainly,
| the one which is the mental equivalent of the word 'homme' -- in short,
| its interpretant.  Whatever a word addresses then or 'stands to', is its
| interpretant or identified symbol.  ...
|
| The interpretant of a term, then, and that which it stands to are identical.
| Hence, since it is of the very essence of a symbol that it should stand 'to'
| something, every symbol -- every word and every 'conception' -- must have an
| interpretant -- or what is the same thing, must have information or implication.
|
| (Peirce, 'Writings: Chronological Edition', CE 1, 466-467).

o~~~~~~~~~o~~~~~~~~~o~EVIHCRA~o~~~~~~~~~o~~~~~~~~~o

Some Other Beads On This Wire:

http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00892.html
http://suo.ieee.org/email/msg00893.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html
http://suo.ieee.org/email/msg02611.html
http://suo.ieee.org/email/msg02617.html
http://suo.ieee.org/email/msg05088.html
http://www.vcu.edu/cgi-bin/wa?A2=ind0106&L=complexity-l&D=0&P=10578

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 13

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Bridge Over Semiotic Waters
Date:  Fri, 29 Jun 2001 09:06:14 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Standardize Unto Others <standard-upper-ontology@ieee.org>

There a couple of critical passages in Peirce's work
that bear on the relations of the interpretive agent
to the interpretant sign, and thus of an interpreter
to the whole sign relation being sampled at a moment.
I am beginning to consider these passages as forming
the "pons asinorum" to the entire realm of semiotics.

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj:  Sop To Cerberus: What In Hades Was CSP Talking About?
Date:  Mon, 21 May 2001 15:33:30 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>, SemioCom <semiocom@listbot.com>,
       Standardize Unto Others <standard-upper-ontology@ieee.org>

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

I trust that will be the end of that -- hah!

Incidental Musements:

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

The fact that Peirce maintained what he himself called
a "non-psychological" view of signs and logic is pretty
much beyond dispute.  What that means, of course, takes
a bit more reading to get clear about.  All in all, it
seems to me that the contrasts between these sorts of
passages illustrates a number of issues:

1.  In reading a complex thinker, say Peirce, Dickinson, Melville,
    Einstein, Bohr, Heisenberg, Rosen, to name a few, who happens
    to write for several different audiences, and whose manner of
    expression, if not always whose Big Idea, happens to develop
    over time, it is crucial to sort out the illustrative cases
    from the generic examples of what is overall being conveyed.

2.  For all the same reasons, in the case of such a thinker,
    it is critical to make an unbiased and wide selection
    from the diversity of their writings in order to get
    even a glimmer of what is primary and what is not.

3.  It is a curious property of the English language that
    the "or" construction, for instance, as used above in
    the phrase "cause, or determinant" can be employed to
    convey any one of the following logical operations:

    a.  inclusive disjunction
    b.  exclusive disjunction
    c.  equivalence ("id est")
    d.  exemplification ("for example")
    e.  generalization ("more broadly")
    f.  retraction of an over-generalization

    Consequently, one is forced to read what Peirce says
    in many other places in order to get at how he groks
    the relationship between "cause" and "determination".
    Anybody who desires to do this might well begin here:

    http://suo.ieee.org/email/msg04784.html
    http://suo.ieee.org/email/msg04785.html
    http://suo.ieee.org/email/msg04786.html
    http://suo.ieee.org/email/msg04787.html
    http://suo.ieee.org/email/msg04791.html
    http://suo.ieee.org/email/msg04794.html
    http://suo.ieee.org/email/msg04795.html
    http://suo.ieee.org/email/msg04796.html
    http://suo.ieee.org/email/msg04797.html
    http://suo.ieee.org/email/msg04798.html
    http://suo.ieee.org/email/msg04802.html
    http://suo.ieee.org/email/msg04814.html
    http://suo.ieee.org/email/msg04956.html
    http://suo.ieee.org/email/msg04958.html
    http://suo.ieee.org/email/msg04962.html
    http://suo.ieee.org/email/msg05000.html
    http://suo.ieee.org/email/msg05056.html
    http://suo.ieee.org/email/msg05078.html
    http://suo.ieee.org/email/msg05111.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  SUO: Re: Semiotics Formalization
Date:  Sat, 23 Sep 2000 20:01:59 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Stand Up Ontology <standard-upper-ontology@ieee.org>

Semiotic SIG,

Here is a passage from Peirce that is decisive in clearing up
the relationship between the interpreter and the interpretant,
and, not by coincidence, has some bearing on the placement of
concepts as symbols, as their principal aspects are refracted
across the spectrum of sign modalities.

| I think we need to reflect upon the circumstance that every word
| implies some proposition or, what is the same thing, every word,
| concept, symbol has an equivalent term -- or one which has become
| identified with it, -- in short, has an 'interpretant'.
|
| Consider, what a word or symbol is;  it is a sort of representation.
| Now a representation is something which stands for something.  ...
| A thing cannot stand for something without standing 'to' something
| 'for' that something.  Now, what is this that a word stands 'to'?
| Is it a person?  We usually say that the word 'homme' stands to
| a Frenchman for 'man'.  It would be a little more precise to say
| that it stands to the Frenchman's mind -- to his memory.  It is
| still more accurate to say that it addresses a particular remembrance
| or image in that memory.  And what 'image', what remembrance?  Plainly,
| the one which is the mental equivalent of the word 'homme' -- in short,
| its interpretant.  Whatever a word addresses then or 'stands to', is its
| interpretant or identified symbol.  ...
|
| The interpretant of a term, then, and that which it stands to are identical.
| Hence, since it is of the very essence of a symbol that it should stand 'to'
| something, every symbol -- every word and every 'conception' -- must have an
| interpretant -- or what is the same thing, must have information or implication.
|
| (Peirce, 'Writings: Chronological Edition', CE 1, 466-467).

o~~~~~~~~~o~~~~~~~~~o~EVIHCRA~o~~~~~~~~~o~~~~~~~~~o

Some Other Beads On This Wire:

http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00892.html
http://suo.ieee.org/email/msg00893.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html
http://suo.ieee.org/email/msg02611.html
http://suo.ieee.org/email/msg02617.html
http://suo.ieee.org/email/msg05088.html
http://www.vcu.edu/cgi-bin/wa?A2=ind0106&L=complexity-l&D=0&P=10578

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 14

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  CSP's Sop to Cerberus, Causation, Determination, & Semiosis
Date:  Thu, 05 Jul 2001 01:00:33 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  oca@cc.newcastle.edu.au

OCA Demics,

I am sorry if it seems like I am dumping a lot of 'canned goods'
on you, but half my brain is already on vacation, and I am in
no condition to do any fresh thinking -- and I knew as soon
as I said it that some wiseacre would ask "which half?" ...

This is the tail end of a very long series of discussions that ranged
from the Peirce List to the SUO List, partly occasioned by some wag
who asked "What the Hell was CSP Talking About?", and partly due to
what appears to be a very recalcitrant misunderstanding that folks
often have about what Peirce described as his "non-psychological"
view of logic.  Just to light the fuse, I have tossed in a few
links to a study I started on Peirce's Theory of Information,
wherein a notion of 'determination' and its distinction from
any notion of 'causation' becomes critical to comprehend.

The other thing to watch out for in trying to get at Peirce's meaning
is not to construe the word "sign" too narrowly, since its application
goes far beyond the purely linguistic domain.  For me, the best guides
to the subject are Peirce's more explicit definitions of a sign relation,
which are intended to be used like any other definitions of formal objects.
Here is what I regard as one of the clearest and the most useful definitions:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Basic Definition of a Sign Relation

| A sign is something, 'A', which brings something, 'B',
| its 'interpretant' sign determined or created by it,
| into the same sort of correspondence with something, 'C',
| its 'object', as that in which itself stands to 'C'.
|
| CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.

The biggest trouble with this definition is that it sends
one off to look up what Peirce meant by "correspondence"
and "determination", since a lot of misunderstanding has
arisen from contemporary readers who supply their own,
very typically anachronistic senses for these terms.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

On Peirce's "Sop To Cerberus" Passage

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Causation, Determination, Information, & Semiosis

| Of triadic Being the multitude of forms
| is so terrific that I have usually shrunk
| from the task of enumerating them;  and for
| the present purpose such an enumeration would
| be worse than superfluous:  it would be a great
| inconvenience.  In another paper, I intend to
| give the formal definition of a sign, which I
| have worked out by arduous and long labour.
| I will omit the explanation of it here.
|
| Suffice it to say that a sign endeavors
| to represent, in part at least, an Object,
| which is therefore in a sense the cause, or
| determinant, of the sign even if the sign
| represents its object falsely.  But to say
| that it represents its Object implies that
| it affects a mind, and so affects it as,
| in some respect, to determine in that mind
| something that is mediately due to the Object.
| That determination of which the immediate cause,
| or determinant, is the Sign, and of which the
| mediate cause is the Object may be termed the
| 'Interpretant' ...
|
| Charles Sanders Peirce, CP 6.347

The fact that Peirce maintained what he himself called
a "non-psychological" view of signs and logic is pretty
much beyond dispute.  What that means, of course, takes
a bit more reading to get clear about.  All in all, it
seems to me that the contrasts between these sorts of
passages illustrates a number of issues:

1.  In reading a complex thinker, say Peirce, Dickinson, Melville,
    Einstein, Bohr, Heisenberg, Rosen, to name a few, who happens
    to write for several different audiences, and whose manner of
    expression, if not always whose Big Idea, happens to develop
    over time, it is crucial to sort out the illustrative cases
    from the generic examples of what is overall being conveyed.

2.  For all the same reasons, in the case of such a thinker,
    it is critical to make an unbiased and wide selection
    from the diversity of their writings in order to get
    even a glimmer of what is primary and what is not.

3.  It is a curious property of the English language that
    the "or" construction, for instance, as used above in
    the phrase "cause, or determinant" can be employed to
    convey any one of the following logical operations:

    a.  inclusive disjunction
    b.  exclusive disjunction
    c.  equivalence ("id est")
    d.  exemplification ("for example")
    e.  generalization ("more broadly")
    f.  retraction of an over-generalization

    Consequently, one is forced to read what Peirce says
    in many other places in order to get at how he groks
    the relationship between "cause" and "determination".
    Anybody who desires to do this might well begin here:

    http://suo.ieee.org/email/msg04784.html
    http://suo.ieee.org/email/msg04785.html
    http://suo.ieee.org/email/msg04786.html
    http://suo.ieee.org/email/msg04787.html
    http://suo.ieee.org/email/msg04791.html
    http://suo.ieee.org/email/msg04794.html
    http://suo.ieee.org/email/msg04795.html
    http://suo.ieee.org/email/msg04796.html
    http://suo.ieee.org/email/msg04797.html
    http://suo.ieee.org/email/msg04798.html
    http://suo.ieee.org/email/msg04802.html
    http://suo.ieee.org/email/msg04814.html
    http://suo.ieee.org/email/msg04956.html
    http://suo.ieee.org/email/msg04958.html
    http://suo.ieee.org/email/msg04962.html
    http://suo.ieee.org/email/msg05000.html
    http://suo.ieee.org/email/msg05056.html
    http://suo.ieee.org/email/msg05078.html
    http://suo.ieee.org/email/msg05111.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 15

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Discussion of Semiotics
Date:  Sat, 18 Aug 2001 00:18:41 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Edwina Taborsky <taborsky@primus.ca>
  CC:  Mishtu Banerjee <mishtu_banerjee@telus.net>

Edwina Taborsky wrote (ET):

ET: As to your post:

ET: (1) Peirce does indeed reject the psychological -- numerous times.

He says that he has a "non-psychological conception of logic".
This does not amount to any wholesale rejection of psychology --
indeed, Peirce did ground-breaking work in experimental psy.
I have discussed this issue numerous times in the OCA group
and also in several other fora, for instance, here:

http://suo.ieee.org/ontology/msg02121.html

For convenience, here is a copy of the note:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

A recent inquiry about my gloss on the functional particle "non",
as used by Peirce in his remark on the "non-psychological" nature
of his theory of signs, leads me to believe that some further bit
of clarification may be necessary.  It is, above all, important to
distinguish Peirce's view from any sort of "anti-psychologism" with
which it might otherwise be confused.  Indeed, it is from Peirce that
I came to acquire my own brands of "anti-anti-ism" and "anti-ism-ism".

Just for accuracy, I restate Peirce's original definitions and remarks:

| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time.  Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'.  It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized.  (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'.  A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'.  This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.

Just for context, I recite my earlier remarks:

A "sign" is -- surprise! surprise! -- anything
at all that satifies a/the definition of a sign.
For pragmaticians, Peircean style, there are any
one of a number (76 to 88 the last time somebody
took the trouble to count) putative "definitions"
of a sign, but most sensible folks believe that
they all boil down to pretty much the same idea.
The most important feature of Peirce's concept
is that being a sign is not an absolute or an
essential property, but a relational property.
I have been working on the extensional side
of understanding sign relations, mostly just
because less careful work has been done from
that standpoint so far.  Here, one views the
category or the variety of "sign relations"
much as one might view "groups", namely, as
a highly diverse family of 3-place relations,
satisfying an extremely simple definition or
a highly "non-categorical" axiom set, but
by no means being anywhere near as simple
as the definition might deceive one into
believing at the outset.

My personal best explanation so far is here:

| Second, Peirce's claim that his definition of a sign involves
| no reference to human thought means no necessary reference.
| The adjective "non-psychological" that he often attaches to
| this conception of signs and logic is not intended to be
| exclusive of human thought but to expand the scope of the
| concepts beyond it (Peirce, NEM 4, 21).  The prefix "non"
| is better read as an acronym for "not of necessity," and
| is commonly used in mathematical discourse in just this way.
| It extends the use of a concept into wider domains than the
| paradigm cases upon which our original intuitions were formed.
|
| A definition of signs and their processes which is not limited
| by prior restriction to human psychology can be used to investigate
| human thought as a species of natural process.  There is considerable
| power in this naturalistic viewpoint.  It allows us to put human thought
| in a context of other sign processes, to ask what might be the specific
| differences that distinguish it, and to consider its evolution through
| different orders of complexity. 

Full paper at:

http://www.chss.montclair.edu/inquiry/fall95/awbrey.html

I began to introduce these ideas to the SUO List here:

http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html

Just to extract the core from my personal
favorite one of Peirce's definitions:

| A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm

A punctuation mark, space, character, sentence, paragraph, book,
rock, painting, sculpture, building, person, whole person's life,
the entire cosmos, and so on, can all be signs, of some "object",
that is, "objective" or "pragma", to some interpreter.  Or not.

Since the time that I adduced this material, initially
in response to one reader's feigned or real puzzlement
as to how we thinkers of a Peircean persuasion use the
term "sign", I have observed that some readers, well,
actually, the same reader, appear just as curiously
oblivious to the sense of the modal context that I
introduced through the use of the auxiliary "can",
the relational context that is marked throughout,
and the optative context that was qualified by
the closing comment "Or not", but I have come
to appreciate the fact that attentions waver,
and reading skills vary.  It caint be helped.

Anyway, finally, here is my appended clarification:

My remark was limited to a particular and, yes, slightly peculiar usage,
one that tends to come up more in describing collections of mathematical
systems that are subject to a variable set of axioms than in describing
the elements of a fixed domain.  For example, a very common situation
occurs when folks have been discussing, say, the sort of structure
that is officially called an "algebra", say, X, which somewhere in
the list of its axioms contains an associative law -- in other words,
"for all x, y, z in X, x(yz) = (xy)z" -- and then they get bored with
that and decide to generalize the family of structures under review by
removing that axiom from the list.  The new subject will then typically
be called "non-associative algebras".  But note that all of the original
algebras fall under the heading of "non-associative algebras".  This is
a longstanding usage that Peirce would have known quite well -- some of
the few theorems in math that still bear the Peirce's name are in the
field of non-associative algebras.  Moreso in the 19th Century, they
used the word "mock" as a similar sort of analogizing or generalizing
functor, as memorialized in Lewis Carroll's (C.L. Dodgson's) Mock Turtle --
CLD is alluding to the issue of associativity here, as a part of the joke
is over whether a "Mock (Turtle Soup)" is a "(Mock Turtle) Soup".  Ergot,
to summit all up, mathematicians are some really strangely chirping birds.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

ET: And if logic, which is the basis of semiotics, ...

Ay, there's the rub.  It is rather semiotics that is the basis of logic.
That's what it means for logic to be the "formal" branch of semiotics.
For Peirce, formal = quasi-necessary => normative.  See this note:

http://suo.ieee.org/ontology/msg03070.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Logic, in its general sense, is, as I believe I have shown, only another name for
|'semiotic' ([Greek: semeiotike]), the quasi-necessary, or formal, doctrine of signs.
| By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the
| characters of such signs as we know, and from such an observation, by a process which
| I will not object to naming Abstraction, we are led to statements, eminently fallible,
| and therefore in one sense by no means necessary, as to what 'must be' the characters
| of all signs used by a "scientific" intelligence, that is to say, by an intelligence
| capable of learning by experience.  As to that process of abstraction, it is itself
| a sort of observation.  The faculty which I call abstractive observation is one which
| ordinary people perfectly recognize, but for which the theories of philosophers sometimes
| hardly leave room.  It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question, "Should I wish for
| that thing just the same, if I had ample means to gratify it?"  To answer that question, he
| searches his heart, and in doing so makes what I term an abstractive observation.  He makes
| in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what
| modifications the hypothetical state of things would require to be made in that picture, and
| then examines it, that is, 'observes' what he has imagined, to see whether the same ardent
| desire is there to be discerned.  By such a process, which is at bottom very much like
| mathematical reasoning, we can reach conclusions as to what 'would be' true of signs
| in all cases, so long as the intelligence using them was scientific.  (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editor's Note: From an unidentified fragment, c. 1897.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

And so, as I said before, this leaves room in the genus semiotics,
on the negative side of the differentia "formal", for a descriptive
semiotics, which might conceivably have a non-trivial overlap with
the descriptive science of psychology.

ET: And if logic, which is the basis of semiotics, is non-psychological,
    then semiotics is also non-psychological.  Semiotics is most certainly
    not the 'psychological version' of logic.  I don't have the time to check
    into my Peirce volumes but I've located his rejection of the psychological
    numerous times.  He rejects the 'sop to Cerberus'.

Actually, to the contrary, Peirce 'uses' the sop as it was meant to be used,
for to toss a sop to Cerberus is indeed to use that sop for all it is worth.

The passage that you have in mind is here:

http://suo.ieee.org/ontology/msg02683.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Those of you who do not know the reference deserve an explanation.
There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432
| in 'Charles S. Peirce:  Selected Writings (Values in a Universe of Chance)',
| Edited with an Introduction & Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

A word to the wise is sufficient,
in no way universally sufficient.

Notice that this self-described "definition" of a Sign
is also self-labelled as an approximate definition, or
as a special application of a Lost Lenore (= Eurydice)
that might have been the lamented "broader conception".
As anybody, almost anybody, can plainly see, this sop
to Cerberus has to be taken with a due grain of salt
(= Lot's Wife).

I trust that will be the end of that -- hah!

Jon Awbrey

Incidental Musements:

http://www.bibleinfo.com/Asp/DisplayFullFAQ.asp?FAQid=32

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

ET: (2) As for 'formal' -- that's not what I mean by nominal
    or a nominalist type of representation.  I am not saying
    that representation is invalid.  Of course a sign is
    a representation of an object.  My point was that
    it was not a dyadic nominalist representation but
    a transformative, relational, representation.
    The key word about this action was that it
    is relational process rather than a system
    of substitution of X for Y.

But it seems that using "representation" that way
in a semiotic context is just asking for trouble.

ET: (3) Semiosis would have to include multiple levels of codal organization 
    and therefore, would operate in both a connotative (horizontal level)
    and denotative (introduction of hierarchical differences) manner.
    The Dynamic Interpretant, for example, is a denotative reference.

Nothing about the definition of a sign relation prevents the
same entity from filling all three roles, even in the very
same "elementary sign relation" (ESR), that is to say,
in the very same triple of the form <o, s, i>.
Every symbol has an object of acquiring
a certain character of interpretant.

ET: (4) What you call 'syntactic' (sign to sign) I would call 'semantic'.
    One unit referring to another unit.

I do not speak that way.  It is my opinion that this way of speaking
volatilizes semantics.  If one sign transits to another another sign
in the same sign relation, that is just a sign process, or semiosis.
If a sign literally "refers to" an entity that also happens to be
a sign, that is, denotes it as its object, then we have entered
the realm of "higher order signs", on which I have done a bit
of work for my dissertation.  Here are a couple of excerpts:

http://suo.ieee.org/ontology/msg00703.html
http://suo.ieee.org/ontology/msg00973.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Reflection SIG,

Here is a preliminary foray into a Section
of my Dissertation where I begin to take up
the bearing of "higher order sign relations"
on the motley crew of intellectual operations
that we cast together and set in motion under
the heading of "reflection".

o~~~~~~~~~o~~~~~~~~~o~DISSERTATION~o~~~~~~~~~o~~~~~~~~~o

3.4.9  Higher Order Sign Relations:  Introduction

When interpreters reflect on their own use of signs they require an
appropriate technical language in which to pursue these reflections.
For this they need signs that refer to sign relations, signs that
refer to the elements and components of sign relations, and signs
that refer to the properties and classes of sign relations.
All of these additional signs can be placed under the
description of "higher order" (HO) signs, and the
extended sign relations that involve them can be
referred to as "higher order" (HO) sign relations.

Whether any forms of observation and reflection can be conducted
outside the medium of language is not a question I can address here.
It is apparent as a practical matter, however, that stable and sharable
forms of knowledge depend on the availability of an adequate language.
Accordingly, there is a relationship of practical necessity that binds the
conditions for reflective interpretation to the possibility of extending
sign relations through higher orders.  At minimum, in addition to the
signs of objects originally given, there must be signs of signs
and signs of their interpretants, and each of these HO signs
requires a further occurrence of HO interpretants to continue
and complete its meaning within a HO sign relation.  In general,
HO signs can arise in a number of independent fashions, but one
of the most common derivations is through the specialized devices
of quotation.  This establishes a contingent relation between
reflection and quotation.

This entire topic, involving the relationship of reflective interpreters
to the realm of HO sign relations and the available operators for quotation,
forms the subject of a recurring investigation that extends throughout the
rest of this work.  This section introduces only enough of the basic concepts,
terminology, and technical machinery that is necessary to get the theory of
HO signs off the ground.

By way of a first definition, a "higher order" (HO) sign relation
is a sign relation, some of whose signs are "higher order" (HO) signs.
If an extra degree of precision is needed, HO signs can be distinguished
in a variety of different "species" or "types", to be taken up next.

In devising a nomenclature for the required species of HO signs,
it is a good idea to generalize slightly, designing an analytic
terminology that can be adapted to classify the HO signs of
arbitrary relations, not just the HO signs of sign relations.
The work of developing a more powerful vocabulary can be put
to good account at a later stage of this project, when it
is necessary to discuss the structural constituents of
arbitrary relations and to reflect on the language that
is used to discuss them.  However, by way of making
a gradual approach, it still helps to take up the
classification of HO signs in a couple of passes,
first considering the categories of HO signs as
they apply to sign relations and then discussing
how the same ideas are relevant to arbitrary
relations.

Here are the species of HO signs that can be used to discuss the
structural constituents and intensional genera of sign relations:

1.  Signs that denote signs, that is, signs whose objects are signs
    in the same sign relation, are called "higher ascent" (HA) signs.

2.  Signs that denote dyadic components of elementary sign relations,
    that is, signs whose objects are elemental pairs or dyadic actions
    having any one of the forms <o, s>, <o, i>, <s, i>, are called
    "higher employ" (HE) signs.

3.  Signs that denote elementary sign relations, that is,
    signs whose objects are elemental triples or triadic
    transactions having the form <o, s, i>, are called
    "higher import" (HI) signs.

4.  Signs that denote sign relations, that is, signs whose objects are
    themselves sign relations, are called "higher upshot" (HU) signs.

5.  Signs that denote intensional genera of sign relations, that is,
    signs whose objects are properties or classes of sign relations,
    are called "higher yclept" (HY) signs.

http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

REF SIG:

"Reflection", as I currently understand and use the term,
appears to involve at least the following sorts of ideas:

An agent, a community, or a system is said to be "reflective"
to the extent that it can accept, acknowledge, generate, manage,
recognize, and reconcile, as such, descriptions of its own conduct.

"Conduct" is a technical term that means
"action or behavior in regard to an object".

"Object", of course, is being used here in the "pragmatic" sense of the word
that encompasses all varieties of "objects and objectives", whether they be
abstract or concrete, existent or inexistent, indifferent or intentional,
and whether they be past, present, or prospective.

I sometimes use the more specific term "critical reflection"
to indicate this particular meaning of the word "reflection".

I would not want to call this a formal definition --
it may need a bit of work before it could be that --
it is more like a survey of the notions that come
to mind, at least one mind, under this topic head.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 16

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Inquiry Into Isms -- k-adic versus k-tomic
Date:  Wed, 22 Aug 2001 01:45:06 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Organization Complexity Autonomy <oca@cc.newcastle.edu.au>
  CC:  Arisbe <arisbe@stderr.org>,
       Generic Ontology Group <ontology@ieee.org>

At 12:34 AM 8/21/01 -0400, Jon wrote:

JA: Here is an old note I've been looking for since we started on this bit about isms,
    as I feel like I managed to express in it somewhere my point of view that the key
    to integrating variant persepectives is to treat their contrasting values as axes
    or dimensions rather than so many points on a line to be selected among, each in
    exclusion of all the others.  To express it briefly, it is the difference between
    k-tomic decisions among terminal values and k-adic dimensions of extended variation.

(snip)

JA: But I think that it is safe to say, for whatever else
    it might be good, tomic thinking is of limited use in
    trying to understand Peirce's thought. 

HP: The way I understood Peirce's -adic thinking depended on
    irreducibility.  This would distinguish them from, say, the
    three binary relations that make up the sides of a triangle,
    or a linear operator on three (or n) elements.  I also assumed
    that this was a conceptual irreducibility or even an ontological
    irreducibility.  Using normal language (since I can't follow Peirce's
    many variations), I would call "sign/interpreter/referent" such an
    irreducible triadic relation, since it is easy to see that no single
    member or pair of the three make any sense without all three. 

HP: Am I too far off base here?  I am not at all sure I understand what else
    Peirce includes in "irreducible".  Could you find some examples or quotes
    that would explain his concept of irreducible?

OK, YAFI (you asked for it).  As it happens, this is precisely what I just used up
one of the better years of my life trying to explain in the SUO discussion group,
and so I have a whole lot of material on this, most of it hardly scathed by any
dint of popular assimilation or external use.

I see a couple of separate questions in what you are asking:

1.  What is the qualitative character of the 3-adic sign relation?  In particular,
    is it better to comprehend it in the form <object, sign, interpretive agent>,
    or is it best to understand it in the form <object, sign, interpretant sign>?

2.  What is reducible to what in what way, and what not?

The answer to the first question is writ
in what we who speak in Peircean tongues
dub the "Parable of the Sop to Cerberus".
Peirce would often start out explaining
his idea of the sign relation, for the
sake of a gentle exposition, in terms
of Object, Sign, and Interpreter, and
then follow with a partial retraction
of the Agent to the Interpretant Sign
that occupies the alleged agent's mind.
Here is the locus classicus for this bit:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432,
| in 'Charles S. Peirce: Selected Writings (Values in a Universe of Chance)',
| Edited with Introduction and Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

http://suo.ieee.org/ontology/msg02683.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Peirce's truer technical conception can be garnered
from another legendary bit of narrative exposition,
the story of the "French Interpretant's Memory":

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Here is a passage from Peirce that is decisive in clearing up
the relationship between the interpreter and the interpretant,
and, not by coincidence, has some bearing on the placement of
concepts as symbols, as their principal aspects are refracted
across the spectrum of sign modalities.

| I think we need to reflect upon the circumstance that every word
| implies some proposition or, what is the same thing, every word,
| concept, symbol has an equivalent term -- or one which has become
| identified with it, -- in short, has an 'interpretant'.
|
| Consider, what a word or symbol is;  it is a sort
| of representation.  Now a representation is something
| which stands for something.  ...  A thing cannot stand for
| something without standing 'to' something 'for' that something.
| Now, what is this that a word stands 'to'?  Is it a person?
|
| We usually say that the word 'homme' stands to a Frenchman for 'man'.
| It would be a little more precise to say that it stands 'to' the
| Frenchman's mind -- to his memory.  It is still more accurate
| to say that it addresses a particular remembrance or image
| in that memory.  And what 'image', what remembrance?
| Plainly, the one which is the mental equivalent of
| the word 'homme' -- in short, its interpretant.
| Whatever a word addresses then or 'stands to',
| is its interpretant or identified symbol.  ...
|
| The interpretant of a term, then, and that which it stands to
| are identical.  Hence, since it is of the very essence of a symbol
| that it should stand 'to' something, every symbol -- every word and
| every 'conception' -- must have an interpretant -- or what is the
| same thing, must have information or implication.  (CE 1, 466-467).
|
| Charles Sanders Peirce, 'Chronological Edition', Volume 1, pages 466-467.

http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

As it happens, this is exactly the sort of conception of semiosis
that I need in my own work for building bridges between the typical
brands of tokens that are commonly treated in abstract semiotics and
the kinds of states in the configuration spaces of dynamic systems
that are the actual carriers of these signals.  Which explains
why I discuss this passage toward the end of the introduction
to my dissertation and make critical use of it throughout.

HP: I would say the triad "DNA (sign) / code or cell (interpreter) / protein (referent)"
    is the primeval case.  This apparently ontological irreducibility is one reason
    the origin of life is so mysterious, but that is another problem.

I am not sure about this, since I do not know for certain what the object of life is.
It would be just as easy to say that the protein is yet another interpretant sign in
a process whose main object is to simply to continue itself in the form to which it
would like to become accustomed.  The only way I know to decide would be to check
my favorite definition, but there is always a bit of play in the way that it can
be made to fit any particular concrete process.

HP: There are many other types of more or less epistemological  irreducible triads or n-adics,
    popularly known as non-linear systems.  The classical physics case is the three-body problem
    (three masses accelerated by Newton's 2nd law and attracting each other by Newton's law of
    gravitation).  By "more or less epistemological" I just mean that it is unsolvable by any
    closed exact integration, but we can still compute approximate orbits by numerical methods.
    Still, it is easy to see the irreducibility is built into the laws.  However, to a physicist,
    calling this a sign/interpreter/referent relation would be entirely gratuitous ("What can be
    done with fewer assumptions is done in vain with more." -- Ockham). 

HP: What intrigues me as a hierarchy theorist is that the irreducible "sign/interpreter/referent"
    triad at the cognitive level requires an interpreting brain that is some kind of irreducible
    n-adic network (where n >>3).  The brain is initially constructed from cells organized largely
    by the genes.  At that lower level, the "DNA/code/protein irreducibility" works only because
    "coding" itself requires an irreducible triad: "messengerRNA/ribosomes/polypeptides."  At a
    lower level still, all this depends on enzymes which are defined by, and only function as,
    an irreducible triad:  "substrate/enzyme/product".  Furthermore, the function of the enzyme
    depends on its folding into the right shape which is an irreducible n-body problem.  So, it's
    irreducible n-adics all the way down.

It looks like my brain's eyes are too blurry right now
to get to the irreducibility question, so I will save
it for the morrow.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

26 Jul 2001 • 12:34 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Inquiry Into Inquiry
Date: Thu, 26 Jul 2001 12:34:03 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy

o~~~~~~~~~o~~~~~~~~~o~~~~~~ARCHIVE~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Inquiry Into Inquiry
Date: Fri, 24 Mar 2000 23:56:13 -0500
From: Jon Awbrey
  To: Peirce List

There are a few notes of inquiry that I would like to pluck out of their
recent entanglements in the "Qualitative Induction" thread, because they
resonate, in their fundametal tenor, with a wider concern of mine, and I
think perhaps many of yours, too, issues that I have been treating in my
Thesis under the theme of the "Inquiry into Inquiry".  Against my common
practice, I will try to state these questions here, at least, at first,
as succinctly as I possibly can, and then return to my readings to seek
out their answering chords, whether in our customary canon, or elsewhere.
I can no longer continue to play on distant echoes and other impressions
that I seem to hear being harped back to me from my dim and dimmer past.

Here are the questions, with only such accompaniment as I need
to conduct the clearest faithful sense of their meaning to you:

(1a)  Is inquiry a fit subject for inquiry?

In other words:

(1b)  Is inquiry a subject that can be inquired into?

To render certain, normally understood, aspects of this question more
explicit, and, at the same time, to accord the benefit of certain doubts
to "nominal thinkers", that is, to those who ordinarily call themselves by
the name of "nominalists", the question can be rephrased in the following way:

(1c)  Does the sign "inquiry" denote an object that can be inquired into
      with any hope of success?

The next question, that follows all but immediately upon the first, is this:

(2a)  What is a true theory of inquiry?

To ask the question more modestly, as befits the modest condition of
our current understanding -- well, mine, at least -- the question is
better asked in the following form:

(2b)  What signs do we have of what a true theory of inquiry would be like?

Those are the questions.

I have feeling that they will be enough to occupy me for a while.

Now, just let me say one or two things about the various ways that
I presently plan to approach these questions, if not being so bold
and so blunt as to think that they will bring me to approach their
answers any time soon.

In doing this, since the oh-so-grandiose title of "theory" so often
conveys the wrong impression, I hope that you will permit me to use
a motley assembly of more humble terms in its place, picking out the
roughly equivalent substitute that best fits the setting, the tone,
and the order of grandiloquence that has a chance of being revealed
in the offing, the outcome, or the upshot of the inquiry in question.
Among these proxies I will number the following set as my favorites:

{"account", "description", "indication", "sign", "story", "theory"}.

No, on second thought, on third thought, and that ought to be enough
for a pragmatic thinker, I am going to hold off on laying out my plans,
all the better to afford you the chance and the opportunity to stake out
your own.

Dream most fitfully, as will I,

Jon Awbrey

26 Jul 2001 • 15:00 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 26 Jul 2001 15:00:11 -0400
From: Jon Awbrey
  To: W.M. Jaworski
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

W.M. Jaworski wrote:
> 
> JA: |          Z
>     |          o
>     |          |\
>     |          | \
>     |          |  \
>     |          |   \
>     |          |    \  Rule
>     |          |     \
>     |          |      \
>     |          | A   > \
>     |          |  \ /   \
>     |    Fact  | <-o-D   o Y
>     |          |  / \   /
>     |          | I   > /
>     |          |      /
>     |          |     /
>     |          |    /  Case
>     |          |   /
>     |          |  /
>     |          | /
>     |          |/
>     |          o
>     |          X
>     |
>     | Figure 1.  Basic Structure & Terminology
> 
> WMJ: What is A, I, D, o ?  How this subgraph is connected to XYZ graph?
>      Probably this is explained in your other submissions or figures.
>      Classical case of logically joined but physically dis-joined.

A = Abduction
D = Deduction
I = Induction

o = Decoration

The arrows in the center were supposed (superimposed?) to form
what is clearly a not-so-mnemonic device to indicate this data:

| Deduction takes a Case, the minor premiss of the form X => Y,
| matches it with a Rule, the major premiss of the form Y => Z,
| then adverts to a Fact, the bound outcome of the form X => Z.
| 
| Induction takes a Case of the form X => Y,
| matches it with a Fact of the form X => Z,
| then adverts to a Rule of the form Y => Z.
|
| Abduction takes a Fact of the form X => Z,
| matches it with a Rule of the form Y => Z,
| then adverts to a Case of the form X => Y.

> When I use this ancient scheme, attaching its medieval labels
> of "Case", "Fact", "Rule", I will always try to remember to
> capitalize these quaint terms of art, so as not to confuse
> them with their more common usage.  So the points X, Y, Z
> represent 'terms', while the edges represent 'propositions',
> reading Case YX, Fact ZX, Rule ZY in the following ways as
> implications or as predications, according to one's taste.
> 
> o~~~~~~~~~~~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> | Proposition       | Case YX | Fact ZX | Rule ZY |
> o~~~~~~~~~~~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> | Predication       |  Y of X |  Z of X |  Z of Y |
> o~~~~~~~~~~~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> | Implication       | (X (Y)) | (X (Z)) | (Y (Z)) |
> |                   |         |         |         |
> |                   |  X=>Y   |  X=>Z   |  Y=>Z   |
> o~~~~~~~~~~~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Never fear -- you will get to see all of this again.

Jon Awbrey

26 Jul 2001 • 15:45 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 26 Jul 2001 15:45:07 -0400
From: Jon Awbrey
  To: W.M. Jaworski, Paul Prueitt
  CC: Arisbe, Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~ARCHIVE~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Theory of Inquiry, Types of Inference, Missing the Bus
Date: Fri, 18 May 2001 13:00:20 -0400
From: Jon Awbrey
  To: Arisbe, SemioCom, Standard Upper Ontology
  CC: Cathy Legg, Arien Malec

Inquiry SIG,

Because it took me literally a half an hour to find this
thread under the subject line where I left it last, I am
restarting it under a title more reflective of its topic.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Theory of Inquiry, Types of Inference, Missing the Bus

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 1

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj:  Theory of Inquiry
Date:  Sat, 29 Apr 2000 15:06:01 -0400
From:  Jon Awbrey
  To:  Peirce List

Arien Malec wrote:

AM:  When Chomsky questioned whether for Peirce inductive procedures provide
     only post hoc guidance to abduction (note that I'm moving to a paraphrase
     of selected quotations from a paper I haven't read), I suspect he is asking
     whether the familiar sort of induction (generalization from sample to whole)
     plays a part in abduction, or whether that sort of reasoning is post hoc.

Jon Awbrey wrote:

JA:  Can you tell me which statements that Chomsky made are the ones that you
     interpret to say that he questions "whether for Peirce inductive procedures
     provide only post hoc guidance to abduction"?  I either missed them or read
     them in another way.

Cathy Legg wrote:

CL:  I guess I'm having trouble getting my head around how
     induction could play this this sort of role, given that
     abductions arise when a phenomenon appears surprising and
     irregular.  Would this be a possible example -- I'm waiting
     for my morning bus and it doesn't arrive:  surprise.  I then
     think -- in the past sometimes my bus hasn't arrived when it's
     a public holiday I've forgotten about:  this case should be the
     same (induction), I then form the hypothesis that it is a public
     holiday (abduction).

Jon Awbrey wrote:

JA:  Here is my analysis of your "Missing the Bus"
     problem, to the extent that it can be represented
     within the constraints of "propositional models"
     or "sentential logic".

JA:  C = Current situation, that is, your current situation under
     the circumstances of the problem in question, represented by
     a "circle" in a venn diagram.  This is just a cheap propositional
     gimmick for covering, to some extent, the indexical characterisitics
     of the situation in question without resorting to using variables
     that range over domains of "individual situations".

JA:  Next, consider the alternative possibilities:

     Proposition X  =  [C => A]
                    =  [In the Current situation, the bus Arrives]

     Proposition Y  =  [C => ~A]
                    =  [In the Current situation, the bus does Not Arrive]

JA:  As it happens, X is your expectation, while Y is your observation.
     This difference between your expectation and your observation is
     what you affectively experience as a surprise.

JA:  Let me stress this.  The observed fact is Y, but what renders it
     surprising is its difference from X, and this occurs on the point
     of detaching its consequent.

JA:  Incidentally, it is this "differential" aspect of inquiry
     that led me, starting about a decade ago, to begin to develop
     a "differential logic", extending "propositional calculus" in
     almost precisely the same way that differential calculus extends
     analytic geometry.

JA:  But let us get back to your situation.

JA:  The way that induction enters this situation
     is as a component of previous cycles of inquiry
     that led to the formation of a rule, even if it is
     only a "probable approximate rule", more or less to
     the following effect:

     Proposition K  =  [B => A]
                    =  [In the Best case scenario, the bus Arrives]

JA:  It does not affect the analysis at all if you have in mind another
     sort of descriptor than "best", say, "normal", "ordinary", or so on,
     so long as you acknowledge the conducive function or the mediating role
     of any middle term like B.

JA:  When you get to the bus stop, you are actually in a somewhat confused,
     indeterminate, uncertain, or vague state of mind, in the sense that
     you have probably not even stopped to ask yourself the question:

JA:  Question Q  =  [Is it really true that J?]

     where:

     Proposition J  =  [C => B]
                    =  [The Current situation is a Best case scenario]

JA:  Consequently, you have walked, or ran, as is frequently the case,
     right into your current situation, operating under the influence
     of something like the following form of automatic deduction:

      (Case J):  C => B
      (Rule K):  B => A
     -------------------
      (Fact X):  C => A

JA:  And this is just where we came in, with the discrepancy between
     the expected fact X : C => A and the observed fact Y : C => ~A.

JA:  The surprise that you meet with, instead of the bus, might lead you
     question all sorts of things.  Any number of speculations might come
     to mind.  Among the more rational possibilities, the surprise might
     cause you to inquire into any and all of the premisses that fed into
     the above deduction, if not the axioms of the logic that you happen
     to be employing at the time.

JA:  But let us suppose that you focus on the case C => B, as it is most
     frequently the case that is the cause of the problem, and therefore,
     in accord with a higher order induction in the inquiry into inquiry,
     it is most frequently the case that rational people consider first.

JA:  And so, after reflecting on the situation, and eliciting certain features
     of how your habitual reasoning processes fed into it, quasi modo intuitio,
     you decide to vary the description of the case, in this case, from saying
     that C => B to asking whether it might not be true that C => ~B, that is,
     asking yourself, "Can it be that the current situation is not actually the
     best (modal, normal, ordinary, usual, ...) case, and that this is the cause
     of my expectation being disappointed?"

JA:  Oops!  I've run out of time for today, so I will have to look at the
     rest later, but I think that the foregoing is the gist of how I see
     the process of inquiry working its way out in situations like these.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 2

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: Theory of Inquiry
Date: Tue, 02 May 2000 02:34:14 -0400
From: Jon Awbrey
  To: Peirce List

JA:  I am replying to my own previous reply to you as a way of
     continuing my analysis of your example, to the extent
     that it can be represented in propositional terms.
 
JA:  I am going to introduce a type of diagram that I often
     use in articulating these sorts of logical situations.

JA:  To present what we have so far in this style of depiction,
     I can summarize the analysis I have already given as follows:

|   A                                                          (A)
|    o                                                         o
|     \                                                       /
|      \ *                                                 * /
|       \                                                   /
|        \  *                                           *  /
|         \                                               /
|          \   *                                     *   /
|           \                                           /
|            \    *                               *    /
|             \                                       /
|              \     *                         *     /
|               \                                   /
|                \      *                   *      /
|                 \                               /
|                  \       B            (B)      /
|                   \                           /
|                    \      *           *      /
|                     \                       /
|                      \     *         *     /
|                       \                   /
|                        \    *       *    /
|                         \               /
|                          \   *     *   /
|                           \           /
|                            \  *   *  /
|                             \       /
|                              \ * * /
|                               \   /
|                                \*/
|                                 o
|                                 C
|
| Figure 1.  Missing the Bus
|
| A  =  Arriving bus situations,
| B  =  Best case situations,
| C  =  Current situation.

It is my guess that something like this style of geometric figure
was used by Aristotle, and may have been a common sort of picture
at the time, at least, this is the impression that I get from the
way that he uses two different styles of language for indicating
the various kinds of logical relationships that are relevant to
the fundamental types of reasoning situation that he discusses.
For instance, Aristotle often uses the geometric label of the
line segment AB to indicate the premiss B => A.  Of course,
this may just be a fluke of Greek grammar, or of its later
transcription.

The point elements in these diagrams represent the "propositions"
that one is contemplating with respect to domain of objects, persons,
situations, and so on.  Alternatively, one may treat them as the "terms"
of the problem:  Major, Middle, Minor, and so on.

The line elements in these diagrams represent the "logical relations"
that are being considered between certain pairs of propositions, or else
the premisses that are being contemplated between various pairs of terms,
where roughly vertical lines indicate "implications", the antecedent lower
and the consequent higher, and where roughly horizontal placements indicate
relationship of "alteration" (change) or "alternation" (diversity), that is,
the situation among a number of alternatives, exclusive or inclusive, that
are available for changing or choosing among.

The language that labels various line elements (premisses or relations)
as Cases, Facts, or Rules was added later, but I will use it freely to
talk about the different roles of premisses within the various forms
of reasoning.

One other thing, I often use the equivalent notations:

   (A)  =  ~A  =  A'  =  Not A.

Among other things, this gives the following equivalence:

   "A => B"  =  "(A (B))".

OK, I think that will be enough of a set up to get this going.

| Data:
|
| Alternative Facts:  (C (A)) versus  ( C ((A))), that is, (C  A)
| Alternative Cases:  (C (B)) versus  ( C ((B))), that is, (C  B)
| Alternative Rules:  (B (A)) versus  ((B)((A))), that is, (A (B))

We have the surprising Fact C => (A), represented by the line segment (A)C.
The reason that this Fact is surprising is that we automatically expected
a different Fact, namely, C => A.  And, assuming the current situation C,
which we always do -- since this whole intervention of C is just a gimmick
for supplying a pivot to our thought -- we were led moreover to expect A,
the arrival of the bus.

If we stop to think about it, we realize that there is a middle term that
we have been taking for granted, say B, the benign situation, the best case
scenario (assuming that the best case means catching the bus), or perhaps
the modal, normal, ordinary, or usual case, if you like those terms better.

The name "reflection" seems to fit the process by which we can become aware
of the previously automatic, implicit, and probably unconscious deduction
that led to a current expectation, the one that is subject to conflict with
a current observation, thereby generating a dilemma, a problem, or a surprise.

Nota Bene.  Actually, I use the word "problem" more specifically
to refer to a difference between an intention and an observation,
but that is another, yet related story.

In the process of reflecting on the "program" of a habitual deduction, we become
able to identify the intermediate and the middle terms that go "into it", and at
this point we become able to contemplate their deliberate variation.  In this way,
we pass from the class of propositions that are schematized by "B" to one or two
in the class of propositions that are summarized by "~B", thereby guessing a new
Case, for example, that the current situation has the marks of a public holiday,
or C => H, where H => ~B, and is thus not beneficial for our immediate purposes.

Jon Awbrey

26 Jul 2001 • 16:56 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 26 Jul 2001 16:56:28 -0400
From: Jon Awbrey
  To: Howard Pattee
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

We seem to be about the business of marking explicitly what's given implicitly.
But is it a mark against our ephemeris that celestial bodies do not consult it
for their itineraries, nor have the eyes in their orbs to read our fine prints,
that the planets are enlightened by the sun on their courses and their destiny
by some adumbration other than differential equations in plain black and white?

Just an initial impression that comes to mind.
I am still working my way through the rest
of the issues that you are raising here.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP quoting AE:

| The whole of science is nothing more than a refinement of everyday thinking.
| It is for this reason that the critical thinking of the physicist cannot
| possibly be restricted to the examination of concepts of his own special
| field.  He cannot proceed without considering critically a much more
| difficult problem, the problem of analyzing the nature of everyday
| thinking.
|
| Einstein, "Physics and Reality", 1936.

| What, precisely, is 'thinking'?  When, at the reception of sense impressions,
| memory-pictures emerge, this is not yet 'thinking'.  And when such pictures form
| series, each member of which calls forth another, this too is not 'thinking'.  When,
| however, a certain image turns up in many such series, then -- precisely through such
| return -- it becomes an ordering element for such a series, in that it connects series
| that are in themselves unconnected.  Such an element becomes an instrument, a concept.
| I think that the transition from free association or 'dreaming' to thinking is
| characterized by the more or less dominating role which the concept plays in it.
| It is by no means necessary that the concept must be connected with sensorily
| cognizable and reproducible sign (word);  but when this is the case,
| thinking becomes, by means of that fact, communicable.
|
| Einstein, "Autobiographical Notes", 1944.

HP: It is now generally accepted, by physicists at least, that the relation between
    sense impressions and such unifying concepts cannot be articulated by means of
    any method or logic, but arises as a type of aesthetic or "vague instinct that
    must be felt" (Poincare).  I don't "think" it's going to rain the logical way
    Dewey and Jon do.  I feel it's going to rain.

HP: As Polanyi ["Personal Knowledge"] expressed it:  "I believe that by now three things
    have been established beyond reasonable doubt:  the power of intellectual beauty to
    reveal truth about nature;  the vital importance of distinguishing this beauty from
    merely formal attractiveness, and the delicacy of the test between them, so difficult
    that it may baffle the most penetrating scientific minds."

HP: I have more confidence in empirical approaches to inquiry.
    The analytic Peircian pragmatic "canonical" approach that
    Jon describes is certainly closer to what we have been
    indoctrinated with in our western culture.  But that is
    not what actually goes on in the brain.  My conversion
    from the canonical approach evolved from teaching a course,
    "The Psychology of Problem Solving," over a period of 25 years.
    There is now much empirical evidence of how inquiry actually takes
    place from many quarters:

HP: (1) the introspection of creative scientists [e.g., Hadamard,
        'The Psychology of Invention in the Mathematical Field', Polanyi,
        'Personal Knowledge', Ghiselin, 'The Creative Process',  Miller,
        'Imagery in Scientific Thought', Lakatos, 'History of Science and
        its Rational Reconstructions', Feyerabend, 'Against Method', etc.],

HP: (2) the more recent models of distributed, concurrent networks and evolved behavior --
        including agent-based approaches to artificial life and artificial intelligence [e.g.,
        Brooks, 'Cambrian Intelligence', Hinton and Sejnowski, eds., 'Unsupervised Learning',
        Arkins, 'Behavior-Based Robotics', Mitchell, 'An Introduction to Genetic Algorithms', etc.],

HP: (3) on empirical knowledge of how brains actually integrate their evolved
        instincts, senses, and individual experiences [e.g., Abbott and Sejnowski, eds.,
        'Neural Codes and Distributed Representations', Rugg, ed., 'Cognitive Neuroscience'].

HP: What is now evident is that by the time we are using words and logics of any type
    where thinking is explicit and communicable, we are no longer in the creative mode in
    which images and concepts emerge from our instincts, memories, and sense impressions.
    Furthermore, the creative mode is by its nature a sub-symbolic mode, or more precisely,
    a sub-thinking mode.  (Whether it is still explicit enough to be called symbolic or
    a sign activity is only a matter of definition.)  The brain's activities in even the
    simplest pattern recognition or one-bit decision involves hundreds of millions of
    neurons in which instinct, memory, models, and sensory inputs are concurrently
    seeking some  kind of metastability.  This network dynamic activity is so
    complex, diffused, and delicate that any attempt to impose rules, methods,
    and logic would only disturb and limit the emergence of novel ideas.

JA: In the pragmatic way of thinking everything has a purpose,
    and the purpose of each thing is the first thing we should
    try to note about it.  The purpose of inquiry is to reduce
    doubt and lead to a state of belief, which a person in that
    state will usually call knowledge or certainty.

HP: This is not the case for many physicists.  The purpose of models is to reduce ambiguity,
    not doubt.  Doubt should always be a dominant emotion since it is the primary check
    against overenthusiasm and error.  The state of "belief" is especially dangerous,
    since no model is complete, and very likely will be replaced.  Belief is for the
    religious.  What physicists seek first in their models is clarity, elegance,
    and empirical decidability.

JA: For our present purposes, the first feature to note in
    distinguishing these modes of reasoning is whether they
    are exact or approximate in character.  Deduction is the
    only type of reasoning that can be made exact, always
    deriving true conclusions from true premisses, while
    induction and abduction are unavoidably approximate
    in their mode of operation, involving elements of
    fallible judgment and inescapable error in their
    application.

HP: Paraphrasing Einstein:
    Insofar as deductive reasoning ("the propositions of mathematics")
    is exact ("certain") it does not apply to reality;  and insofar
    as it applies to reality it is not exact ("certain").

JA: Abductive reasoning is the mode of operation which is involved
    in shifting from one paradigm to another.  In order to reduce
    the overall tension of uncertainty in a knowledge base, it is
    often necessary to restructure our perspective on the data in
    radical ways, to change the channel that parcels out information
    to us.  But the true value of a new paradigm is typically not
    appreciated from the standpoint of another model, that is, not
    until it has had time to reorganize the knowledge base in ways
    that demonstrate clear advantages to the community of inquiry
    concerned.

HP: Abduction, as I understand it, is not reasoning.  It is sub-rational, and I would
    say sub-symbolic.  Computers lack the knowledge base acquired from 4 billion years
    of surviving in a complex environment as well as the vast distributed network, senses,
    and body actions necessary to efficiently integrate this mass of experience.  Most of
    this was acquired by natural selection and integrated into our metabolism, hormonal
    and motor controls, senses, pattern recognition, perceptions, motivations, brains,
    thoughts, imagination -- the whole organism.  It's not likely we can pull this off
    in silicon except for simple, closed domains.

26 Jul 2001 • 18:32 • Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry
Date: Thu, 26 Jul 2001 18:32:50 -0400
From: Jon Awbrey
  To: Arisbe, Organization Complexity Autonomy
  CC: Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):
 
JA: I would like to try to start a thread about this thing
    that many people call "inquiry", which I think of as a strategic way of
    talking about "scientific method", without getting into, at first, at
    least, the issue of whether there really is such a "method", but also as a
    way of including all of those less formalized ways that everyday reasoning
    manages to take us from highly confused and uncertain states of mind about
    some problem or question to states of mind that are slightly more clear and
    settled, at least enough to be capable of engaging in competent courses of
    action with regard to the issues in question.

SS: This process I call development.

JA: That sounds bound to confound biologist and psychologist alike, but if
    you wished to retro-sociate to "research" then it might be apt enough to
    slip by cerber and sensor alike.

SS: Not only them, but economists too.  I am developing a general theory of development,
    applicable to all material systems because it is cast in very general (thermodynamic,
    information theoretic) terms.  The canonical mode of development is from more vague
    to more definite;  from hot to cool.

JA: How is this relevant to ontology?  Well, because you might say
    that inquiry is the process by which ontologies come into being.

SS: In a process of construction.

JA: Loose or Strict?

SS: Both

So it can have the sense of "construal", that is, "interpretation"?

JA: My design recommendation, therefore, is that we should remember
    to give the system for managing ontologies a "built in" facility
    for inquiry -- at least, to make it amenable to the overall drift
    and dynamics of inquiry, and better, to make it more fully capable
    of supporting continued inquiry on the parts of its human users.

SS: One way is to make the constructions vague to one degree or other,
    so that they can become more definite "in the long run"?

JA: Not sure. The words "general" and "vague" are a supple-mentary pair
    of "terms of art" in Peircean pragmatude, and so I will have to check
    whether we are using them to mean the same things.

SS: I do mean vague, and not general (which is an explicit model of
    vagueness constructed from instances that might have descended
    from the same vague precursor).  Of course, logicians take
    vagueness to be a problem.

SS: My attitude is that it is generative, and therefore of keen interest
    in understanding the world.  Unfortunately, a result of this disdain
    by logicians is that there is hardly a logic of vagueness, which Peirce
    slightly pointed to.  Fuzziness is is partly OK, but the sets are crisp.
    Second order fuzziness is better, but ...

Well, there is much discussation to be pondered here.
I am still not sure if we use "vaguity" the same way.
I will dig up some choice quotes from Peirce on this
so we can compare and contrast.  Roughly, "general"
is extensional while "vague" is intensional.  But
the fact that Peirce's pointers were slighted is
not to say that his pointers were slight, as you
will soon have the opportunity to see.

Jon Awbrey

26 Jul 2001 • 23:20 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 26 Jul 2001 23:20:12 -0400
From: Jon Awbrey
  To: Howard Pattee
  CC: Arisbe, Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: We seem to be about the business of marking explicitly what's given implicitly.
    But is it a mark against our ephemeris that celestial bodies do not consult it
    for their itineraries nor have the eyes in their orbs to read our fine prints,
    that the planets are enlightened by the sun on their courses and their destiny
    by some adumbration other than differential equations in plain black and white?

HP: To a pragmatist it is "true" that celestial bodies are not affected by our ephemerides,
    but in principle every experimental inquiry not only disturbs our brain but disturbs
    the universe.  That is why physicists are not pragmatists.  Whether it is a "mark
    against the measuring device that the electron consults" the slits and detectors
    is only a matter of how far you care to push the metaphor.

I do not know if it's fitting to make the poet serve as the exegete of his own poem,
but I know that it's a role that I enjoy on the order of having my proverbial teeth
pulled, and I always feel like it's doomed to be almost as successful as explaining
a joke, but then again, did I ever let the sheerest obstruction of futility stop me?

The point that I am trying to make is one about the status of our graven models.
All I am saying is that the world of signs is here to stay, at least so long as
we are storing our mind by means of our accounts and our keeping book on nature.

There is indeed a metaphor that prevails on this scene that I am trying to sketch,
but it's not the simile that appears to be presently preveiling on your view, and
perhaps because the one I mean is far more literal in one dimension and away more
fingoral in other dimensions than any you would hypothesize me willing to pretend.

So it scarcely disturbs my image of the scene if there be a residual perturbation
twixt the writing of what we wot to write and the writhing of what we know wot of.
Indeed, I quite literarily thrive on it.  No, I mean quite literally, if only for
the nonce and the novelty of it, that the stars do not need to read the mail that
star fanatics write to each other just to know how to act like the stars they are.

HP: As I emphasize in my view of inquiry, when you get to the "fine print" and
    equations-of-motion stage not much of importance (for a theory of inquiry)
    is going on (only storage, communication, and maybe prediction).

I am going to let you pause and reflect on that one.

HP: It's what's happening implicitly in our brain when we are imagining
    how we want to interact with the universe (i.e., make measurements),
    and what's happening implicitly in the measurement process itself
    that we can't clearly articulate.

Many Regards,

Jon Awbrey

27 Jul 2001 • 00:00 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Fri, 27 Jul 2001 00:00:00 -0400
From: Jon Awbrey
  To: W.M. Jaworski, Paul Prueitt
  CC: Arisbe, Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj:  Re: Theory of Inquiry, Types of Inference, Missing the Bus
Date:  Fri, 18 May 2001 16:56:28 -0400
From:  Jon Awbrey
  To:  Arisbe, SemioCom, Standard Upper Ontology
  CC:  Cathy Legg, David Low, Arien Malec,
       John F Sowa, David Whitten

Inquiry SIG,

Here is the next installment in my analysis
of Cathy Legg's "Missing the Bus" paradigma.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 3

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: Theory of Inquiry
Date: Tue, 02 May 2000 12:40:12 -0400
From: Jon Awbrey
  To: Peirce List

Cathy,

This is part three in my syllogistic or "propositional constraint reasoning" (PCR)
analysis of your "Missing the Bus" problem.  I quote your original statement for
the sake of our fellow travellers who are just now arriving at the bus stop.

| I guess I'm having trouble getting my head around how induction
| could play this sort of role, given that abductions arise when
| a phenomenon appears surprising and irregular.  Would this be
| a possible example -- I'm waiting for my morning bus and it
| doesn't arrive:  surprise.  I then think -- in the past
| sometimes my bus hasn't arrived when it's a public holiday
| I've forgotten about:  this case should be the same (induction),
| I then form the hypothesis that it is a public holiday (abduction).

I left off last time at the point where you were just beginning to
contemplate the possibility that your current situation might fall
under the case description of a public holiday, thereby explaining
the absence of the expected bus, and a hypothesis which, if true,
would reduce your affective sense of surprise at the accustomed
bus not being there at the place time that you were accustomed
to observe it.

Now, if you're like me, you might eventually think to look up,
and then to look around your surrounding neighborhood, to see
if you can observe any further evidence or any other naturally
occurring signs that might bear on your new hypothesis one way
or another.

This, of course, brings us to the deductive phase of our present inquiry.
And, equally of course, our immedately present phase of deduction must be
distinguished from all of those previous deductions, not to mention their
Promethean and Epimethean (fore and aft) bracketings by all of those previous
bits of abductive and inductive reasoning that went to make up what were no doubt
many previous cycles, and a multitude of parallel cycles, and a countless array
of epicycles upon our deferents to an inquiry that may be indefinitely deferred.

Well, after that importunate word from our spontaneity,
I think that it is due time to get back to our story.
We've all been waiting for this bus long enough!

I hope you will excuse me if I import a bit of my local color
and project it on your local situation -- what is the spatial
analogue of "anachronism"? -- since I do not know all of your
public holidays, nor even whether the ones we are likely to
share in common are celebrated on precisely the same dates.

But if I had been on a residential street here, through most of last week,
when this "missing of the bus" caper was alleged to have happened, I could
have looked up and looked around and seen all of the gaily colored balloons,
the flapping ribbons, and the many other festive decorations that were put out
on the houses and the trees by all of the neighborhood parents who were throwing
together to treat their collective broods to an Easter Egg Hunt.  So that would
have served to confirm the hypothesis of a holiday, more or less, and perhaps
it may even have altered my sense of what was "best", "benign", "beneficial":
trudging off on my accustomed way, in pursuit of my habitual goal, or else
stopping to enjoy the signs of another custom, and even to follow them   
but that is another story altogether!

Anyway, it behooves me to try to size up the present situation of inquiry.
Let me unfold the map again, and make a few additional notations upon it.

|   A      D                                                   (A)
|    o      o                                                  o
|     \                                                       /
|      \ *     *                                           * /
|       \                                                   /
|        \  *     *                                     *  /
|         \                                               /
|          \   *     *                               *   /
|           \                                           /
|            \    *     *                         *    /
|             \                                       /
|              \     *     *                   *     /
|               \                                   /
|                \      *     *             *      /
|                 \                               /
|                  \       B     *      (B)      /
|                   \                           /
|                    \      *       *   *      /
|                     \                       /
|                      \     *         H     /
|                       \                   /
|                        \    *       *    /
|                         \               /
|                          \   *     *   /
|                           \           /
|                            \  *   *  /
|                             \       /
|                              \ * * /
|                               \   /
|                                \*/
|                                 o
|                                 C
|
| Figure 2.  Missing the Bus, Again
|
| A  =  Arriving bus situations,
| B  =  Best case situations,
| C  =  Current situation,
| D  =  Decoration situations,
| H  =  Holiday situations.

I think that this pretty graphically says what I've been striving to say
in the last thousand words or so, and I am tempted to leave it at that,
but temptations to desist, you will have observed, are the sorts of
temptations I can easily resist!  So let me attempt to sum it up
all over again, this time once again in schematic symbols and
in more verbose but descriptive phrases.

Abduction of a Case:

Fact:     C => (A),     In the current situation, the bus is not arriving.
Rule:     H => (A),     If it is a holiday, the bus would not be arriving.
-----------------------------------------------------------------------------
Case:     C =>  H ,     Perhaps the current situation is a holiday.

Once again, the validity of this abduction as a form of reasoning, in the only way
that its form of non-demonstrative inference can be said to be valid, depends on the
validity of the corresponding deduction, from Case C=>H and Rule H=>~A to Fact C=>~A.
And it needs to be remembered that the utility of this deduction, which only concludes
what has already been observed, is that it reduces the surprise of that observation.

Deduction of a Fact:

Case:     C => H ,     In the current situation, it is a holiday.
Rule:     H => D ,     If it is a holiday, there will be decorations.
-----------------------------------------------------------------------------
Fact:     C => D ,     In the current situation, there will be decorations.

The inductive phase, in this situation, consists of looking up and testing
whether the prediction is observed.  I have been studying for few years now,
and still remain a bit puzzled, as to how exactly this meaning of induction
fits in logically, if it does at all, with the other meaning of induction,
namely, of a non-demonstrative inference from a Case and a Fact to a Rule.

And that is just about where I came in,
And that is just about where I go out,

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Inquiry SIG,

I will have to wait for the appropriate permissions from
my fellow non-travellers before I can reveal the further
non-adventures of our earnest non-pilgrims to the public.

Perhaps we ought to occupy the meantime by returning to
our consideration of the sort of occasion that prompted
me to recall this non-epic story, namely the visitation
of that avatar of entropy, that embodiment of confusion,
that mythical end-user, upon the site of David's office:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JS:  Your observation is falsified by every SQL database in the world.
     The facts are in the DB, which any authorized user is allowed to
     update.  The definitions and constraints are stored separately,
     and only the DB administrator is allowed to modify them.  There
     is a major difference in the ease of modifying the two kinds of
     assertions.

JA:  Here's a chance for me to ask some of my favorite questions again:

     1.  a.  What forms of reasoning are involved in the decision of
             a DBA [or a KBA] to create, modify, remove a concept
             [in/of/from] the conceptual base?

         b.  Can these putative forms of reasoning
             be computationally formalized?

DW:  I'm not John, but if I as a DBA might answer:

DW:  I don't create, modify, or remove a concept [in/of/from] a conceptual base.

JA:  I was trying to be concise for a change, the price of which
     is that I had to try and paint this image of changing bases
     in very broad brush stokes indeed.  See my amendments above.
     You may well speculate on how I decided what amends to make.

JA:  It may serve a little to think of a Deductive Data Base or a Knowledge Base,
     but really all I have in mind here is any sort of significant restructuring.

DW:  I create, modify, or remove
     a field/column/data-element
     from a file/table/structure.

JA:  Now, if you really think about it, a table is like a concept,
     namely, a concept of some relation that you find to be of use.
     Think about the way a medical research database changes when
     somebody hypothesizes a new disease entity, starts to keep
     tabs on its signs, symptoms, test results, mortality data,
     and then either confirms or discards the notion.

DW:  Some of those fields/columns/data-elements represent
     concepts or groups of concepts.  Some do not.

JA:  You hadda go and make me say it:
     "Everything is just a concept".
     (Sorta).

DW:  I usually recognize that someone has a need/concept that is not being
     adequately represented by the existing database so I need to change it.
     If intent can be computationally formalized, then the reasoning should
     be capable of being computationally formalized.

DW:  Most systems don't have any representation of intent.
     A barely adequate one might have intent represented in
     a user help manual.  A system that integrates its help
     system with the actual working of the program is very
     rare.  In some better cases, the help system is only
     text associated with the operations being performed
     so that context sensitive help may be provided.

     2.  a.  What entropic pressures or informational tensions
             determine a decision to introduce, modify, delete
             concepts, symbols, terms to/in/from the manifold
             of those already present in the system?

         b.  Can these pressures or tensions be localized and measured?

DW:  Do you include an end-user dropping by my office with
     a confused look on their face as an entropic pressure?

JA:  Good example.  Now tell me, why are they confused?
     What is confusion, anyway?  Now that I mention it,
     how did I get so confused about what confusion is?

JA:  Serially now, folks, entropy is just a measure on
     a distribution, say, a distribution of things you
     might choose from as being true, or as being good
     things to do if & when you do decide what is true.

^                        ^                        ^
|                        |                        |
o                        o--------o               o        o--------o
|                        |        |               |        |        |
|                        |        |               |        |        |
|                        |        |               |        |        |
o-----------------o      o        |               o        |        |
|                 |      |        |               |        |        |
|                 |      |        |               |        |        |
|                 |      |        |               |        |        |
o--------o--------o      o--------o--------o      o--------o--------o
  Thing1   Thing2          Thing1   Thing2          Thing1   Thing2

 High Entropy Case        Low Entropy Case 1       Low Entropy Case 2

JA:  So high entropy, or high uncertainty, means that you do not know much
     about what is true or what to do in the question of Thing1 and Thing2.
     It really does not matter if it is categorical goo or imperative stew,
     when you are confused, it really does not matter all that much to you.

DW:  What about an error-report on the system exceptions log?

DW:  What about a failure description generated by
     an internal consistency check program?

DW:  and what is the manifold of my data base system?
     is this like the manifold of math?
     or the manifold of a car?

JA:  I Know But I Kant Tell You.

DW:  Are you talking about localizing and measuring
     the decisions or the tensions and pressures?
     Or are you talking about local-izing in some
     physical sense?  or just localized in some
     conceptual cluster?

JA:  It's an essay question.
     You get to use your imagination.
     Give me time to make something up.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Now, what do all of these "moments of inquiry" (MOI?) have in common?
Painted in very broad strokes, we can discern two very rough species:

1.  The "Problem" situation, very sketchily characterized as a discrepancy
    between a situation that one Intends and a situation that one Observes.

2.  The "Surprise" situation, very sketchily characterized as a difference
    between a situation that one Expects and a situation that one Observes.

And thereby hangs a tale --
An epic tale if any tale is.

Jon Awbrey

27 Jul 2001 • 10:54 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Fri, 27 Jul 2001 10:54:35 -0400
From: Jon Awbrey
  To: W.M. Jaworski
  CC: Arisbe, Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

W.M. Jaworski wrote:
> 
> JA:
> |   A      D                                                   (A)
> |    o      o                                                  o
> |     \                                                       /
> |      \ *     *                                           * /
> |       \                                                   /
> |        \  *     *                                     *  /
> |         \                                               /
> |          \   *     *                               *   /
> |           \                                           /
> |            \    *     *                         *    /
> |             \                                       /
> |              \     *     *                   *     /
> |               \                                   /
> |                \      *     *             *      /
> |                 \                               /
> |                  \       B     *      (B)      /
> |                   \                           /
> |                    \      *       *   *      /
> |                     \                       /
> |                      \     *         H     /
> |                       \                   /
> |                        \    *       *    /
> |                         \               /
> |                          \   *     *   /
> |                           \           /
> |                            \  *   *  /
> |                             \       /
> |                              \ * * /
> |                               \   /
> |                                \*/
> |                                 o
> |                                 C
> |
> | Figure 2.  Missing the Bus, Again
> |
> | A  =  Arriving bus situations,
> | B  =  Best case situations,
> | C  =  Current situation,
> | D  =  Decoration situations,
> 
> wmj: Nice picture.
>      Would state machine graph carry more information?
>      You could 'overload' states/nodes ('situations')
>      and edges/transitions with attributes.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

WM(?),

These are this stick-figure versions of my long-time (coming? gone?)
project to integrate logic and information theory, which, like all my
best ideas, I later discovered had "already been chewed" (ABC'd) by CSP,
who lectured on this topic that he called "Information Theory" at Harvard,
in 1865!  Oh, Per Via, a recent reading of John Collier's draft article
on "Information" for the Stanford Encyclopedia of Philosophy is tempting
me to start using his moniker of "distinction theory" for the whole shebang,
which, of course, has its echoes of Spencer-Brown's 'Laws of Form' (LOF).

http://www.newcastle.edu.au/department/pl/Staff/JohnCollier/information/information.html

It shall be soon enough, once we get this scaffold built,
to start insistine on color schemes to paint the ceiling.

Jon Awbrey

27 Jul 2001 • 14:08 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Fri, 27 Jul 2001 14:08:56 -0400
From: Jon Awbrey
  To: W.M. Jaworski
  CC: Arisbe, Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Jon Awbrey wrote:
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> W.M. Jaworski wrote:
> >
> > JA:
> > |   A      D                                                   (A)
> > |    o      o                                                  o
> > |     \                                                       /
> > |      \ *     *                                           * /
> > |       \                                                   /
> > |        \  *     *                                     *  /
> > |         \                                               /
> > |          \   *     *                               *   /
> > |           \                                           /
> > |            \    *     *                         *    /
> > |             \                                       /
> > |              \     *     *                   *     /
> > |               \                                   /
> > |                \      *     *             *      /
> > |                 \                               /
> > |                  \       B     *      (B)      /
> > |                   \                           /
> > |                    \      *       *   *      /
> > |                     \                       /
> > |                      \     *         H     /
> > |                       \                   /
> > |                        \    *       *    /
> > |                         \               /
> > |                          \   *     *   /
> > |                           \           /
> > |                            \  *   *  /
> > |                             \       /
> > |                              \ * * /
> > |                               \   /
> > |                                \*/
> > |                                 o
> > |                                 C
> > |
> > | Figure 2.  Missing the Bus, Again
> > |
> > | A  =  Arriving bus situations,
> > | B  =  Best case situations,
> > | C  =  Current situation,
> > | D  =  Decoration situations,
> >
> > wmj: Nice picture.
> >      Would state machine graph carry more information?
> >      You could 'overload' states/nodes ('situations')
> >      and edges/transitions with attributes.
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> WM(?),
> 
> These are the stick-figure versions of my long-time (coming? gone?)
> project to integrate logic and information theory, which, like all my
> best ideas, I later discovered had "already been chewed" (ABC'd) by CSP,
> who lectured on this topic that he called "Information Theory" at Harvard,
> in 1865!  Oh, Per Via, a recent reading of John Collier's draft article
> on "Information" for the Stanford Encyclopedia of Philosophy is tempting
> me to start using his moniker of "distinction theory" for the whole shebang,
> which, of course, has its echoes of Spencer-Brown's 'Laws of Form' (LOF).
> 
> http://www.newcastle.edu.au/department/pl/Staff/JohnCollier/information/information.html
> 
> It shall be soon enough, once we get this scaffold built,
> to start insistine on color schemes to paint the ceiling.
> 
> Jon Awbrey
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

On Second Thought (I'm a Peircean, I get three),
while you're waiting for the tour bus you might
want to flip through a few of these old touring
guides and travel brochures:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Analytic Differential Ontology (ADO)

http://suo.ieee.org/ontology/msg00072.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Differential Analytic Turing Automata (DATA)

http://suo.ieee.org/email/msg03004.html
http://suo.ieee.org/email/msg03026.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Shroud of Turing (SOT)

http://suo.ieee.org/email/msg02714.html
http://suo.ieee.org/ontology/msg00308.html
http://www.virtual-earth.de/CG/cg-list/msg03669.html
http://www.virtual-earth.de/CG/cg-list/msg03677.html
http://stderr.org/pipermail/arisbe/2001-January/000167.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Here's the nub'o't.

A 'finite automaton' (FA -- "alonglongwaytorun") can always and rather facilely
be transposed into the key of a single proposition in ZOL, which lends its airs
to be not only played and appreciated but through-de-com-posed by whatchamacall
a "propositional constraint reasoner" (PCR), if a bit preversely to confound by
its zound the recombinant d'n'alogist again.  But once it hast been transcribed
into a score of such a genre, all sorts of generalizations on the theme and all
mannerisms of vastening variations now open up efore the mind's ear and virtual
audacity of listening possibilities.  To the likes of wot all I will recur anon.

Many Earguards,

Jon Awbrey

Incidental Musement:

http://www.stratfordfestival.ca/2001/playbill/soundofmusic.html

27 Jul 2001 • 22:50 • Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Inquiry
Date: Fri, 27 Jul 2001 22:50:49 -0400
From: Jon Awbrey
  To: Arisbe, Organization Complexity Autonomy
  CC: SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

SS: This process [of inquiry] I call development.

JA: That sounds bound to confound biologist and psychologist alike,
    but if you wished to retro-sociate to "research" then it might
    be apt enough to slip by cerber and sensor alike.

SS: Not only them, but economists too. I am developing a general theory of development,
    applicable to all material systems because it is cast in very general (thermodynamic,
    information theoretic) terms.  The canonical mode of development is from more vague
    to more definite;  from hot to cool.

I have occasionally used the term "differentiation" for this process:

| What is inquiry and how is it related to the theory of signs? 
|
| We examine the structure of inquiry as articulated by Peirce and Dewey.  In this model,
| inquiry begins with a surprising phenomenon or a problematic situation.  Whether felt as
| pleasant wonderment or as painful bewilderment, we feel driven to some activity that will
| return us to our prior equilibrium.  This may issue in a search for explanation that reduces
| the surprise or for a plan of action that resolves the problem.  The ensuing activities share
| a common form, the differentiation of a pattern.  In our consternation, we recognize a variety
| of features, some of which can be varied as part of our capacity for free choice.  The problem
| or surprise is present because of its difference from something.  As a surprise, what happens
| is different from what we habitually expect.  As a problem, what happens is different from
| what we hopefully intend.  To change the systematic expectation against which background
| a surprising phenomenon originally figured, we must discover some freedom to change what
| generated that expectation, and so to modify our personal model of the world.
|
| Jon Awbrey & Susan Awbrey,
|"Interpretation as Action: The Risk of Inquiry",
|'Inquiry: Critical Thinking Across the Disciplines",
| Volume 15, Number 1 (Autumn 1995), Pages 40-52.
|
| http://www.chss.montclair.edu/inquiry/fall95/awbrey.html

JA: How is this relevant to ontology?  Well, because you might say
    that inquiry is the process by which ontologies come into being.

SS: Just so, and how they become stabilized as well (in senescence --
    from which they can be readily perturbed).

SS: In a process of construction.

JA: Loose or Strict?

SS: Both

JA: So it can have the sense of "construal", that is, "interpretation"?

SS: Yes, as in the social construction of knowledge.

Copacetic!

SS: My attitude is that [vagueness] is generative, and
    therefore of keen interest in understanding the world.
    Unfortunately, a result of this disdain by logicians is
    that there is hardly a logic of vagueness, which Peirce
    slightly pointed to.  Fuzziness is  partly OK, but the
    sets are crisp.  Second order fuzziness is better, but ...

JA: Well, there is much discussation to be pondered here.
    I am still not sure if we use "vaguity" the same way.
    I will dig up some choice quotes from Peirce on this
    so we can compare and contrast.  Roughly, "general"
    is extensional while "vague" is intensional.

SS: An interesting point.  This allows 'vague' to be generative
    by incorporating more descriptors into its sentence as further
    and further qualifiers.  In contrast, 'general' can but extend
    its hegemony.

Yes, I think so, at least, provisionally.  It was with (lack of exhaustive) respect
to these dual notions, dichotomies and dualities being anathematic to Peirce, and so
with trying to compound their synthesis or to discern their tertium quid that Peirce
first came to the shores of what he named the "Theory of Information" (TOI), around
about 1865, by the evidence of his Harvard University and Lowell Institute Lectures.

More To Come ...

Jon Awbrey

28 Jul 2001 • 01:23 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sat, 28 Jul 2001 01:23:00 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology,
      Topic Map Mail, W.M. Jaworski

o~~~~~~~~~o~~~~~~~~~o~~~~~~ARCHIVE~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Theory of Inquiry, Types of Inference, Types of Signs
Date: Sun, 20 May 2001 00:08:01 -0400
From: Jon Awbrey
  To: Arisbe, SemioCom, Standard Upper Ontology
  CC: Cathy Legg, David Low, Arien Malec,
      Jean-Marc Orliaguet, John F Sowa,
      David Whitten

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Theory of Inquiry, Types of Inference, Types of Signs

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Inquiry SIG,

This continues the series of discussions that arose
in the Peirce Forum last year, as I recall, incited
by some complimentary remarks that Chomsky makes in
connection with discussing hypothesis formation and
Peirce's problem of "giving a rule to abduction".

In this episode, the three-way connection among Peirce's
Three Categories, the Three Types of Inference, and the
Three Types of Signs engaged the attention of the party.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 4

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: Arguments and the Categories
Date: Thu, 11 May 2000 01:30:01 -0400
From: Jon Awbrey
  To: Peirce List

Arien Malec wrote:

AM:  In being forced, by Jean-Marc's helpful criticism, to defend my
     incidental description of abduction as corresponding to iconicity,
     I have taken a closer look at what Peirce has to say about the
     relationship between the categories in the only place, so far
     as I know, in the CP were Peirce discusses the relationship:
     the Minute Logic (ripped and scattered throughout the CP,
     but the directly relevant sections form the first part
     of the second volume of the CP, and especially 2.95-97).
     It would be relevant and important to the discussions
     relating arguments and the categories to present what
     Peirce has to say about them.  To the extent possible,
     this is a presentation, summarization, and interpretation
     of what Peirce himself has to say, rather than an exposition
     of my own views on the matter.

David Low wrote:

DL:  Another place to look is in MS 312 (1903), published in Ann Turrisi's
     'Pragmatism as a Principle and Method of Right Reasoning'.  A passage
     of special interest is on p.276 where Peirce says:

     | And as to the connection between the three categories and the
     | three modes of inference ... Abduction, or the suggestion of
     | an explanatory theory, is inference though an Icon, and is
     | thus connected with Firstness;  Induction, or trying how
     | things will act, is inference through an Index, and is
     | thus connected with Secondness;  Deduction, or
     | recognition of the relations of general ideas,
     | is inference through a Symbol, and is thus
     | connected with Thirdness.

DL:  This, it seems to me, reaffirms his opinion of 1867 (CP 1.559):

     | In an argument, the premisses form a representation of the
     | conclusion, because they indicate the interpretant of the
     | argument, or representation representing it to represent
     | its object.  The premisses may afford a likeness, index,
     | or symbol of the conclusion.  In deductive argument, the
     | conclusion is represented by the premisses as by a general
     | sign under which it is contained.  In hypotheses, something
     | like the conclusion is proved, that is, the premisses form a
     | likeness of the conclusion.  Take for example, the following
     | argument:
     |
     | M is, for instance, p1, p2, p3, and p4;
     | S is p1, p2, p3, and p4:
     | Therefore S is M.
     |
     | Here the first premiss amounts to this, that 'p1, p2, p3, and p4'
     | is a likeness of M, and thus the premisses are or represent a
     | likeness of the conclusion.  That it is different with induction
     | another example will show.
     |
     | s1, s2, s3, and s4 are taken as samples of the collection M;
     | s1, s2, s3, and s4 are P:
     | Therefore All M is P.
     |
     | Hence the first premiss amounts to saying that
     | 's1, s2, s3, and s4' is an index of M.  Hence
     | the premisses are an index of the conclusion.

DL:  There is also a passage in MS 315 (1903) that is pertinent:

     | I have already explained to you briefly what these three
     | modes of inference, Deduction, Induction, and Abduction
     | are.  I ought to say that when I described induction
     | as the experimental testing of a hypothesis, I was
     | not thinking of  experimentation in the narrow sense
     | in which it is confined to cases in which we ourselves
     | deliberately create the peculiar conditions under which we
     | desire to study a phenomenon.  I mean to extend it to every
     | case in which, having ascertained by deduction that a theory
     | would lead us to anticipate under certain circumstances phenomena
     | contrary to what we should expect if the theory were 'not' true,
     | we examine the cases of that sort to see how far those predictions
     | are borne out.  (p. 249).

DL:  In this extended sense of induction, Peirce says we can still
     be reasoning retroductively (cf. CP 8.231), and thus we would
     have the assurance of an icon.  If we return to the phenomena
     and then find how nearly the consequences agree with the actual
     facts, we then move to induction (cf. CP 8.233).  So, a part of
     the process of arriving at the hypothesis to be tested against
     the external is first, precision, then dissociation, then
     discrimination (e.g., MS 645).  These stages, Peirce says,
     take place before phenomenological enquiry, but if we were
     to apply the categories to these prephenomenological, or perhaps
     I should say 'mathematical' stages, I think precision would have
     the assurance of an icon, dissociation the assurance of an index,
     and discrimination the assurance of a symbol.  Note, however, that
     the inductive stage of the prephenomenological investigation is not
     tested against the phenomenological world, thus the logic of abduction
     cannot interfere with or limit the phenomenological logic of induction.

DL:  This thread began with Chomsky I recall, and I suppose from
     the little I know about what he said that I would agree that
     the number of possible permutations in language are infinite,
     but that is true only until we bump the prephenomenological
     up against the phenomenological.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

David,

Allow me to diagram some of these forms of arguments, so that everybody can
plainly see some of the reasons why Peirce says a few of the things he does.

Abduction to a Case:

    M is, for instance, P^1, P^2, P^3, and P^4;
    S is P^1, P^2, P^3, and P^4:
    Therefore S is M.

    Here the first premiss amounts to this,
    that "P^1, P^2, P^3, and P^4" is a likeness of M,
    and thus the premisses are or represent a likeness
    of the conclusion.

Peirce's analysis of this pattern of abductive argument
can be understood according to the following paraphrase:

 Fact:  S => P^1,  S => P^2,  S => P^3,  S => P^4.
 Rule:  M => P^1,  M => P^2,  M => P^3,  M => P^4.
---------------------------------------------------
 Case:  S => M.

When X => each of A, B, C, D, ...
then X => the Greatest Lower Bound (GLB) of A, B, C, D, ..., which is to say,
then X => the Logical Conjunction, A & B & C & D, to give it a nickneme, "N",
then X => N.

Most succinctly, the argument can be summarized as follows:

Where N = P^1 & P^2 & P^3 & P^4:

 Fact:  S => N.
 Rule:  M => N.
----------------
 Case:  S => M.

In this abduction, it is the GLB or the Conjunction
of the ostensible predicates that is the operative
predicate of the argument, in other words, the one
that is common to both the Fact and the Rule.

Finally, the reason why one can say that N is an iconic sign
of the object M is that N can be taken to denote M by virtue
of the qualities that they share, namely, P^1, P^2, P^3, P^4.

The situation can be diagrammed as follows:

|                   P^1   P^2         P^3   P^4
|                    o     o           o     o
|                     \*    \         /    */|
|                      \ *   \       /   * / |
|                       \  *  \     /  *  /  |
|                        \   * \   / *   /   |
|                         \    *\ /*    /    |
|                          o     N     o     |
|                          |     | *   |     |
|                          |     |   * |     |
|                          |     |     |     |
|                          |     |     | *   |
|                          |     |     |   * |
|                          o     |     o     M
|                           \    |    /    *
|                            \   |   /   *
|                             \  |  /  *
|                              \ | / *
|                               \|/*
|                                o
|                                S
|
| Figure 3.  Abduction to the Case S => M

I will put off the example of Induction to a Rule until tommorrow,
as this requires a bit of extra work, mainly by way of digging up
the supplementary texts that are necessary to explain one or two
peculiarities of Peirce's language, as he was wont to use it in
the 1860's.

Until Then,

Jon Awbrey

28 Jul 2001 • 02:00 • Inquiry Into Inquiry

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Subj: OCA: Re: Inquiry Into Inquiry
Date: Sat, 28 Jul 2001 02:00:00 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology,
      Topic Map Mail, W.M. Jaworski

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Subj: Theory of Inquiry, Types of Inference, Types of Signs
Date: Sun, 20 May 2001 12:00:06 -0400
From: Jon Awbrey
  To: Arisbe, SemioCom, Standard Upper Ontology
  CC: Cathy Legg, David Low, Arien Malec,
      Jean-Marc Orliaguet, John F Sowa,
      David Whitten

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| "And hast thou slain the Jabberwock?
|  Come to my arms, my beamish boy!
|  O frabjous day! Callooh! Callay!"
| He chortled in his joy.
|
| Lewis Carroll (Charles Lutwidge Dodgson) "Jabberwocky" <<<---<<<
| http://www76.pair.com/keithlim/jabberwocky/poem/jabberwocky.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Inquiry SIG,

This completes, at least for a while, my retrospective account
of "What I Did Last Summer".  When it is said and done, I will
turn to elaborating its logical implications and its practical
consequences for the application that we have before us, given
e-special aptness and recursive reference to the criterion of
a "Body Electric Of Maintainable Ontology Software" (BEOMOS).

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 5

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Subj: Re: Arguments and the Categories
Date: Thu, 11 May 2000 14:04:08 -0400
From: Jon Awbrey
  To: Peirce List

For ease of reference, and to keep the analyses
of Abduction and Induction on the same page for
the purposes of comparison, I will repeat here
the fundamentals of what happened last time,
making just a couple of additional remarks,
and then moving on to the new material.

Abduction to a Case:

| M is, for instance, P^1, P^2, P^3, and P^4;
| S is P^1, P^2, P^3, and P^4:
| Therefore S is M.
|
| Here the first premiss amounts to this,
| that "P^1, P^2, P^3, and P^4" is a likeness of M,
| and thus the premisses are or represent a likeness
| of the conclusion.

Peirce's analysis of this pattern of abductive argument
can be understood according to the following paraphrase:

 Fact:  S => P^1,  S => P^2,  S => P^3,  S => P^4.
 Rule:  M => P^1,  M => P^2,  M => P^3,  M => P^4.
---------------------------------------------------
 Case:  S => M.

When X => each of A, B, C, D, ...
then X => the Greatest Lower Bound (GLB) of A, B, C, D, ..., which is to say,
then X => the Logical Conjunction, A & B & C & D, to give it a nickneme, "N",
then X => N.

Most succinctly, the argument can be summarized as follows:

Where N = P^1 & P^2 & P^3 & P^4:

 Fact:  S => N.
 Rule:  M => N.
----------------
 Case:  S => M.

In this piece of Abduction, it is the GLB or the Conjunction
of the ostensible Predicates that is the operative Predicate
of the Argument, to wit, the Predicate that is Common
to both the Fact and the Rule of the Inference.

Finally, the reason why one can say that N is an iconic sign
of the object M is that N can be taken to denote M by virtue
of the qualities that they share, namely, P^1, P^2, P^3, P^4. 

Notice that the iconic denotation is symmetric, at least in principle,
that is, icons are icons of each other as objects, at least potentially,
whether or not a particular interpretive agent is making use of their
full iconicity during a particular phase of semeiosis.

The situation is diagrammed in Figure 3.

|                   P^1   P^2         P^3   P^4
|                    o     o           o     o
|                     \*    \         /    */|
|                      \ *   \       /   * / |
|                       \  *  \     /  *  /  |
|                        \   * \   / *   /   |
|                         \    *\ /*    /    |
|                          o     N     o     |
|                          |     | *   |     |
|                          |     |   * |     |
|                          |     |     |     |
|                          |     |     | *   |
|                          |     |     |   * |
|                          o     |     o     M
|                           \    |    /    *
|                            \   |   /   *
|                             \  |  /  *
|                              \ | / *
|                               \|/*
|                                o
|                                S
|
| Figure 3.  Abduction to the Case S => M

In a diagram like this, even if one does not bother to
show all of the implicational or the subject-predicate
relationships by means of explicit lines, then one may
still assume the "transitive closure" of the relations
that are actually shown, along with any that are noted
in the text that accompanies it.

We pick up the story with the following episode of Induction.

Induction to a Rule:

| S^1, S^2, S^3, and S^4 are taken as samples of the collection M;
| S^1, S^2, S^3, and S^4 are P:
| Therefore All M is P.
|
| Hence the first premiss amounts to saying
| that "S^1, S^2, S^3, and S^4" is an index of M.
| Hence the premisses are an index of the conclusion.

As it happens, I think that I can explain what I just called a "peculiarity"
of Peirce's language here, simply by referring to our ordinary informal usage,
and this will save me the trouble of looking through his early writings, where
I recall seeing this usage before.  Remember, our common logical, mathematical,
and set-theoretic language of "unions" and "intersections" was not fully worked
out at this time (1860's), at least, not in all the glories or mirages, depending
on your point of view, of its current axiomatic treatment.  Of course, these old
folks had the concepts, more or less, but if I remember correctly from my first
encounter with Peirce's work -- and my memory is always a doubtful proposition
when I'm talking about three days, much less thirty years! -- Peirce was still
at this time, or soon to be, writing about "aggregations" and "compositions",
and these of two kinds, "absolute" and "relative", but the intuitive meanings
that were attached to the "absolute" or the "non-relative" variety of terms,
and bounded by their corresponding concepts and their rudimentary definitions,
were analogous to but not exactly identical to our modern notions of "unions"
and "intersections", that is, the set-theoretic operations that are associated
with the logical usage of "OR" and "AND", respectively.

So what you have to understand -- what all this preambling is leading up to --
is the following multiplicity of meaning in Peirce's usage at this point,
namely, that the "AND" in his account of Abduction and the "AND" in his
account of Induction are two different words, or tokens of the same
polymorphous sign, if you will, but with a diversity of meanings,
the first corresponding to conjunction and intersection, and the
second corresponding to disjunction and union.  And this is just
done in accord with a perfectly natural natural language idiom.

Now, if you will just try to remember the way that we often speak
in informal circumstances and in ordinary language -- I know, it
gets harder to remember all the time! -- but it is true that we
often use the word "AND", especially when referring to samples
of "dry goods", like handfuls of beans and bags of wool, to
speak of their more aggregarious union, and not so much,
since it barely makes sense in this setting, of their
contentious intersection.

Peirce's analysis of this pattern of inductive argument
can be understood according to the following paraphrase:

 Case:  S^1 => M,  S^2 => M,  S^3 => M,  S^4 => M.
 Fact:  S^1 => P,  S^2 => P,  S^3 => P,  S^4 => P.
---------------------------------------------------
 Rule:  M => P.

When X <= each of A, B, C, D, ...
then X <= the Least Upper Bound (LUB) of A, B, C, D, ..., which is to say,
then X <= the Logical Disjunction, A v B v C v D, to give it a nomen, "L",
then X <= L.

More succinctly, the argument can be summarized as follows:

Where L = S^1 v S^2 v S^3 v S^4:

 Case:  L => M.
 Fact:  L => P.
----------------
 Rule:  M => P.

In this bit of Induction, it is the LUB or the Disjunction
of the ostensible Subjects that is the operative Subject
of the Argument, to wit, the Subject that is Common
to both the Case and the Fact of the Inference.

Finally, the reason why one can say that L is an indexical sign
of the object M is that L can be taken to denote M by virtue of
the instances that they share, namely, S^1, S^2, S^3, S^4.

Notice that the indexical denotation is symmetric, at least in principle,
that is, indices are indices of each other as objects, at least potentially,
whether or not a particular interpretive agent is making use of their full
indiciality during a particular phase of semeiosis.

The situation is diagrammed in Figure 4.

                                 P
                                 o
                                /|\*
                               / | \ *
                              /  |  \  *
                             /   |   \   *
                            /    |    \    *
                           o     |     o     M
                           |     |     |   * |
                           |     |     | *   |
                           |     |     |     |
                           |     |   * |     |
                           |     | *   |     |
                           o     L     o     |
                          /    */ \*    \    |
                         /   * /   \ *   \   |
                        /  *  /     \  *  \  |
                       / *   /       \   * \ |
                      /*    /         \    *\|
                     o     o           o     o
                    S^1   S^2         S^3   S^4

Figure 4.  Induction to the Rule M => P

Now, depending on the architectronic principles and the basic parameters
of one's personal favorite framework for ontology, whether it is one of
the standard ones, for instance:  (1) yet another version of set theory,
(2) what the mathematicians, by waylay of an admitted theft of Kant and
even of Carnap, though as of yet an unconfessed theft of Peirce, are wont
to call "Category Theory", or (3) the exceptions that prove the rule, to wit,
any old or any new "Ontological Hierarchy" (OH), "Objective Framework" (OF),
or whatever "Form of Synthesis-Analysis" (FOSA) for pragmatic objects that
Ontogenies Recapitulating Phylogenies can rustle up from the grubstake of
even the slightest, all too human imagination, then the fearful symmetry
and the vertical revertigo of Abduction and Induction may or may not be
broken and stop right here.  For it does not hold in general, that is
to say, across every sort of ontology that might be conceived, that
the Anode (the way up) and the Cathode (the way down) lend their
lines of conduction and succession to be switched at will --
I am sure that you can imagine the dire consequences that
might ensue if one's brain and one's body were not wired
for that option!  But the matter of this concern is
a charge that I must defer to another time.

Jon Awbrey

P.S.  I feel like I ought to roll the credits about here,
      but the task of tracing back through this thread of
      inquiry, in order to enumerate all of the characters
      that are contributary to it, would certainly delay its
      release beyond the "must see" summer season!  So I will
      have to leave that scholarly duty to a moment of leisure
      and a calmer time, or else to some indefinitely ultimate,
      e-future, e-ventual, e-masochistic, e-telexial e-historian!
J.A.

28 Jul 2001 • 19:33 • Inquiry Into Inquiry

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Subj: OCA: Re: Inquiry Into Inquiry
Date: Sat, 28 Jul 2001 19:33:52 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy, SemioCom,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Joseph Ransdell wrote:
> 
> Jon Awbrey wrote:
> 
> > These are the stick-figure versions of my long-time (coming? gone?)
> > project to integrate logic and information theory, which, like all my
> > best ideas, I later discovered had "already been chewed" (ABC'd) by CSP,
> > who lectured on this topic that he called "Information Theory" at Harvard,
> > in 1865!  Oh, Per Via, a recent reading of John Collier's draft article
> > on "Information" for the Stanford Encyclopedia of Philosophy is tempting
> > me to start using his moniker of "distinction theory" for the whole shebang,
> > which, of course, has its echoes of Spencer-Brown's 'Laws of Form' (LOF).
> >
> > http://www.newcastle.edu.au/department/pl/Staff/JohnCollier/information/information.html
> 
> Peirce also did something which looks like an adumbration of the
> beginnings of an information theory in a published work in 1867,
> "Upon Logical Comprehension and Extension," treating information
> as breadth (or extension) times depth (or comprehension), then
> following that up with definitions of various logical conceptions
> (generalization, induction, abstraction, specification, supposition,
> determination, restriction, descent) in terms of increase or decrease
> of information, the whole thing being based on the 1867 category paper.
> Okay, so who reads the Proceedings of the American Academy of Arts and
> Sciences, where it originally appeared.  But it has been readily available
> since the early 1930's in volume 2 of the Collected Papers, and in view of
> the all the raving about Frege's discovery of the Sinn-Bedeutung distinction --
> which Peirce, in effect, traces back to Aristotle via dozens of other versions
> of what I take to be substantially the same distinction -- one would think the
> material in that paper would deserve some sort of mention by historians of logic.

I know, I know, I find it utterly shocking.
I have to admit that, dependent as I was
on 'Collected Papers' and other hacked up
anthologies, that I did not get the full
significance of Peirce's earliest work,
even before 1865, and that I had bought
this idea of a "radical staging" in his
work whereby he did not get sophisticated
until late in life -- that is, until the
'Chronological Edition' started coming out --
when I discovered, much to my edification
and surprise, that most of late work was
a kind of return, with a few twists for
sure, Möbius-like, to his first and some
of his best ideas.

> But I couldn't find any reference to it in John Collier's information article
> that you refer to, nor do I recall anybody ever referring to it for any reason.
> Is it all so far off the point as that?

Well, that was a draft that John sent out for comment,
and so I will pass on your reflections to him, but it
is our constant vigil to learn what each other knows
until one day, just maybe, it amounts to something.
 
> Maybe it is because it is done prior to the discovery of the notation for
> the logic of relatives, but one would think it would be adaptable to the
> latter, if there was anything promising in it.  By 1867 Peirce almost
> certainly did understand that the task was to find such a notation
> and I would have thought the rationale for polyadic predicates is
> already laid out in the 1867 categories article.  But maybe what
> he says about information simply is not promising enough or just
> wrong-headed.  I decided long ago to devote another lifetime to
> the concept of information in order to have a little time to
> think about other things in this one, so I don't know and
> can't even hazard a guess.

What can I tell you?  To my way of thinking the Big Muddy of Logic
has been flowing in regress since circa 1870.  People will imagine
that I am hyperbolic, and that will give me time to demonstrate it.

Actually, Peirce's conception of information, that forms a continuing source
of amazement to me how he developed it all from purely logical considerations,
is in principle, however roughly polished, a more admantine paragon of the art
than the ones that we routinely, all too routinely use today, ab initio solving
many of the problems to which later thinkers keep on adverting, like the need to
coordinate quantitative weighs and means with qualitative measures of reasoning.

> But what do you think, Jon?  Is it another case of someone later reinventing
> the wheel, so why mention Peirce -- invoking the usual principle of "Yes,
> but what has he done for us recently?"  Or is it just not worth mentioning,
> or what?  Does it have any relation to any of the stuff that John Collier
> talks about?

On jugera ...

Jon Awbrey

28 Jul 2001 • 22:48 • Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: OCA: Inquiry
Date: Sat, 28 Jul 2001 22:48:09 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

SS: I am developing a general theory of development, applicable to all
    material systems because it is cast in very general (thermodynamic,
    information theoretic) terms. The canonical mode of development is from
    more vague to more definite; from hot to cool.

JA: I have occasionally used the term "differentiation" for this process:

| What is inquiry and how is it related to the theory of signs? 
|
| We examine the structure of inquiry as articulated by Peirce and Dewey.  In this model,
| inquiry begins with a surprising phenomenon or a problematic situation.  Whether felt as
| pleasant wonderment or as painful bewilderment, we feel driven to some activity that will
| return us to our prior equilibrium.  This may issue in a search for explanation that reduces
| the surprise or for a plan of action that resolves the problem.  The ensuing activities share
| a common form, the differentiation of a pattern.  In our consternation, we recognize a variety
| of features, some of which can be varied as part of our capacity for free choice.  The problem
| or surprise is present because of its difference from something.  As a surprise, what happens
| is different from what we habitually expect.  As a problem, what happens is different from
| what we hopefully intend.  To change the systematic expectation against which background
| a surprising phenomenon originally figured, we must discover some freedom to change what
| generated that expectation, and so to modify our personal model of the world.
|
| Jon Awbrey & Susan Awbrey,
|"Interpretation as Action: The Risk of Inquiry",
|'Inquiry: Critical Thinking Across the Disciplines",
| Volume 15, Number 1 (Autumn 1995), Pages 40-52.
|
| http://www.chss.montclair.edu/inquiry/fall95/awbrey.html

SS: Yes, this is unavoidable since the creation of subclasses by increasng
    specification (the basic model of development) necessarily generates
    trees because of coordinate subclasses emerging out of potentiality.
    Differentiation ensues if more than one subclass survives (and
    continues in each as long as a lineage of subsubclasses
    continues to survve).

The paragraph that I cited from Sue's amd my paper was the residue
of a much longer discussion that was cut down due to space limits,
but the sense of it was, insofar as I can remember it all, just
a bit different from your description of an autonomous external
system.  You see, I am mediately and ultimately concerned with
how we each determine our own conduct, as agents immersed in
streams of half-congealed, half-dissolved activity, trying
to reflect and to critique as best we can the nearity of
our previous approximations to some eternally cherished
ideal.  And so my sense of statistics is very personal,
like the Savage Mind that I am.  Out of the confusion
that we face on a moment of inquiry's birth, or even
conception, we must discern some hint of a form that
tells us which way might just be the best way to go.
That is what I mean by "differentiation", the third
art, the art of distinction, elsewise yclept as the
art of discretion, the highest partitioner of value
that makes its case between those other two arts,
the art of acquisition and the art of production.

JA: Roughly, "general" is extensional while "vague" is intensional.

SS: An interesting point.  This allows 'vague' to be generative by
    incorporating more descriptors into its sentence as further and
    further qualifiers. In contrast, 'general' can but extend its
    hegemony.

JA: Yes, I think so, at least, provisionally.  It was with (lack of exhaustive) respect
    for these dual notions, dichotomies and dualities being anathematic to Peirce, and so
    with trying to compound their synthesis or to discern their tertium quid that Peirce
    first came to the shores of what he named the "Theory of Information" (TOI), around
    about 1865, by the evidence of his Harvard University and Lowell Institute Lectures.

SS: Cool on "Theory of Information", since the process of subclass generation
    is the reduction of informational constraints (emerged from vagueness) to
    information neat (as in NPI).

I did not understand this sentence much.
Is "cool" good or bad?  What is NPI?

SS: I note further that 'general' can only extend its hegemony IF 'vagueness' differentiated
    more plentifully into a bigger tree.  So it is not so dichotomous with 'vagueness' as
    one might think.  It is its backward projection.

I am not sure if we are talking about the same things by means of these words.
Is backward projection the same thing as inverse projection, id est, a fiber?

Jon Awbrey

28 Jul 2001 • 23:00 • Inference, Information, Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Inference, Information, Inquiry
Date: Sat, 28 Jul 2001 23:00:20 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard, John, Stan, & OCAsional Readers,

I am forwarding this follow-up message from Joe Ransdell
about a reference that is relevant to the discussion of
inference, information, inquiry, and so on, especially
with regard to the topics of generality and vagueness,
and their further relationships to various notions of
determination, extension, and so-called "comprehension"
(the slightly more correct term for what most of us will
probably continue to discuss under the more popular common
name of "intension").

The Plot Thickens ...

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~FORWARD~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: Inquiry Into Inquiry
Date: Sat, 28 Jul 2001 13:59:17 -0500
From: Joseph Ransdell
  To: Arisbe

I forgot to mention, in my message about Peirce's information theory,
that the paper referrred to is available on-line at:

http://www.iupui.edu/~peirce/web/writings/v2/w2/w2_06/v2_06.htm

It appears in Vol. 2 of the 'Collected Papers' and Vol. 2 of the 'Writings' as well.
The 'Collected Papers' version is better, though, since it appends some additional
material from 1893, and is followed also by Peirce and Ladd-Franklin's entry on
"Signification and Application" in the 1902 Baldwin's Dictionary.

Joe Ransdell

o~~~~~~~~~o~~~~~~~~~o~DRAWROF~o~~~~~~~~~o~~~~~~~~~o

29 Jul 2001 • 00:44 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 29 Jul 2001 00:44:48 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, SemioCom, Standard Upper Ontology,
      Topic Map Mail, W.M. Jaworski

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj: Inquiry & Analogy
Date: Mon, 21 May 2001 00:06:16 -0400
From: Jon Awbrey
  To: Arisbe, SemioCom, Standard Upper Ontology

Inquiry SIG,

Here is an excerpt from a paper that I wrote a few years ago
on some relationships that exist between inquiry and analogy
in Peirce's way of analyzing their component phases over the
three types of inference.  Specifically, in a first approach,
he treats reasoning by analogy, just as Aristotle before him,
as a combination of deduction and induction, while the first
two stages of the inquiry process are tantamount to the dual
of this link-up, bringing into train abduction and deduction.

In this excerpt I consider the "Example of the Three Wisdoms"
from CSP's Harvard Lectures "On the Logic of Science" (1865),
the quote that I recently gave on the "Determination" thread:

http://suo.ieee.org/email/msg05056.html

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Document History:
|
| Project: Intelligent Systems Engineering
| Heading: Inquiry and Analogy
| Contact: Jon Awbrey
| Version: Draft 3.0
| Created: 1995 Feb 11
| Revised: 2001 May 20
| Faculty: F. Mili and M.A. Zohdy
| Setting: Oakland University, Rochester, MI
| Excerpt: "Types of Reasoning in C.S. Peirce"

Types of Reasoning in C.S. Peirce

Here we present one of Peirce's earliest treatments of the three types of reasoning,
from his Harvard Lectures of 1865 "On the Logic of Science".  It illustrates how the
same proposition might be reached from three different directions, as the result of
an inference in each of the three modes.

| We have then three different kinds of inference.
| Deduction  or inference 'à priori',
| Induction  or inference 'à particularis',
| Hypothesis or inference 'à posteriori'.
|
| CSP, CE 1, 267.

|     If I reason that certain conduct is wise because
| it has a character which belongs 'only' to wise things,
| I reason 'à priori'.
|
|     If I think it is wise because it once turned out
| to be wise, that is, if I infer that it is wise on
| this occasion because it was wise on that occasion,
| I reason inductively ['à particularis'].
|
|     But if I think it is wise because a wise man does it,
| I then make the pure hypothesis that he does it because
| he is wise, and I reason 'à posteriori'.
|
| CSP, CE 1, 180.
|
| Charles Sanders Peirce, "Harvard Lectures 2 & 8, 1865",
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Suppose we let:

| A  =  "Wisdom",
| B  =  "a certain character",
| C  =  "a certain conduct",
| D  =  "done by a wise man",
| E  =  "a certain occasion".

Recognizing that a little more concreteness will aid the understanding,
let us make the following substitutions in Peirce's example:

| B  =  "Benevolence", a certain character,
| C  =  "Conributes to Charity", a certain conduct,
| E  =  "Earlier today", a certain occasion.

The converging operation of all three reasonings is shown in Figure 1.

|     D  =  Done by a Wise Man
|      \*
|       \ *
|        \  *
|         \   *
|          \    *
|           \     *
|            \      *
|             \       A  =  A Wise Act
|              \     /| *
|               \   / |   *
|                \ /  |     *
|                 .   |       B  =  A Certain Character
|                / \  |     *
|               /   \ |   *
|              /     \| *
|             /       C  =  A Certain Conduct
|            /      *
|           /     *
|          /    *
|         /   *
|        /  *
|       / *
|      /*
|     E  =  A Certain Occasion
|
| Figure 1.  A Thrice Wise Act

The common proposition that concludes each argument
is AC, to wit, "contributing to charity is wise".

Deduction could have obtained the Fact AC from
the Rule AB, "benevolence is wisdom", along with
the Case BC, "contributing to charity is benevolent".

Induction could have gathered the Rule AC, after a manner of
saying that "contributing to charity is exemplary of wisdom",
from the Fact AE, "the act of earlier today is wise", along
with the Case CE, "the act of earlier today was an instance
of contributing to charity".

Abduction could have guessed the Case AC, in a style of expression
stating that "contributing to charity is explained by wisdom", from
the Fact DC, "contributing to charity is done by this wise man", and
the Rule DA, "everything that is wise is done by this wise man".  Thus,
a wise man, who happens to do all of the wise things that there are to do,
may nevertheless contribute to charity for no good reason, and even be known
to be charitable to a fault.  But on seeing the wise man contribute to charity
we may find it natural to conjecture, in effect, to consider it as a possibility
worth examining further, that charity is in deed a mark of his wisdom, not just
an accidental trait or an immaterial peculiarity -- in essence, that wisdom is
the 'reason' he contributes to charity.

29 Jul 2001 • 01:11 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 29 Jul 2001 01:11:09 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology,
      Topic Map Mail, W.M. Jaworski

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj: Inquiry & Analogy
Date: Mon, 21 May 2001 12:12:02 -0400
From: Jon Awbrey
  To: Arisbe, SemioCom,
      Standard Upper Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Mark how readily each pliant string
| Prepares itself and as an off'ring
| The tribute of some gentle sound does bring.
| Then altogether in harmonious lays
| To the sublimest pitch themselves they raise,
| And loudly celebrate their Master's praise.
|
| Henry Purcell, 1685

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Inquiry SIG,

Here is another excerpt from my report on "Inquiry and Analogy".
This gives the source for the concept of "abductive inference",
that Peirce abducted from Aristotle's 'Prior Analytics'.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Document History:
|
| Project: Intelligent Systems Engineering
| Heading: Inquiry and Analogy
| Contact: Jon Awbrey
| Version: Draft 3.0
| Created: 1995 Feb 11
| Revised: 2001 May 20
| Faculty: F. Mili and M.A. Zohdy
| Setting: Oakland University, Rochester, MI
| Excerpt: "Aristotle's 'Apagogy'"

Aristotle's 'Apagogy':  Abductive Reasoning as Problem Reduction

Peirce's notion of abductive reasoning was derived from Aristotle's treatment
of it in the 'Prior Analytics'.  Aristotle's discussion begins with an example
that may appear incidental, but the question and its analysis are echoes of an
important investigation that was pursued in one of Plato's Dialogues, the 'Meno'.
This inquiry is concerned with the possibility of knowledge and the relationship
between knowledge and virtue, or between their objects, the true and the good.
It is not just because it forms a recurring question in philosophy, but because
it preserves a certain correspondence between its form and its content, that we
shall find this example increasingly relevant to our study.

A couple of notes on the reading may be helpful.  The Greek text seems to
imply a geometric diagram, in which directed line segments AB, BC, AC are
used to indicate logical relations between pairs of the terms in A, B, C.
We have two options for reading these line labels, either as implications
or as subsumptions, as in the following two paradigms for interpretation.

1.  Implications:

    "AB"  =  "A <= B",
    "BC"  =  "B <= C",
    "AC"  =  "A <= C".

2.  Subsumptions:

    "AB"  =  "A subsumes B",
    "BC"  =  "B subsumes C",
    "AC"  =  "A subsumes C".

Here, "X subsumes Y" means that "X applies to all Y",
or that "X is predicated of all of Y".  When there is
no danger of confusion, we may write this as "X >= Y".

| We have Reduction ['apagoge', or 'abduction']:  (1) when it is obvious
| that the first term applies to the middle, but that the middle applies
| to the last term is not obvious, yet nevertheless is more probable or
| not less probable than the conclusion;  or (2) if there are not many
| intermediate terms between the last and the middle;  for in all such
| cases the effect is to bring us nearer to knowledge.
|
| (1) E.g., let A stand for "that which can be taught", B for "knowledge",
| and C for "morality".  Then that knowledge can be taught is evident;
| but whether virtue is knowledge is not clear.  Then if BC is not less
| probable or is more probable than AC, we have reduction;  for we are
| nearer to knowledge for having introduced an additional term, whereas
| before we had no knowledge that AC is true.
|
| (2) Or again we have reduction if there are not many intermediate terms
| between B and C;  for in this case too we are brought nearer to knowledge.
| E.g., suppose that D is "to square", E "rectilinear figure", and F "circle".
| Assuming that between E and F there is only one intermediate term -- that the
| circle becomes equal to a rectilinear figure by means of lunules -- we should
| approximate to knowledge.
|
| Aristotle, "Prior Analytics", Book 2, Chapter 25.
|'Aristotle, Volume 1', Translated by H.P. Cooke & H. Tredennick,
| Loeb Classical Library, William Heinemann, London, UK, 1938.

The method of abductive reasoning bears a close relation to the sense of reduction
in which we speak of one question reducing to another.  The question being asked
is "Can virtue be taught?"  The type of answer which develops is the following.
If virtue is a form of understanding, and if we are willing to grant that
understanding can be taught, then virtue can be taught.  In this way
of approaching the problem, by detour and indirection, the form of
abductive reasoing is used to shift the attack from the original
question, whether virtue can be taught, to the hopefully easier
question, whether virtue is a form of understanding.

The logical structure of the process of hypothesis formation in
the first example follows the pattern of "abduction to a case",
whose abstract form is diagrammed and schematized as follows.

|                   T  =  Teachable
|                   o
|                   |\
|                   | \
|                   |  \
|                   |   \
|                   |    \
|                   |     \
|                   |      \   R U L E
|                   |       \
|                   |        \
|               F   |         \
|                   |          \
|               A   |           \
|                   |            o U  =  Understanding
|               C   |           /
|                   |          /
|               T   |         /
|                   |        /
|                   |       /
|                   |      /   C A S E
|                   |     /
|                   |    /
|                   |   /
|                   |  /
|                   | /
|                   |/
|                   o
|                   V  =  Virtue
|
| Figure Omega.  Teachability, Understanding, Virtue
|
| T  =  Teachable (didacton),
| U  =  Understanding (epistemé),
| V  =  Virtue (areté).
|
| T is the Major term,
| U is the Middle term,
| V is the Minor term.
|
| TV  =  [T of V]  =  Fact in Question,
| TU  =  [T of U]  =  Rule in Donation,
| UV  =  [U of V]  =  Case in Question.
|
| Schema for Abduction to a Case:
|
|  Fact:  V => T?
|  Rule:  U => T.
| ----------------
|  Case:  V => U?

29 Jul 2001 • 14:42 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 29 Jul 2001 14:42:23 -0400
From: Jon Awbrey
  To: Douglas McDavid
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Douglas McDavid wrote:
> 
> Jon --
> 
> << Big snip >>
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> | This paper is based upon the theory already established,
> | that the function of conceptions is to reduce the manifold
> | of sensuous impressions to unity, and that the validity of
> | a conception consists in the impossibility of reducing the
> | content of consciousness to unity without the introduction
> | of it.
> |
> | Charles Sanders Peirce, "On a New List of Categories", 14 May 1867,
> | In 'Writings of Charles S. Peirce:  A Chronological Edition, Vol. 2,
> | 1867-1871', Indiana University Press, Bloomington, IN, 1984, page 49,
> | Customarily cited as (CE 2, 49).  Cf. 'Collected Papers', CP 1.545.
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> << Little snip >>
> 
> I don't want to put this on the list because
> I don't want to distract you or them.  But ...
> 
> "reducing the content of consciousness to unity"
> 
> Query:  What is this, that anyone would want to do it?  I've lived a long,
> information- and experience-filled 54 years, and I have never felt a need
> or desire to> reduce the content of consciousness to unity.  I don't have
> a clue as to what it could possibly mean.  I've come across this in my
> desultory explorations of CSP, and it seems that this was a major item
> on the research agenda of the day.
> 
> Reduction to unity?  Sorry, I don't get it.
> 
> Thanks,
> 
> Doug

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Doug,

Not to worry about distracting the distraught,
and the ONTarion Sublist is so far an idyllic
enough place to talk about any old thing, far
from the hue, the cry, and the madding crowd.

The phrase you pick is the one where I said
that Peirce echoes Kant, and to get what it
means you only have to call up to your mind
a typical moment when inquiry begins, where
before there is sheer chaos, confusion, and
the booming buzzing mutter of the 10^4 bits,
a state so annoising and irritating that no
body but no body can help to want to remote
the self from it, just like Lake Co-Product,
A Nice Place To Be From.  To get outta here
requires an abductive seizure of the moment,
a grasp of the thistle, a leap of the fates,
that will bring a Form to constellation and
precipitation in the psyche of the affected
agent.  Thus the "reduction of the manifold
of sensuous impressions to a unity" is just
an act that you must persist in per-forming
through every moment of your waking or even
dreaming existence, to wit, to conceit some
concept that begriffs the Many into the One.

Or Sum Ding Like That ...

Jon Awbrey

29 Jul 2001 • 16:16 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 29 Jul 2001 16:16:01 -0400
From: Jon Awbrey
  To: Howard Pattee
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

I'm going to make another attempt to address the issues of your initial comment,
and also to clarify the metaphorical responses that I have issued along the way.

Wish Me Luck!

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP quoting AE:

| The whole of science is nothing more than a refinement of everyday thinking.
| It is for this reason that the critical thinking of the physicist cannot
| possibly be restricted to the examination of concepts of his own special
| field.  He cannot proceed without considering critically a much more
| difficult problem, the problem of analyzing the nature of everyday
| thinking.
|
| Einstein, "Physics and Reality", 1936.

| What, precisely, is 'thinking'?  When, at the reception of sense impressions,
| memory-pictures emerge, this is not yet 'thinking'.  And when such pictures form
| series, each member of which calls forth another, this too is not 'thinking'.  When,
| however, a certain image turns up in many such series, then -- precisely through such
| return -- it becomes an ordering element for such a series, in that it connects series
| that are in themselves unconnected.  Such an element becomes an instrument, a concept.
| I think that the transition from free association or 'dreaming' to thinking is
| characterized by the more or less dominating role which the concept plays in it.
| It is by no means necessary that the concept must be connected with sensorily
| cognizable and reproducible sign (word);  but when this is the case,
| thinking becomes, by means of that fact, communicable.
|
| Einstein, "Autobiographical Notes", 1944.

HP: It is now generally accepted, by physicists at least, that the relation between
    sense impressions and such unifying concepts cannot be articulated by means of
    any method or logic, but arises as a type of aesthetic or "vague instinct that
    must be felt" (Poincare).  I don't "think" it's going to rain the logical way
    Dewey and Jon do.  I feel it's going to rain.

HP: As Polanyi ["Personal Knowledge"] expressed it:  "I believe that by now three things
    have been established beyond reasonable doubt:  the power of intellectual beauty to
    reveal truth about nature;  the vital importance of distinguishing this beauty from
    merely formal attractiveness, and the delicacy of the test between them, so difficult
    that it may baffle the most penetrating scientific minds."

HP: I have more confidence in empirical approaches to inquiry.
    The analytic Peircian pragmatic "canonical" approach that
    Jon describes is certainly closer to what we have been
    indoctrinated with in our western culture.  But that is
    not what actually goes on in the brain.  My conversion
    from the canonical approach evolved from teaching a course,
    "The Psychology of Problem Solving," over a period of 25 years.
    There is now much empirical evidence of how inquiry actually takes
    place from many quarters:

HP: (1) the introspection of creative scientists [e.g., Hadamard,
        'The Psychology of Invention in the Mathematical Field', Polanyi,
        'Personal Knowledge', Ghiselin, 'The Creative Process',  Miller,
        'Imagery in Scientific Thought', Lakatos, 'History of Science and
        its Rational Reconstructions', Feyerabend, 'Against Method', etc.],

HP: (2) the more recent models of distributed, concurrent networks and evolved behavior --
        including agent-based approaches to artificial life and artificial intelligence [e.g.,
        Brooks, 'Cambrian Intelligence', Hinton and Sejnowski, eds., 'Unsupervised Learning',
        Arkins, 'Behavior-Based Robotics', Mitchell, 'An Introduction to Genetic Algorithms', etc.],

HP: (3) on empirical knowledge of how brains actually integrate their evolved
        instincts, senses, and individual experiences [e.g., Abbott and Sejnowski, eds.,
        'Neural Codes and Distributed Representations', Rugg, ed., 'Cognitive Neuroscience'].

HP: What is now evident is that by the time we are using words and logics of any type
    where thinking is explicit and communicable, we are no longer in the creative mode in
    which images and concepts emerge from our instincts, memories, and sense impressions.
    Furthermore, the creative mode is by its nature a sub-symbolic mode, or more precisely,
    a sub-thinking mode.  (Whether it is still explicit enough to be called symbolic or
    a sign activity is only a matter of definition.)  The brain's activities in even the
    simplest pattern recognition or one-bit decision involves hundreds of millions of
    neurons in which instinct, memory, models, and sensory inputs are concurrently
    seeking some  kind of metastability.  This network dynamic activity is so
    complex, diffused, and delicate that any attempt to impose rules, methods,
    and logic would only disturb and limit the emergence of novel ideas.

JA: In the pragmatic way of thinking everything has a purpose,
    and the purpose of each thing is the first thing we should
    try to note about it.  The purpose of inquiry is to reduce
    doubt and lead to a state of belief, which a person in that
    state will usually call knowledge or certainty.

HP: This is not the case for many physicists.  The purpose of models is to reduce ambiguity,
    not doubt.  Doubt should always be a dominant emotion since it is the primary check
    against overenthusiasm and error.  The state of "belief" is especially dangerous,
    since no model is complete, and very likely will be replaced.  Belief is for the
    religious.  What physicists seek first in their models is clarity, elegance,
    and empirical decidability.

JA: For our present purposes, the first feature to note in
    distinguishing these modes of reasoning is whether they
    are exact or approximate in character.  Deduction is the
    only type of reasoning that can be made exact, always
    deriving true conclusions from true premisses, while
    induction and abduction are unavoidably approximate
    in their mode of operation, involving elements of
    fallible judgment and inescapable error in their
    application.

HP: Paraphrasing Einstein:
    Insofar as deductive reasoning ("the propositions of mathematics")
    is exact ("certain") it does not apply to reality;  and insofar
    as it applies to reality it is not exact ("certain").

Yes, I think I said that.

JA: Abductive reasoning is the mode of operation which is involved
    in shifting from one paradigm to another.  In order to reduce
    the overall tension of uncertainty in a knowledge base, it is
    often necessary to restructure our perspective on the data in
    radical ways, to change the channel that parcels out information
    to us.  But the true value of a new paradigm is typically not
    appreciated from the standpoint of another model, that is, not
    until it has had time to reorganize the knowledge base in ways
    that demonstrate clear advantages to the community of inquiry
    concerned.

HP: Abduction, as I understand it, is not reasoning.  It is sub-rational, and I would
    say sub-symbolic.  Computers lack the knowledge base acquired from 4 billion years
    of surviving in a complex environment as well as the vast distributed network, senses,
    and body actions necessary to efficiently integrate this mass of experience.  Most of
    this was acquired by natural selection and integrated into our metabolism, hormonal
    and motor controls, senses, pattern recognition, perceptions, motivations, brains,
    thoughts, imagination -- the whole organism.  It's not likely we can pull this off
    in silicon except for simple, closed domains.

I fully understand, I guess, why anybody would want to say this,
especially if they judge ab-apodictic, approximate, contingent,
and non-demonstrative manners of inference against the bar of
deductive reasoning.  But it seems fairly clear when you come
to examine it that some patterns of abduction and induction
just plain work better than others in the long run, and so
our concern is one of accounting for how this can be so.
I have been posting a bunch of stuff on these topics
and will be interested in your reactions to them.

JA: We seem to be about the business of marking explicitly what's given implicitly.
    But is it a mark against our ephemeris that celestial bodies do not consult it
    for their itineraries, nor have the eyes in their orbs to read our fine prints,
    that the planets are enlightened by the sun on their courses and their destiny
    by some adumbration other than differential equations in plain black and white?

JA: Just an initial impression that comes to mind.
    I am still working my way through the rest
    of the issues that you are raising here.

The point here is that a different order of being comes into play
when being begins relating itself to itself via the automediation
of signs.  Being a material and a natural thinker, I see this all
taking place within the order of matter and nature, as an utterly
internal development, differentiation, and "ontologogenesis" of a
cosmos, if you catch my drift, but nothing about saying this does
anything to diminish the import of the formal aspect of its being.

I hope this acts to reduce the metaphor of senseless impressions to a eusemy.
I will keep this phyle intact and try to develop its phylogogenesis as we go.

Jon Awbrey

29 Jul 2001 • 17:30 • Inquiry Into Inquiry

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Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 29 Jul 2001 17:30:10 -0400
From: Jon Awbrey
  To: W.M. Jaworski
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

W.M. Jaworski wrote (WMJ):
Doug McDavid wrote (DM):
Jon Awbrey wrote (JA):

DM: I've come across this [to reduce the content of consciousness to unity]
    in my desultory explorations of CSP, and it seems that this was a major
    item on the research agenda of the day.

DM: Reduction to unity?  Sorry, I don't get it.

WMJ: Reduction of your "Inquiry Driven Systems" (IDS) document:
     http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
     to a topic map?  Seems not doable now.  Enhancing IDS by a topic map?  Why?
     To allow navigation over the IDS document and perform a documented "inquiry"
     into IDS document.  Interested?  If yes then recover from the IDS an initial
     list of the sets (not set members!) and their characteristics and put in the
     table:

     | Name, Cardinality, Type, Comment
     |
     | where:  type ::= crisp | fuzzy | rough

I had been hoping that this Topic Maps lingo would be one those that I could learn
simply by hanging around long enough in a place where folks are already talking it,
if only people will tolerate my baby talk long enough for me to get the hang of it,
but I am still struggling through Guy's helpful tutorial, and every time I look at
the official grammar book I am banked back into the gutters of an utter despair by
the circumstunces of all of my most favored notions being snookered there in turns
of english the angles whereof are beyond my cue and outside my corner of pocketing.

If you catch my drift ...

But I still have the greatest e-thusiasm for the mission ...

So, yes, I be interested, and I will try to repay in some way, in kind, in time.

But I will need to ask a whole bunch of really basic questions,
and I trust that you will be of a flexible style of mind if it
transpires in time that the Tailors of TMesis will need to cut
a wider swatch of fabric in order to fully address our inquiry.

First question:
What do you mean here by "set"?
(I said that it would be basic!)

WMJ: How to deal with the relationships between sets?
     Will be done in the next steps.

WMJ: BTW I am prepare to allocate my free labor to the "enhancing".

WMJ: Reduction of research to unity of loose talk?  Sorry, I don't get it.

WMJ: To reduce verbiage about CSP (if any), please refer to
     specific pages of the book "Knowledge Representation"
     by John F. Sowa.

Sorry, I fear that I learned my Peirce so long ago
that the manifold of my sensible impressions about
inquiry will naturally be reduced to this equinity.

Looking Forward Tuit,

Jon Awbrey

> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> Douglas McDavid wrote:
> >
> > Jon --
> >
> > << Big snip >>
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > | This paper is based upon the theory already established,
> > | that the function of conceptions is to reduce the manifold
> > | of sensuous impressions to unity, and that the validity of
> > | a conception consists in the impossibility of reducing the
> > | content of consciousness to unity without the introduction
> > | of it.
> > |
> > | Charles Sanders Peirce, "On a New List of Categories", 14 May 1867,
> > | In 'Writings of Charles S. Peirce:  A Chronological Edition, Vol. 2,
> > | 1867-1871', Indiana University Press, Bloomington, IN, 1984, page 49,
> > | Customarily cited as (CE 2, 49).  Cf. 'Collected Papers', CP 1.545.
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > << Little snip >>
> >
> > I don't want to put this on the list because
> > I don't want to distract you or them.  But ...
> >
> > "reducing the content of consciousness to unity"
> >
> > Query:  What is this, that anyone would want to do it?  I've lived a long,
> > information- and experience-filled 54 years, and I have never felt a need
> > or desire to> reduce the content of consciousness to unity.  I don't have
> > a clue as to what it could possibly mean.  I've come across this in my
> > desultory explorations of CSP, and it seems that this was a major item
> > on the research agenda of the day.
> >
> > Reduction to unity?  Sorry, I don't get it.
> >
> > Thanks,
> >
> > Doug
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> 
> Doug,
> 
> Not to worry about distracting the distraught,
> and the ONTarion Sublist is so far an idyllic
> enough place to talk about any old thing, far
> from the hue, the cry, and the madding crowd.
> 
> The phrase you pick is the one where I said
> that Peirce echoes Kant, and to get what it
> means you only have to call up to your mind
> a typical moment when inquiry begins, where
> before there is sheer chaos, confusion, and
> the booming buzzing mutter of the 10^4 bits,
> a state so annoising and irritating that no
> body but no body can help to want to remote
> the self from it, just like Lake Co-Product,
> A Nice Place To Be From.  To get outta here
> requires an abductive seizure of the moment,
> a grasp of the thistle, a leap of the fates,
> that will bring a Form to constellation and
> precipitation in the psyche of the affected
> agent.  Thus the "reduction of the manifold
> of sensuous impressions to a unity" is just
> an act that you must persist in per-forming
> through every moment of your waking or even
> dreaming existence, to wit, to conceit some
> concept that begriffs the Many into the One.
> 
> Or Sum Ding Like That ...
> 
> Jon Awbrey
> 
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

29 Jul 2001 • 20:01 • Inquiry

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Subj: OCA: Re: Inquiry
Date: Sun, 29 Jul 2001 20:01:07 -0400
From: Jon Awbrey
  To: Stanley N Salthe
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

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Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

SS: [Differentiation during development as modeled by increasing specification]
    is unavoidable since the creation of subclasses by increasing specification
    (the basic model of development) necessarily generates trees because of
    coordinate subclasses emerging out of potentiality.

SS: Differentiation ensues if more than one subclass survives (and continues
    in each as long as a lineage of subsubclasses continues to survive).

JA: The paragraph that I cited from ['Interpretation as Action: The Risk of Inquiry']
    was the residue of a much longer discussion that was cut down due to space limits,
    but the sense of it was, insofar as I can remember it all, just a bit different
    from your description of an autonomous external system.

SS: I would say 'system modeled externally'.

By "autonomous external system", I mean an object system that is being regarded,
and to a pertinent approximation usefully so, as a system in which we ourselves,
as "agents of construal" (interpreters & observers) are negligible participants.
Is that what you mean by "system modeled externally"?

JA: You see, I am mediately and ultimately concerned with how we each determine our own conduct,
    as agents immersed in streams of half-congealed, half-dissolved activity, trying to reflect
    and to critique as best we can the nearity of our previous approximations to some eternally
    cherished ideal.  And so my sense of statistics is very personal, like the Savage Mind that
    I am.  Out of the confusion that we face on a moment of inquiry's birth, or even conception,
    we must discern some hint of a form that tells us which way might just be the best way to go.
    That is what I mean by "differentiation", the third art, the art of distinction, elsewise
    yclept as the art of discretion, the highest partitioner of value that makes its case
    between those other two arts, the art of acquisition and the art of production.

SS: OK, I would say that you are taking an internalist perspective, trying to get at generativity,
    which is in general not accessible to typical externalist (global, fully explicit, totalizing,
    atemporal) discourse.

Not sure.  I always tend to become a bit suspicious of any discourse, whether my own or others,
that becomes too littered with these insuperable suffixes "-ism" and "-ist", and I do not think
that any tried and true pragmatician such as I keep trying to be would rush to accept any such
label as either "externalist" or "internalist".

Side question: Are you using "generativity" in the sense of Chomsky?

SS: It is not, I think, clear that in this discourse the kind of choice
    you refer to can be represented.  Different choices would not, I think,
    be available to the system AS choices.  "Hints of forms", OK, "confusion".
    OK, "conception" and "birth", yes, "hints" perhaps.  So, "distinction" --
    definitely not.  No distinctions would be available internally in my view.
    Distinctions are pre-eminently externalist things.  They are too crisp
    for vague internality.  Vague groping guided by tendencies, OK.
    Fuzzy distinctions might be more believable.

Again, I am not sure what all is being suggested here -- I was hoping to givvie up
the discussion of fuzzy concepts to a more disentangled thread, as I threaded to
do with that old post on "Fuzzy Stuff" -- but I think that these issues are what
drives me to use various families and sundry samples of triadic sign relations
as my conceptual framework of choice.  Here, the "object domain" contains any
old thing that we purport to make an object of "discussion and thought" (DAT),
the domains of signs and interpretant signs contain the signs and mental ideas
that we use to talk about and to think about the objects of the object domain.

JA: Roughly, "general" is extensional while "vague" is intensional.

SS: An interesting point. This allows 'vague' to be generative by incorporating more
    descriptors into its sentence as further and further qualifiers.  In contrast,
    'general' can but extend its hegemony.

JA: Yes, I think so, at least, provisionally.  It was with (lack of exhaustive) respect for
    these dual notions, dichotomies and dualities being anathematic to Peirce, and so with
    trying to compound their synthesis or to discern their tertium quid that Peirce first
    came to the shores of what he named the "Theory of Information" (TOI), around about
    1865, by the evidence of his Harvard University and Lowell Institute Lectures.

SS: Cool on "Theory of Information", since the process of subclass generation
    is the reduction of informational constraints (emerged from vagueness) to
    information neat (as in NPI).

JA: I did not understand this sentence much.  Is "cool" good or bad?

SS: Oh, sorry -- I meant "Theory of Information" fits well as a label for
    the way some of us think of development using modern information theory.

Cool!

JA: What is NPI?

SS: The negentropy theory of information.
    That is, information is a reduction
    in possibilities ontologically, or
    of uncertainty epistemologically.

Gosh, I feel so dense!  "What the heck is the 'P' for?", asked Princess Principia.

Negative Probability Integral?

SS: I note further that 'general' can only extend its hegemony IF 'vagueness' differentiated
    more plentifully into a bigger tree.  So it is not so dichotomous with 'vagueness' as one
    might think.  It is its backward projection.

JA: I am not sure if we are talking about the same things by means of these words.
    Is backward projection the same thing as inverse projection, id est, a fiber?

SS: What I mean is that generality is constructed from particular instances,
    gradually uniting fewer and fewer properties of more and more instances.
    But instances themselves were developed out of a vague precursor, by
    differentiation among them during their development.  Thus, as Peirce
    suggests (somewhere) generality is a kind of explicit model of vagueness.
    So, what I was saying is that if a given vagueness developed into a greater
    tree of definite descendents, then the generality that can be constructed with
    respect to these will have greater hegemony.

Give me some more clues and I will try to find this.
I do not have the CD of CP yet -- maybe some party
on the Arisbe list will perk up and help us find it?

Jon Awbrey

30 Jul 2001 • 01:54 • Inquiry Into Inquiry

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Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 30 Jul 2001 01:54:05 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Standard Upper Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Well, I sorta thought we said this in the title,
not to mention repeatedly throughout the article:

| "Interpretation as Action : The Risk of Inquiry"
|
| The fallibility of signs is shared with the human activities of interpretation and inquiry,
| and bears a relation to the situated character of all dynamic processes of determination.
| |
| | If doubt and indeterminateness were wholly within the mind --
| | whatever that may signify -- purely mental processes ought
| | to get rid of them.  But experimental procedure signifies
| | that actual alteration of an external situation is necessary
| | to effect the conversion.  A 'situation' undergoes, through
| | operations directed by thought, transition from problematic
| | to settled, from internal discontinuity to coherency and
| | organization.  (Dewey, TQFC, p. 185).
| |
| | John Dewey, "The Quest for Certainty", in J.A. Boydston (ed.),
| |'John Dewey:  The Later Works, 1925-1953, (Vol 4: 1929)',
| | Southern Illinois University Press, Carbondale, IL, 1988.

This attitude toward object reality derives from Peirce's ground-breaking,
cornerstone-laying work to discern the "Logic of Science", real science,
with which he was very much acquainted, however labeled or libeled as
a "mere logician" he may've been by some people, who had been content
until his time, as many still are, to lounge in their armchairs
and listen to the facile fantasias of the Mills Brothers.

Some emphasis added,

Jon Awbrey

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H H Pattee wrote (some emphasis lost):
> 
> I am not sure how I fit into this discussion. Jon obviously has enough comments to answer without
> my adding more. Anyway, here is another view of inquiry. I am not sure how Jon's discussion of
> inquiry gets into the observable world of science. As a non-logician, it seems to me Jon is just
> inquiring into Peirce and logical strings and graphs. If this is Peirce's main contribution I can
> understand  why scientists do not pay him much attention. Inquiry to most scientists does not
> really depend on this type of logical analysis, but on imagination and observation. I don't know
> of any cases of discovery in science, or even mathematics, where logical analysis played the
> creative role. Of course, in math proofs require logic, but rarely is logic the source of the
> inquiry.
> 
> I think for most scientists "inquiry" means exploration or looking for something entirely new in
> our experience. After all, modern scientific inquiry did not begin with logic but with the
> extension of our natural senses by instruments and by the extension of our natural imagination by
> mathematics. Modern biology began with the microscope, chemistry with the analytic balance and
> chemical indicators, and physics with the telescope, theodolite, and mathematics. Chronometers,
> galvanometers, spectroscope, mass spectrometers, centrifuges, chromatography, radioactive tracers,
> particle accelerators, and especially mathematics, are the essential prostheses for our senses and
> brains without which scientific inquiry would have come to a dead end like scholasticism.
> 
> The real problem for scientific inquiry is: How do we know what are we looking for? This is an old
> problem. Meno asked Socrates, "But how will you look for something when you don't in the least
> know what it is? How on earth are you going to set up something you don't know as the object of
> your search? To put it another way, even if you come right up against it, how will you know that
> what you have found is the thing you didn't know?" This is the big question, but Socrates gives
> one of his sillier answers: "The soul, since it is immortal and has been born many times, and has
> seen all things both here and in the other world, has learned everything that there is."
> Therefore, he concludes: . . . "learning is nothing but recollection."
> 
> It is not the metaphysics of reincarnation that is silly here (I'm in favor of it). It is
> Socrates' lack of understanding of   problem identification. As we are all too well aware today,
> if you don't know what you are looking for, access to an infinite database (no matter how well
> indexed, and whether it is in an immortal soul or in an infinitely fast computer) is not a
> solution. In fact, the more the data, the worse the problem. You still don't know what you are
> looking for. I think Peirce worried about this problem too, but I don't think he found an adequate
> answer. Jon may have another opinion.
> 
> There have been two extreme approaches to this problem. At one extreme is the assumption of
> initial total ignorance. Then blind search and natural selection is the only hope. Of course, this
> requires many trials and memory of failures and successes (i.e., the Darwinian solution:
> replication, heritable variation, and natural selection, also assumed by evolutionary
> epistemologists, a la Campbell, Popper, et al.). The other extreme, a physical equivalent of
> Socrates omniscient soul, is a Laplacean omnipotent determinism where free will and ignorance are
> just illusions and have nothing to do with the inexorable course of events. Neither of these
> extremes alone makes much sense in terms of current physics and biology. Today the active
> controversy in evolution is over finding a suitable balance between chance and determinism, that
> is, between Darwinian blind search and selection and non-selective self-organizing (dynamic)
> processes.
> 
> I think there are two misconceptions of the search problem. The first is that the search space it
> too large. The main criticism of the creationists, intelligent design theists, and even the
> self-organizing anti-Darwinians, is that the search space for the totally ignorant is so large
> that successful blind search is too improbable. But the evidence is clear that in the course of
> evolution organisms have greatly increased their searchable domains by adding more sensors and
> motor controls; and as I pointed out above, science also depends for its progress on greatly
> increasing its searchable domains by instrumentation. Enlarging the searchable domain is not the
> problem, it is part of the answer to evolution and learning. What would be the evolutionary future
> of organisms if their inquiries were restricted to a fixed set of sensors (or a fixed logic)? The
> second misconception is that "blind" applies to the entire search process. But "blind" applies
> only to a simple initial event in a highly organized living system that has adapted to a highly
> ordered environment. This is a genetic form or analog of intelligence. Similarly, there is at some
> level in every creative idea a blind search, but usually in the context of highly developed
> problem domain.
> 
> I think the most significant change in attitudes towards this balance between determinism and
> chance in the last 20 years has been the loss of dominance of logic-based, hard-programmed
> problem-solving, as in GOFAI (good old fashioned AI) and the renewed appreciation of the power of
> biological analogs like neural nets and genetic algorithms to discover solutions and integrate
> behaviors. Most important, however, has been the realization that blind search and selection
> requires strong, open-ended interactions with a rich, highly-ordered (i.e., descriptively
> compressible) environment (as has been partially simulated by environmentally "embedded autonomous
> robots") What is still missing in these robots is the open-ended ability to construct new sensors.
> It appears that only with this unrestricted "sensing" of a rich, ordered environment does a
> balanced coupling of self-organization and blind search and natural selection become effective.
> 
> Here are a few references on these points:
> Brooks, R., "Intelligence without reason." In 12th Int. Conf. on AI, Morgan Kauffman, 1991.
> Campbell, D., "Evolutionary epistemology." In The Philosophy of Karl Popper, Schilpp, ed.,
> Open Court, 1974.
> Cariani, P. "Some epistemological implications of devices that construct their own sensors
> and effectors."  In Artificial Life II, Langton, et al, eds., Addison-Wesley, 1992.
> Clark, A., "Being there." MIT Press, 1997.
> Conrad, M., "The geometry of evolution." BioSystems 24, 61-81, 1990.
> Dawkins, R., "The evolution of evolution." Artificial life I, Langton, ed.,
> Addison-Wesley, 1989, p.201.
> 
> This is one view of inquiry.  I suspect I am missing something about Jon's view.
> 
> Howard
> Howard H. Pattee
> Systems Science and Industrial Engineering Dept.
> SUNY Binghmaton, Binghamton, NY 13902-6000
> http://www.ssie.binghamton.edu/pattee

30 Jul 2001 • 08:16 • Inquiry Into Inquiry

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Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 30 Jul 2001 08:16:30 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy, SemioCom,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Mishtu Banerjee wrote (MB):

MB: By way of re-connecting Peirce the Logician with Peirce the Scientist, I wonder if it is possible
    for anyone on this list to discuss Peirce's scientific work on gravity and sources of error in
    gravity measurements for the coast survey, in terms of the formation of his views on logic.

This is true, and it shows that Peirce knows whereof he speaks when he speaks of science
as she is spoke.  In its relevance to his view of logic it helps to illustrate the fact
that he was a pragmatic thinker and a "real" thinker -- it is my vigil of custom to use
the adjective forms in lieu of the "-isms" -- in every sense of the word "real", to wit,
objective, platonic, scholastic, and so on.  But I will try to focus on issues that are
pertinent to the topics of organization, complexity, autonomy.  For me, the activities
of intelligent agents, and systems witted enough to do some kind of inquiry, however
reflectively, from absently to dimly to fully, which I am guessing that every living
organism has to do in order to maintain its definition as living per se, if only at
the level of its evolutionary quest -- let me catch my breath -- these are examples
of the most complex behavior and the most fascinating conduct that I know.  And all
I want to know while I have yet breath to live is how this inquiry bit is carried off --
and so I return to abductive reason, not to get too carried away by the transport of it.

MB: As I understood it, Peirce's use of logic, was a way of teasing out
    all the implications of a creative guess ... and this is abduction.
    To guess "at the riddle", then to logically work out all the logical
    correlates (necessary implications) of that guess, then to make
    measurements, to confirm or falsify the correlates.

Yes, that is a decent summary of the generic cycle of inquiry.
Of course, nobody ever teases out "all" of the implications
of any good guess, but you already knew that.  Still, this
general idea is only the beginning if you want to fathom
more deeply and exactly how the whole rigamorole can ever
really work, or if you get down one day, as I did one day,
to trying to write computer programs that would genuinely
extend our humane capacity to "do inquiry", as we say.

MB: I always wondered why Popper's book was
    called "The Logic of Scientific Discovery"
    when the logic usually comes after the discovery ...

Well, that's "a cute observation", the likes of which I can "admire", to say we envy,
but if I try to read Popper's line with a bit of interpretive charity, then I would
hazard a guess that the word "Logic" is used here to evoke the idea of "Pattern",
the "condition of posing" (COP), the "way of being" (WOB), to sum in up, the
overall "form, lay, and play" (FLAP) of the activity in question.  It is but
our modish brain-lyzing by a certain "school of analytic philosophy" (SOAP)
that has brought us down the slippery slope of thinking that we can reduce
every notion of that once-hallowed LOGOS to the mere reflex of deduction.

MB: My own, developing view of logic ... is that any given logic depends first
    on making certain distinctions (cuts -- say distinction of right and left
    handedness in organic molecules), and that the logic follows depending on
    the cuts.  Scientific discovery often begins with making new distinctions ...
    but the big discoveries seem to be by cutting through distinctions, and
    showing that two things share the same form (motion of a ball falling
    to earth, motion of the earth around the sun).

This sounds like a plan to me.
I myself long ago epitomized
logic as the "autotomic axe".

Many Regards,

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

> -----Original Message-----
> Subj: Re: Inquiry Into Inquiry
> From: H H Pattee
> Sent: Sunday, July 29, 2001 9:16 PM
>   To: Organization Complexity Autonomy
> 
> I am not sure how I fit into this discussion. Jon obviously has enough comments to
> answer without my adding more. Anyway, here is another view of inquiry. I am not sure
> how Jon's discussion of inquiry gets into the observable world of science. As a
> non-logician, it seems to me Jon is just inquiring into Peirce and logical strings and
> graphs. If this is Peirce's main contribution I can understand  why scientists do not
> pay him much attention. Inquiry to most scientists does not really depend on this type
> of logical analysis, but on imagination and observation. I don't know of any cases of
> discovery in science, or even mathematics, where logical analysis played the creative
> role. Of course, in math proofs require logic, but rarely is logic the source of the
> inquiry.
> 
> I think for most scientists "inquiry" means exploration or looking for something
> entirely new in our experience. After all, modern scientific inquiry did not begin with
> logic but with the extension of our natural senses by instruments and by the extension
> of our natural imagination by mathematics. Modern biology began with the microscope,
> chemistry with the analytic balance and chemical indicators, and physics with the
> telescope, theodolite, and mathematics. Chronometers, galvanometers, spectroscope, mass
> spectrometers, centrifuges, chromatography, radioactive tracers, particle accelerators,
> and especially mathematics, are the essential prostheses for our senses and brains
> without which scientific inquiry would have come to a dead end like scholasticism.
>
> The real problem for scientific inquiry is: How do we know what are we looking for? This
> is an old problem. Meno asked Socrates, "But how will you look for something when you
> don't in the least know what it is? How on earth are you going to set up something you
> don't know as the object of your search? To put it another way, even if you come right
> up against it, how will you know that what you have found is the thing you didn't know?"
> This is the big question, but Socrates gives one of his sillier answers: "The soul,
> since it is immortal and has been born many times, and has seen all things both here and
> in the other world, has learned everything that there is." Therefore, he concludes: ...
> "learning is nothing but recollection."
> 
> It is not the metaphysics of reincarnation that is silly here (I'm in favor of it). It
> is Socrates' lack of understanding of   problem identification. As we are all too well
> aware today, if you don't know what you are looking for, access to an infinite database
> (no matter how well indexed, and whether it is in an immortal soul or in an infinitely
> fast computer) is not a solution. In fact, the more the data, the worse the problem. You
> still don't know what you are looking for. I think Peirce worried about this problem
> too, but I don't think he found an adequate answer. Jon may have another opinion.
> 
> There have been two extreme approaches to this problem. At one extreme is the assumption
> of initial total ignorance. Then blind search and natural selection is the only hope. Of
> course, this requires many trials and memory of failures and successes (i.e., the
> Darwinian solution: replication, heritable variation, and natural selection, also
> assumed by evolutionary epistemologists, a la Campbell, Popper, et al.). The other
> extreme, a physical equivalent of Socrates omniscient soul, is a Laplacean omnipotent
> determinism where free will and ignorance are just illusions and have nothing to do with
> the inexorable course of events. Neither of these extremes alone makes much sense in
> terms of current physics and biology. Today the active controversy in evolution is over
> finding a suitable balance between chance and determinism, that is, between Darwinian
> blind search and selection and non-selective self-organizing (dynamic) processes.
> 
> I think there are two misconceptions of the search problem. The first is that the search
> space it too large. The main criticism of the creationists, intelligent design theists,
> and even the self-organizing anti-Darwinians, is that the search space for the totally
> ignorant is so large that successful blind search is too improbable. But the evidence is
> clear that in the course of evolution organisms have greatly increased their searchable
> domains by adding more sensors and motor controls; and as I pointed out above, science
> also depends for its progress on greatly increasing its searchable domains by
> instrumentation. Enlarging the searchable domain is not the problem, it is part of the
> answer to evolution and learning. What would be the evolutionary future of organisms if
> their inquiries were restricted to a fixed set of sensors (or a fixed logic)? The second
> misconception is that "blind" applies to the entire search process. But "blind" applies
> only to a simple initial event in a highly organized living system that has adapted to a
> highly ordered environment. This is a genetic form or analog of intelligence. Similarly,
> there is at some level in every creative idea a blind search, but usually in the context
> of highly developed problem domain.
> 
> I think the most significant change in attitudes towards this balance between
> determinism and chance in the last 20 years has been the loss of dominance of
> logic-based, hard-programmed  problem-solving, as in GOFAI (good old fashioned AI) and
> the renewed appreciation of the power of biological analogs like neural nets and genetic
> algorithms to discover solutions and integrate behaviors. Most important, however, has
> been the realization that blind search and selection requires strong, open-ended
> interactions with a rich, highly-ordered (i.e., descriptively compressible) environment
> (as has been partially simulated by environmentally "embedded autonomous robots") What
> is still missing in these robots is the open-ended ability to construct new sensors. It
> appears that only with this unrestricted "sensing" of a rich, ordered environment does a
> balanced coupling of self-organization and blind search and natural selection become
> effective.
> 
> Here are a few references on these points:
>
> Brooks, R., "Intelligence without reason." In 12th Int. Conf. on AI, Morgan Kauffman, 1991.
> Campbell, D., "Evolutionary epistemology." In The Philosophy of Karl Popper, Schilpp, ed.,
> Open Court, 1974.
> Cariani, P. "Some epistemological implications of devices that construct their own sensors
> and effectors." In Artificial Life II, Langton, et al, eds., Addison-Wesley, 1992.
> Clark, A., "Being there." MIT Press, 1997.
> Conrad, M., "The geometry of evolution." BioSystems 24, 61-81, 1990.
> Dawkins, R., "The evolution of evolution." Artificial life I, Langton, ed.,
> Addison-Wesley, 1989, p.201.
> 
> This is one view of inquiry. I suspect I am missing something about Jon's view.
> 
> Howard
>
> Howard H. Pattee
> Systems Science and Industrial Engineering Dept.
> SUNY Binghmaton, Binghamton, NY 13902-6000
> http://www.ssie.binghamton.edu/pattee

30 Jul 2001 • 09:40 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 30 Jul 2001 09:40:04 -0400
From: Jon Awbrey
  To: Howard Pattee
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

You continue to rush on ahead of my more plodding ways,
and so I find that I have to keep taking your messages
in several tries to get through their briar patches.

Previously on this thread:

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: I am not sure how I fit into this discussion.  Jon obviously has enough comments
    to answer without my adding more.  Anyway, here is another view of inquiry.  I am
    not sure how Jon's discussion of inquiry gets into the observable world of science.

Pragmaticians are "real" thinkers.  They guess that there is a world beyond them,
that it has properties -- this is, a little Peirce tells me, the authorized sense
of the word "real", as it was originally introduced into our culture's discourse.
My own experience tells me that this "real world" will just keeping on thumping
me in the head, as it were, until I pay attention to the features thereof, and
this forces me, all against my initial inclination, to try to catch its drift.
All the nets that I have to catch it with are made, in the end, of signs and
the types of signs that we know as affects, concepts, impressions, or mental
ideas, and so I must, per force aforesaid, contemplate the relations that
insist, persist, subsist, or systematicaly exist among these arrays of
so-called "real" objects, signs, and their host of interpretant signs.

HP: As a non-logician, it seems to me Jon is just inquiring into Peirce and
    logical strings and graphs.  If this is Peirce's main contribution I can
    understand  why scientists do not pay him much attention.  Inquiry to most
    scientists does not really depend on this type of logical analysis, but on
    imagination and observation.  I don't know of any cases of discovery in science,
    or even mathematics, where logical analysis played the creative role.  Of course,
    in math proofs require logic, but rarely is logic the source of the inquiry.

I am guessing then that you are one of those who does not consider
this art that we call "computer science" to be a "real" science?

HP: I think for most scientists "inquiry" means exploration
    or looking for something entirely new in our experience.
    After all, modern scientific inquiry did not begin with
    logic but with the extension of our natural senses by
    instruments and by the extension of our natural imagination
    by mathematics.  Modern biology began with the microscope,
    chemistry with the analytic balance and chemical indicators,
    and physics with the telescope, theodolite, and mathematics.

Ah, the "2001: A Space Oddity" picture of science!
These instruments just fell from the sky one day,
and science began.  It would explain a lot of
this cargo cultism that I see about me today,
but I have another picture of the motion.

HP: Chronometers, galvanometers, spectroscope, mass spectrometers, centrifuges,
    chromatography, radioactive tracers, particle accelerators, and especially
    mathematics, are the essential prostheses for our senses and brains without
    which scientific inquiry would have come to a dead end like scholasticism.

Yes, I came to the university as a post-sputnik era math and physics major,
and so I heard all the same stories of history, read all the same romantic
accounts of our noble climb from pre-historical slime (=< 1901), but then
I made the "experiment" of actually going out and "observing" what was
actually laid down in some of the old "fossil pits", and lo and behold
I discovered that our "ascent" was far more gradual and rule-governed
than all these romantic novel-ists had been catechizing me to believe.

HP: The real problem for scientific inquiry is:  How do we know what are we looking for?
    This is an old problem.  Meno asked Socrates, "But how will you look for something
    when you don't in the least know what it is?  How on earth are you going to set up
    something you don't know as the object of your search?  To put it another way, even
    if you come right up against it, how will you know that what you have found is the
    thing you didn't know?"  This is the big question, but Socrates gives one of his
    sillier answers:  "The soul, since it is immortal and has been born many times,
    and has seen all things both here and in the other world, has learned everything
    that there is."  Therefore, he concludes:  "learning is nothing but recollection."

Here, now, Howard, you have, in your own inimitable way, a way that I would not even
dare to attempt to imitate, brought us to the very hub and nub of the Big Question.
So I will fortify myself with another cup of coffee, and return with anticipation.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

HP: It is not the metaphysics of reincarnation that is silly here (I'm in favor of it).
    It is Socrates' lack of understanding of problem identification.  As we are all too
    well aware today, if you don't know what you are looking for, access to an infinite
    database (no matter how well indexed, and whether it is in an immortal soul or in an
    infinitely fast computer) is not a solution.  In fact, the more the data, the worse
    the problem.  You still don't know what you are looking for.  I think Peirce worried
    about this problem too, but I don't think he found an adequate answer.  Jon may have
    another opinion.

HP: There have been two extreme approaches to this problem.
    At one extreme is the assumption of initial total ignorance.
    Then blind search and natural selection is the only hope.
    Of course, this requires many trials and memory of failures
    and successes (i.e., the Darwinian solution:  replication,
    heritable variation, and natural selection, also assumed by
    evolutionary epistemologists, a la Campbell, Popper, et al.).

HP: The other extreme, a physical equivalent of Socrates omniscient soul,
    is a Laplacean omnipotent determinism where free will and ignorance are
    just illusions and have nothing to do with the inexorable course of events.
    Neither of these extremes alone makes much sense in terms of current physics
    and biology.  Today the active controversy in evolution is over finding a suitable
    balance between chance and determinism, that is, between Darwinian blind search and
    selection and non-selective self-organizing (dynamic) processes.

HP: I think there are two misconceptions of the search problem.
    The first is that the search space it too large.  The main
    criticism of the creationists, intelligent design theists,
    and even the self-organizing anti-Darwinians, is that the
    search space for the totally ignorant is so large that
    successful blind search is too improbable.  But the
    evidence is clear that in the course of evolution
    organisms have greatly increased their searchable
    domains by adding more sensors and motor controls;
    and as I pointed out above, science also depends for
    its progress on greatly increasing its searchable domains
    by instrumentation.  Enlarging the searchable domain is not
    the problem, it is part of the answer to evolution and learning.
    What would be the evolutionary future of organisms if their inquiries
    were restricted to a fixed set of sensors (or a fixed logic)?

HP: The second misconception is that "blind" applies to the entire search process.
    But "blind" applies only to a simple initial event in a highly organized living
    system that has adapted to a highly ordered environment.  This is a genetic form
    or analog of intelligence.  Similarly, there is at some level in every creative
    idea a blind search, but usually in the context of highly developed problem domain.

HP: I think the most significant change in attitudes towards this balance between
    determinism and chance in the last 20 years has been the loss of dominance of
    logic-based, hard-programmed problem-solving, as in GOFAI (good old fashioned AI)
    and the renewed appreciation of the power of biological analogs like neural nets
    and genetic algorithms to discover solutions and integrate behaviors.

HP: Most important, however, has been the realization that blind search
    and selection requires strong, open-ended interactions with a rich,
    highly-ordered (i.e., descriptively compressible) environment (as has
    been partially simulated by environmentally "embedded autonomous robots")
    What is still missing in these robots is the open-ended ability to construct
    new sensors.  It appears that only with this unrestricted "sensing" of a rich,
    ordered environment does a balanced coupling of self-organization and blind search
    and natural selection become effective.

HP: Here are a few references on these points:

    Brooks, R., "Intelligence without reason."  In 12th Int. Conf. on AI, Morgan Kauffman, 1991.

    Campbell, D., "Evolutionary epistemology." In The Philosophy of Karl Popper, Schilpp, ed.,
    Open Court, 1974.

    Cariani, P. "Some epistemological implications of devices that construct their own sensors
    and effectors."  In Artificial Life II, Langton, et al, eds., Addison-Wesley, 1992.
    
    Clark, A., "Being there." MIT Press, 1997.

    Conrad, M., "The geometry of evolution." BioSystems 24, 61-81, 1990.

    Dawkins, R., "The evolution of evolution." Artificial life I, Langton, ed.,
    Addison-Wesley, 1989, p.201.

HP: This is one view of inquiry.  I suspect I am missing something about Jon's view.

JA: Well, I sorta thought we said this in the title,
    not to mention repeatedly throughout the article:

J&SA: | "Interpretation as Action: The Risk of Inquiry"
      |
      | The fallibility of signs is shared with the human activities of interpretation and inquiry,
      | and bears a relation to the situated character of all dynamic processes of determination.
      | |
      | | If doubt and indeterminateness were wholly within the mind --
      | | whatever that may signify -- purely mental processes ought
      | | to get rid of them.  But experimental procedure signifies
      | | that actual alteration of an external situation is necessary
      | | to effect the conversion.  A 'situation' undergoes, through
      | | operations directed by thought, transition from problematic
      | | to settled, from internal discontinuity to coherency and
      | | organization.  (Dewey, TQFC, p. 185).
      | |
      | | John Dewey, "The Quest for Certainty", in J.A. Boydston (ed.),
      | |'John Dewey:  The Later Works, 1925-1953, (Vol 4: 1929)',
      | | Southern Illinois University Press, Carbondale, IL, 1988.

JA: This attitude toward object reality derives from Peirce's ground-breaking,
    cornerstone-laying work to discern the "Logic of Science", real science,
    with which he was very much acquainted, however labeled or libeled as
    a "mere logician" he may've been by some people, who had been content
    until his time, as many still are, to lounge in their armchairs
    and listen to the facile fantasias of the Mills Brothers.

30 Jul 2001 • 14:22 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 30 Jul 2001 14:22:39 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy, SemioCom,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):

HP: Mishtu's has stated my problem.  How are we to use logical analysis
    in discovery?  How does Jon's and Peirce's approach differ from
    logic-based AI schemes?  I agree that logic can in some cases
    "tease out" some relations among our observations.  When we
    have an excessive amount of details, as in remote sensing
    and gene sequencing, then data-mining logic programs are
    essential.  But no physical laws have been discovered
    this way.  The number of relations is transcomputable.

HP: Mishtu says:  "My own, developing view of logic ... is that any given logic
    depends first  on making certain distinctions (cuts -- say distinction of
    right and left handedness in organic molecules), and that the logic follows
    depending on the cuts."

HP: Poincare agrees with him:  "Logic is nothing but the study of properties
    common to all classifications [cuts, distinctions, observables, etc.]."
    With the provision that,  "... the classification that is adopted is
    immutable."  Therefore, the logic can only follow the cuts and cannot
    escape from the given classifications.  I don't see how logic can make
    the cuts, as Jon's "autotomic axe" seems to suggest.  As I indicated,
    scientific inquiry, or looking for something unknown, is primarily
    a search for new classifications, new cuts, new observables.
    I don't see how logic helps at this stage of inquiry.
    It might even hinder.

Howard, I do not know how to communicate with you.
You are using the word "logic" to mean something
else than I do, and attaching that meaning to
the statements that I am trying to make about
what I call "logic".  Of course that cannot
preserve the sense that I intend to make.
When a person will not hear that one has
another meaning then novel communication
and communication of novelty will cease.

When I go into my local college bookstore and peruse
the textbooks of the subject called "logic" that are
being used today, I "discover", to no real surprise,
that they are almost exactly the same in content and
in scope as the ones that I first cracked open more
than thirty years ago, with the possible exception
of the CD of 'Tarski's World' or 'Turing's World'
tucked under the back cover flap.  You will get
no argument from me, logical XOR imaginative,
that this textbook subject called "logic" is
a pretty paltry panoply of petty principian
paste and pinchsnuff, barely powerful enough
to solve the artificially cooked up textbook
exercises that are spoon-fed through the text.

The sense in which you are using the word "logic" is a relatively "modern" innovation,
not really hammered into stone this way until after 1900, before which time the word
"logic" still bore a hint of the LOGOS, the Form, Formula, Ideal, Pattern, ..., that
the Ancients initially expressed by means of it.  It is not for no reason that the
challenging charge of Warren McCulloch, that blazing writing on the wall, so often
haunts my thoughts about what Logic might have been and what it ought to be again:

o~~~~~~~~~o~~~~~~~~~o~ARISBE~o~~~~~~~~~o~~~~~~~~~o

| Please remember that we are not now concerned with
| the physics and chemistry, the anatomy and physiology,
| of man.  They are my daily business.  They do not contribute
| to the logic of our problem.  Despite Ramon Lull's combinatorial
| analysis of logic and all of his followers, including Leibnitz with
| his universal characteristic and his persistent effort to build logical
| computing machines, from the death of William of Ockham logic decayed.
| There were, of course, teachers of logic.  The forms of the syllogism
| and the logic of classes were taught, and we shall use some of their
| devices, but there was a general recognition of their inadequacy to
| the problems in hand.  Russell says it was Jevons -- and Feibleman,
| that it was DeMorgan -- who said, "The logic of Aristotle is inadequate,
| for it does not show that if a horse is an animal then the head of the horse
| is the head of an animal."  To which Russell replies, "Fortunate Aristotle,
| for if a horse were a clam or a hydra it would not be so."  The difficulty
| is that they had no knowledge of the logic of relations, and almost none
| of the logic of propositions.  These logics really began in the latter
| part of the last century with Charles Peirce as their great pioneer.
| As with most pioneers, many of the trails he blazed were not followed
| for a score of years.  For example, he discovered the amphecks -- that
| is, "not both ... and ..." and "neither ... nor ...", which Sheffer
| rediscovered and are called by his name for them, "stroke functions".
| It was Peirce who broke the ice with his logic of relatives, from
| which springs the pitiful beginnings of our logic of relations of
| two and more than two arguments.  So completely had the traditional
| Aristotelian logic been lost that Peirce remarks that when he wrote
| the 'Century Dictionary' he was so confused concerning abduction, or
| apagoge, and induction that he wrote nonsense.  Thus Aristotelian logic,
| like the skeleton of Tom Paine, was lost to us from the world that it
| had engendered.  Peirce had to go back to Duns Scotus to start again
| the realistic logic of science.  Pragmatism took hold, despite its
| misinterpretation by William James.  The world was ripe for it.
| Frege, Peano, Whitehead, Russell, Wittgenstein, followed by a
| host of lesser lights, but sparked by many a strange character
| like Schroeder, Sheffer, Gödel, and company, gave us a working
| logic of propositions.  By the time I had sunk my teeth into
| these questions, the Polish school was well on its way to glory.
| In 1923 I gave up the attempt to write a logic of transitive verbs
| and began to see what I could do with the logic of propositions.
| My object, as a psychologist, was to invent a kind of least psychic
| event, or "psychon", that would have the following properties:  First,
| it was to be so simple an event that it either happened or else it did
| not happen.  Second, it was to happen only if its bound cause had happened --
| shades of Duns Scotus! -- that is, it was to imply its temporal antecedent.
| Third, it was to propose this to subsequent psychons.  Fourth, these were
| to be compounded to produce the equivalents of more complicated propositions
| concerning their antecedents.  (McCulloch, WIANTAMMKIAAMTHMKAN?, EOM, pages 7-8).
|
| Warren S. McCulloch,
|"What Is a Number that a Man May Know It,
| and a Man, that He May Know a Number",
| The Ninth Alfred Korzybski Memorial Lecture,
|'General Semantics Bulletin', Numbers 26 & 27,
| Institute of General Semantics, Lakeville, CT, 1961,
|'Embodiments of Mind', MIT Press, Cambridge, MA, 1965.
|
| http://stderr.org/pipermail/arisbe/2001-July/000704.html

31 Jul 2001 • 00:42 • Determination

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Determination
Date: Tue, 31 Jul 2001 00:42:21 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy, SemioCom,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Org, Comp, Aut, Et Alia ...

Here are the links to an online study that I began a while back
on Peirce's Theory Of Information, focusing especially on his
earliest ideas about "determination", a notion that I have
always suspected of information-theoretic tendencies, and
this even before I happened to notice its decisive use in
one of his most definitive definitions of a sign relation.

| A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Determination

http://suo.ieee.org/ontology/msg02377.html
http://suo.ieee.org/ontology/msg02378.html
http://suo.ieee.org/ontology/msg02379.html
http://suo.ieee.org/ontology/msg02380.html
http://suo.ieee.org/ontology/msg02384.html  \\ Generality
http://suo.ieee.org/ontology/msg02387.html  // Vagueness
http://suo.ieee.org/ontology/msg02388.html
http://suo.ieee.org/ontology/msg02389.html
http://suo.ieee.org/ontology/msg02390.html
http://suo.ieee.org/ontology/msg02391.html
http://suo.ieee.org/ontology/msg02395.html
http://suo.ieee.org/ontology/msg02407.html
http://suo.ieee.org/ontology/msg02550.html
http://suo.ieee.org/ontology/msg02552.html
http://suo.ieee.org/ontology/msg02556.html
http://suo.ieee.org/ontology/msg02594.html
http://suo.ieee.org/ontology/msg02651.html
http://suo.ieee.org/ontology/msg02673.html
http://suo.ieee.org/ontology/msg02706.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Semiotics Formalization & Sign Relations

http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html
http://suo.ieee.org/email/msg02621.html
http://suo.ieee.org/email/msg04442.html
http://suo.ieee.org/email/msg04529.html

Rambling Dialogues On Sign Relations

http://suo.ieee.org/ontology/msg02400.html
http://suo.ieee.org/ontology/msg02403.html
http://suo.ieee.org/ontology/msg02406.html
http://suo.ieee.org/ontology/msg02413.html
http://suo.ieee.org/ontology/msg02416.html
http://suo.ieee.org/ontology/msg02462.html
http://suo.ieee.org/ontology/msg02463.html
http://suo.ieee.org/ontology/msg02505.html
http://suo.ieee.org/ontology/msg02615.html

Reflection & Higher Order Sign Relations

http://suo.ieee.org/ontology/msg00625.html
http://suo.ieee.org/ontology/msg00703.html
http://suo.ieee.org/ontology/msg00973.html

31 Jul 2001 • 11:33 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Tue, 31 Jul 2001 11:33:47 -0400
From: Jon Awbrey
  To: Arisbe
  CC: Organization Complexity Autonomy, SemioCom,
      Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

That was certainly a long cup of coffee --
actuality, we had to go buy some wheels --
"Old Paint" has been put out to pasture --
where was I?

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: You continue to rush on ahead of my more plodding ways,
    and so I find that I have to keep taking your messages
    in several tries to get through their briar patches.

HP:  Take your time.  Ignore my old postings.  I haven't begun to read all your
     posts and links either.  Already your comments are reducing the dissonances.

That would definitely be a novel experience for me!

HP: I am not sure how I fit into this discussion.  Jon obviously has enough comments
    to answer without my adding more.  Anyway, here is another view of  inquiry.
    I am not sure how Jon's discussion of inquiry gets into the observable 
    world of science.

JA: Pragmaticians are "real" thinkers.  They guess that there is a world beyond them,
    that it has properties -- this is, a little Peirce tells me, the authorized sense
    of the word "real", as it was originally introduced into our culture's discourse.
    My own experience tells me that this "real world" will just keeping on thumping
    me in the head, as it were, until I pay attention to the features thereof, and
    this forces me, all against my initial inclination, to try to catch its drift.
    All the nets that I have to catch it with are made, in the end, of signs and
    the types of signs that we know as affects, concepts, impressions, or mental
    ideas, and so I must, per force aforesaid, contemplate the relations that
    insist, persist, subsist, or systematicaly exist among these arrays of
    so-called "real" objects, signs, and their host of interpretant signs.

IOU:  Insert about here a passage from "IDS: III" on the use of the term "real".

HP: Agreed, but only if "sign" is broadly defined as every actual interaction the
    environment has with the organism (physical, sensual, instinctive, semiotic, etc.).

Yes, as a slight bit of look-ahead in my mind's parser tells me, you are well aware that
the "pragmatic theory of signs" (PTOS) voices the word "sign" with just this expanse
of liberal breadth.  I occasionally use the phrase "data of the senses" (DOT) to
remind my self that all the DOTS that we connect in our percepts and concepts
are also examples of signs in this sense.  But this is not just another case
of gratuitous generalization.  What give the word "sign", in this employment,
a technical content, neither exploded nor imploded, and its utility as a term
of art is just what gives all of our other adoptions, borrowings, conversions,
or "liftings" of ordinary langauge to technical purposes their meaningful use
to these ends, to wit, a definition of some order, rough or sharp, whether
logical or pragmatic or hopefully both.

I have started trying to organize my online links.
There is the beginning of a cumulative accounting
appended to the end of this note.  Here is one
quick link on the "Definition Of A Sign":

http://suo.ieee.org/ontology/msg02034.html

Doleful experience has taught me that it is best to expand our focus a bit
to compass "sign relations", taken as wholes, over and above just isolated
signs, and taken at least at first in extension as sets of 3-tuples of the
form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" of
the "elementary sign relation" (ESR) <o, s, i>.

At this point, I personally find the comparsion with group theory to be compelling.
A "group" is another sort of set of 3-tuples that is subject to a terse definition,
and yet the theory of groups encompasses a wealth of imaginative possibilities and
utilitarian potentials that can scarcely be con-&-sur-veyed in any finite lifetime.

As it happens, one of my many "returns" to mathematics,
after a time in the wilds of philosophy and psychology,
was through the slits of "group representation theory",
but the tale thereby hanging is too long to pursue now.

True Story.  There was once in a university library that I knew quite intimately
a volume on "Group Theory" that had been rebound by the library staff and placed
on the shelves under the cover of "Group Therapy".  Moral Of The Story (MOTS):
The theory of signs is far from being the only subject to have this problem
of 'what'sin'a'name'.

HP: Incidentally, this universal use of "sign" by Peirce is one of the causes he is
    often misunderstood by scientists and mathematicians (as well as normal people)
    who are accustomed to normal usage that implies a non-arbitrary, causal or
    active (verbal, non-displaceable, spatially and temporally) relation to its
    referent (e.g., fever is a sign or signature or signifier of disease).

HP: A symbol usually implies an arbitrary passive (nominal, displaceable) relation
    to its referent.  This is consistent with etymology as well as common usage.
    (I think C.W. Morris develops this view.)

Charles Morris got this fever of signs from Peirce,
but what he did to remediate it is the subject of
many a 2nd, 3rd, 4th, ..., opinion, if not many
a knock-down-drag-out among and between analytic
and pragmatic doctors.  I will try to tiptoe
past the sleeping dogmas without pausing to
enumerate their heads ...

But I will need to introduce the technical distinctions and relations, deployed in PTOS,
of terms like "sign" (the genus), in relation to "icon", "index", "symbol" (the species):

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Semiotic SIG,

For future reference, here is a primer for the
classification of signs in Peircean semiotics:

| Sign
|    Index
|    Icon
|    Symbol
|       Term
|       Proposition
|       Argument
|          Deduction
|          Induction
|          Abduction

By "primer", of course, you may catch my drift
that the whole scheme of classification is set
to "blow up" from this point on, but this much
will do for start, and for my present purposes.

It needs to be understood that this scheme classifies
the aspects of functioning or the modes of being that
any sign may have to some degree, and that almost any
concrete token of a truly effective sign is likely to
have in a significant measure.  So let us not jump to
the facile conclusion that this scheme, or any of the
many schemes that develop, expand, and refine it, are
meant to be taken as mutually exclusive categories of
the signs themselves, even if the whole array of them
aspires, perhaps, to a certain form of exhaustiveness.

My immediate purpose, on the present occasion, is to
begin pinning down the slippery concept of a concept,
in other words, to provide our notions of a notion
with a provisional placement in the semiotic plan.

The way I see it (TWISI), a concept is just a sign
in the mind, in particular, a symbol, which is the
kind of a sign that depends for its interpretation
in an especially integral way on the sign relation
as a whole, which whole sign relation is typically
personified in the hypostasis of an "interpreter".

This means that a concept has a significant portion
of its properties accounted for by its standing as
a symbol, by the mere fact of its membership among
that non-exclusive tribe of signs called "symbols",
which it only partly derives from its mental locus,
and this aside from the manifest aspects of an index
or the manifold attributes of an icon that it has by
dint of being an "affection or impression of the soul".

http://suo.ieee.org/email/msg01111.html

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HP: For example, in mathematics we have the noun symbols, x, y, etc.
    and the verb signs, +, =, etc.  We speak of the "plus sign" because
    it is an operation (that must be performed where and when indicated),
    and the "symbol, x," because it stands, passively, wherever and whenever
    we write it, for whatever we choose.  We also speak of a "STOP sign" because
    in this case the symbol "STOP" is functioning as a verb, a non-displaceable
    operation (actually, it stands for an elliptical imperative sentence:
    "You STOP here and now.").  I won't go into Peirce's other numerous
    eccentric terminologies.

That's okay, I probably will.

I need to take a break here.
I kinda suspect you do, too.

Jon Awbrey

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HP: As a non-logician, it seems to me Jon is just inquiring into Peirce and
    logical strings and graphs.  If this is Peirce's main contribution I can
    understand  why scientists do not pay him much attention.  Inquiry to 
    most scientists does not really depend on this type of logical analysis, 
    but on imagination and observation.  I don't know of any cases of discovery 
    in science, or even mathematics, where logical analysis played the creative 
    role.  Of course, in math proofs require logic, but rarely is logic the
    source of the inquiry.

JA: I am guessing then that you are one of those who does not consider
    this art that we call "computer science" to be a "real" science?

HP: Again, if you don't want to make finer distinctions, then science can mean
    any form of knowledge, just like sign can mean any interaction with an agent.
    I think it is conceptually useful to make a distinction between formal, or
    purely syntactical activities, and activities that require observation or
    measurement. I think most mathematicians and computer theorists strive
    for purely formal systems that can be operated measurement-free and
    semantics-free.  I'm not sure about logicians.  Mostly they try to
    be formalists, but because they often use natural language, they
    cannot prevent tacit semantic biases from slipping in.  I think
    it is an open question whether complete formalism is possible,
    even in mathematics.  I doubt it.  But nevertheless, the ideal
    is worth imagining.

HP: I think for most scientists "inquiry" means exploration
    or looking for something entirely new in our experience.
    After all, modern scientific inquiry did not begin with
    logic but with the extension of our natural senses by
    instruments and by the extension of our natural imagination
    by mathematics.  Modern biology began with the microscope,
    chemistry with the analytic balance and chemical indicators,
    and physics with the telescope, theodolite, and mathematics.

JA: Ah, the "2001: A Space Oddity" picture of science!
    These instruments just fell from the sky one day,
    and science began.  It would explain a lot of
    this cargo cultism that I see about me today,
    but I have another picture of the motion.

HP: I don't appreciate the point of your sarcasm.  What did I actually say that you dispute?
    I did not mean to imply that instruments are sufficient for science, but I think they
    are necessary.  The naked eye sees very little of the universe, large and small.
    As an old instrument-maker myself (I designed and constructed the first compound
    x-ray optics the likes of which are used in the Chandra telescope:

    http://chandra.harvard.edu/

    I can assure you that instruments do not "just fall from the sky"
    (although Chandra will, literally, only too soon.)

HP: Chronometers, galvanometers, spectroscope, mass spectrometers, centrifuges,
    chromatography, radioactive tracers, particle accelerators, and especially
    mathematics, are the essential prostheses for our senses and brains without
    which scientific inquiry would have come to a dead end like scholasticism.

JA: Yes, I came to the university as a post-sputnik era math and physics major,
    and so I heard all the same stories of history, read all the same romantic
    accounts of our noble climb from pre-historical slime (=< 1901), but then
    I made the "experiment" of actually going out and "observing" what was
    actually laid down in some of the old "fossil pits", and lo and behold
    I discovered that our "ascent" was far more gradual and rule-governed
    than all these romantic novel-ists had been catechizing me to believe.

HP: I agree that too many intelligent students like you received a very bad education.
    I am glad you have learned to observe and inquire for yourself.

HP: The real problem for scientific inquiry is:  How do we know what are we looking for?
    This is an old problem.  Meno asked Socrates, "But how will you look for something
    when you don't in the least know what it is?  How on earth are you going to set up
    something you don't know as the object of your search?  To put it another way, even
    if you come right up against it, how will you know that what you have found is the
    thing you didn't know?"  This is the big question, but Socrates gives one of his
    sillier answers:  "The soul, since it is immortal and has been born many times,
    and has seen all things both here and in the other world, has learned everything
    that there is."  Therefore, he concludes:  "learning is nothing but recollection."

JA: Here, now, Howard, you have, in your own inimitable way, a way that I would not even
    dare to attempt to imitate, brought us to the very hub and nub of the Big Question.
    So I will fortify myself with another cup of coffee, and return with anticipation.

HP: I will also temporarily break off here and take a nap.

Yes, logic, by any other name, is known for its dormitive virtues.

o~~~~~~~~~o~~~~~~~~~o~CUMULATIO~o~~~~~~~~~o~~~~~~~~~o

Analytic Differential Ontology (ADO)

http://suo.ieee.org/ontology/msg00072.html
http://suo.ieee.org/ontology/msg00108.html

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Definition Of A Sign (DOAS)

http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg01224.html
http://suo.ieee.org/email/msg04442.html
http://suo.ieee.org/email/msg04529.html
http://suo.ieee.org/email/msg04807.html

Alternates --

http://suo.ieee.org/ontology/msg02034.html
http://stderr.org/pipermail/arisbe/2001-April/000414.html

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Determination

http://suo.ieee.org/ontology/msg02377.html
http://suo.ieee.org/ontology/msg02378.html
http://suo.ieee.org/ontology/msg02379.html
http://suo.ieee.org/ontology/msg02380.html
http://suo.ieee.org/ontology/msg02384.html
http://suo.ieee.org/ontology/msg02387.html
http://suo.ieee.org/ontology/msg02388.html
http://suo.ieee.org/ontology/msg02389.html
http://suo.ieee.org/ontology/msg02390.html
http://suo.ieee.org/ontology/msg02391.html
http://suo.ieee.org/ontology/msg02395.html
http://suo.ieee.org/ontology/msg02407.html
http://suo.ieee.org/ontology/msg02550.html
http://suo.ieee.org/ontology/msg02552.html
http://suo.ieee.org/ontology/msg02556.html
http://suo.ieee.org/ontology/msg02594.html
http://suo.ieee.org/ontology/msg02651.html
http://suo.ieee.org/ontology/msg02673.html
http://suo.ieee.org/ontology/msg02706.html

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Differential Analytic Turing Automata (DATA)

http://suo.ieee.org/email/msg03004.html
http://suo.ieee.org/email/msg03026.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Extensions of Logical Graphs (RefLog, DifLog, HopLog)

http://www.virtual-earth.de/CG/cg-list/msg03351.html
http://www.virtual-earth.de/CG/cg-list/msg03352.html
http://www.virtual-earth.de/CG/cg-list/msg03353.html
http://www.virtual-earth.de/CG/cg-list/msg03354.html
http://www.virtual-earth.de/CG/cg-list/msg03376.html
http://www.virtual-earth.de/CG/cg-list/msg03379.html
http://www.virtual-earth.de/CG/cg-list/msg03381.html

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Higher Order Sign Relations, Quotation, Reflection

http://suo.ieee.org/ontology/msg00625.html
http://suo.ieee.org/ontology/msg00703.html
http://suo.ieee.org/ontology/msg00973.html

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Painted Cacti & Propositional Calculus (PC&PC)

http://stderr.org/pipermail/arisbe/2001-January/000150.html

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Propositional Equation Reasoning Systems (PERS)

http://suo.ieee.org/email/msg04187.html
http://suo.ieee.org/email/msg04305.html
http://suo.ieee.org/email/msg04413.html
http://suo.ieee.org/email/msg04419.html
http://suo.ieee.org/email/msg04422.html
http://suo.ieee.org/email/msg04423.html
http://suo.ieee.org/email/msg04432.html
http://suo.ieee.org/email/msg04454.html
http://suo.ieee.org/email/msg04455.html
http://suo.ieee.org/email/msg04476.html
http://suo.ieee.org/email/msg04510.html
http://suo.ieee.org/email/msg04517.html
http://suo.ieee.org/email/msg04525.html
http://suo.ieee.org/email/msg04533.html
http://suo.ieee.org/email/msg04536.html
http://suo.ieee.org/email/msg04542.html
http://suo.ieee.org/email/msg04546.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Rambling Dialogues On Sign Relations

http://suo.ieee.org/email/msg01233.html
http://suo.ieee.org/email/msg02621.html
http://suo.ieee.org/email/msg04500.html

http://suo.ieee.org/ontology/msg02400.html
http://suo.ieee.org/ontology/msg02403.html
http://suo.ieee.org/ontology/msg02406.html
http://suo.ieee.org/ontology/msg02413.html
http://suo.ieee.org/ontology/msg02416.html
http://suo.ieee.org/ontology/msg02455.html
http://suo.ieee.org/ontology/msg02456.html
http://suo.ieee.org/ontology/msg02462.html
http://suo.ieee.org/ontology/msg02463.html
http://suo.ieee.org/ontology/msg02505.html
http://suo.ieee.org/ontology/msg02615.html

http://stderr.org/pipermail/arisbe/2001-June/000621.html
http://stderr.org/pipermail/arisbe/2001-June/000622.html
http://stderr.org/pipermail/arisbe/2001-June/000623.html
http://stderr.org/pipermail/arisbe/2001-June/000624.html

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Semiotics Formalization

http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Sequential Interactions Generating Hypotheses (SIGH's)

http://suo.ieee.org/email/msg02607.html
http://suo.ieee.org/email/msg02608.html
http://suo.ieee.org/email/msg03183.html

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Shroud of Turing (SOT)

http://suo.ieee.org/email/msg02714.html
http://suo.ieee.org/ontology/msg00308.html
http://www.virtual-earth.de/CG/cg-list/msg03669.html
http://www.virtual-earth.de/CG/cg-list/msg03677.html
http://stderr.org/pipermail/arisbe/2001-January/000167.html

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Sign Relations

http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html
http://suo.ieee.org/email/msg01224.html
http://suo.ieee.org/email/msg01233.html
http://suo.ieee.org/email/msg03033.html
http://suo.ieee.org/email/msg03111.html
http://suo.ieee.org/email/msg03381.html
http://suo.ieee.org/email/msg04442.html
http://suo.ieee.org/email/msg04529.html
http://suo.ieee.org/email/msg04807.html
http://suo.ieee.org/email/msg04810.html
http://suo.ieee.org/email/msg04812.html
http://suo.ieee.org/email/msg04813.html
http://suo.ieee.org/email/msg04820.html
http://suo.ieee.org/email/msg04823.html
http://suo.ieee.org/email/msg04869.html
http://suo.ieee.org/email/msg04870.html
http://suo.ieee.org/email/msg04912.html
http://suo.ieee.org/email/msg05020.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Signs, Information, Logic, Inquiry (SILI)

http://suo.ieee.org/email/msg02534.html
http://suo.ieee.org/email/msg02554.html
http://suo.ieee.org/email/msg02570.html
http://suo.ieee.org/email/msg02590.html

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Ultimate Reckoning Graph Engine (URGE)

http://stderr.org/pipermail/arisbe/2001-January/000168.html

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What Is Information That A Sign May Bear It?

http://stderr.org/pipermail/arisbe/2001-June/000616.html
http://stderr.org/pipermail/arisbe/2001-June/000617.html
http://stderr.org/pipermail/arisbe/2001-June/000618.html
http://stderr.org/pipermail/arisbe/2001-June/000619.html
http://stderr.org/pipermail/arisbe/2001-June/000620.html

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What Language To Use?
Sowa's Top Level Categories,
Sowa's TLC In And Out Of KIF

http://suo.ieee.org/email/msg01949.html
http://suo.ieee.org/email/msg01956.html
http://suo.ieee.org/email/msg01966.html
http://suo.ieee.org/email/msg02463.html
http://suo.ieee.org/email/msg02466.html

http://suo.ieee.org/ontology/msg00048.html
http://suo.ieee.org/ontology/msg00051.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Zeroth-Order Logic (ZOL)

http://suo.ieee.org/email/msg01406.html
http://suo.ieee.org/email/msg01546.html
http://suo.ieee.org/email/msg01561.html
http://suo.ieee.org/email/msg01670.html
http://suo.ieee.org/email/msg01739.html
http://suo.ieee.org/email/msg01966.html
http://suo.ieee.org/email/msg01985.html
http://suo.ieee.org/email/msg01988.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

31 Jul 2001 • 15:15 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Tue, 31 Jul 2001 15:15:06 -0400
From: Jon Awbrey
  To: Howard Pattee
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

I am splicing together the residual loose-ends that I can find of this thread.

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: You continue to rush on ahead of my more plodding ways,
    and so I find that I have to keep taking your messages
    in several tries to get through their briar patches.

HP: Take your time.  Ignore my old postings.  I haven't begun to read all your
    posts and links either.  Already your comments are reducing the dissonances.

JA: That would definitely be a novel experience for me!

HP: I am not sure how I fit into this discussion.  Jon obviously has enough comments
    to answer without my adding more.  Anyway, here is another view of  inquiry.  I am
    not sure how Jon's discussion of inquiry gets into the observable world of science.

JA: Pragmaticians are "real" thinkers.  They guess that there is a world beyond them,
    that it has properties -- this is, a little Peirce tells me, the authorized sense
    of the word "real", as it was originally introduced into our culture's discourse.
    My own experience tells me that this "real world" will just keeping on thumping
    me in the head, as it were, until I pay attention to the features thereof, and
    this forces me, all against my initial inclination, to try to catch its drift.
    All the nets that I have to catch it with are made, in the end, of signs and
    the types of signs that we know as affects, concepts, impressions, or mental
    ideas, and so I must, per force aforesaid, contemplate the relations that
    insist, persist, subsist, or systematicaly exist among these arrays of
    so-called "real" objects, signs, and their host of interpretant signs.

JA: Inserting here a passage from "IDS: III" on the use of the term "real":

| "Inquiry Driven Systems:  An Inquiry Into Inquiry", 1.3.4.14,
| "Application of OF [Objective Framework]:  Generic Level"
|
| In spite of the apparent duality between these patterns of
| composition, there is a significant asymmetry to be observed
| in the way that the insistent theme of realism interrupts the
| underlying genre.  To understand what this means, it is necessary
| to note that the strain of pragmatic thinking I am using here takes
| its definition of "reality" from the word's original Scholastic sources,
| where the adjective "real" means "having properties".  Taken in this sense,
| "reality" is necessary but not sufficient to "actuality", where the word
| "actual" means "existing in act and not merely potentially" (Webster's).
| To reiterate the same thing from the converse direction, actuality is
| sufficient but not necessary to reality.  The distinction between
| the two ideas is further pointed up by the fact that a potential
| can be real, and that its reality can be independent of any
| particular moment in which the power acts.
|
| These "angelic doctrines" would probably remain distant from
| the present concern, were it not for two points of connection:
|
| 1.  Relative to the present genre, the distinction of reality, that can
|     be granted to certain objects of thought and not to others, fulfills an
|     analogous role to the distinction that singles out "sets" among "classes"
|     in modern versions of set theory.  Taking the membership relation "€" as
|     a predecessor relation in a pre-designated hierarchy of classes, a class
|     attains the status of a set, and by dint of this becomes an object of
|     determinate discussion, simply if it has successors.  Pragmatic reality
|     is distinguished from both the medieval and the modern versions, however,
|     by the fact that its reality is always a reality to someone.  This is due
|     to the circumstance that it takes both an abstract property and a concrete
|     interpreter to establish the practical reality of an object.
|
| http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm

HP: Agreed, but only if "sign" is broadly defined as every actual interaction the
    environment has with the organism (physical, sensual, instinctive, semiotic, etc.).

JA: Yes, as a slight bit of look-ahead in my mind's parser tells me, you are well aware that
    the "pragmatic theory of signs" (PTOS) voices the word "sign" with just this expanse
    of liberal breadth.  I occasionally use the phrase "data of the senses" (DOTS) to
    remind my self that all the DOTS that we connect in our percepts and concepts
    are also examples of signs in this sense.  But this is not just another case
    of gratuitous generalization.  What gives the word "sign", in this employment,
    a technical content, neither exploded nor imploded, and its utility as a term
    of art is just what gives all of our other adoptions, borrowings, conversions,
    or "liftings" of ordinary langauge to technical purposes their meaningful use
    to these ends, to wit, a definition of some order, rough or sharp, whether
    logical or pragmatic or hopefully both.

JA: I have started trying to organize my online links.
    There is the beginning of a cumulative accounting
    appended to the end of this note.  Here is one
    quick link on the "Definition Of A Sign":

JA: http://suo.ieee.org/ontology/msg02034.html

JA: Doleful experience has taught me that it is best to expand our focus a bit
    to compass "sign relations", taken as wholes, over and above just isolated
    signs, and taken at least at first in extension as sets of 3-tuples of the
    form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" of
    the "elementary sign relation" (ESR) <o, s, i>.

JA: At this point, I personally find the comparsion with group theory to be compelling.
    A "group" is another sort of set of 3-tuples that is subject to a terse definition,
    and yet the theory of groups encompasses a wealth of imaginative possibilities and
    utilitarian potentials that can scarcely be con-&-sur-veyed in any finite lifetime.

JA: As it happens, one of my many "returns" to mathematics,
    after a time in the wilds of philosophy and psychology,
    was through the slits of "group representation theory",
    but the tale thereby hanging is too long to pursue now.

JA: True Story.  There was once in a university library that I knew quite intimately
    a volume on "Group Theory" that had been rebound by the library staff and placed
    on the shelves under the cover of "Group Therapy".  Moral Of The Story (MOTS):
    The theory of signs is far from being the only subject to have this problem
    of 'what'sin'a'name'.

HP: Incidentally, this universal use of "sign" by Peirce is one of the causes he is
    often misunderstood by scientists and mathematicians (as well as normal people)
    who are accustomed to normal usage that implies a non-arbitrary, causal or
    active (verbal, non-displaceable, spatially and temporally) relation to its
    referent (e.g., fever is a sign or signature or signifier of disease).

HP: A symbol usually implies an arbitrary passive (nominal, displaceable) relation
    to its referent.  This is consistent with etymology as well as common usage.
    (I think C.W. Morris develops this view.)

JA: Charles Morris got this fever of signs from Peirce,
    but what he did to remediate it is the subject of
    many a 2nd, 3rd, 4th, ..., opinion, if not many
    a knock-down-drag-out among and between analytic
    and pragmatic doctors.  I will try to tiptoe
    past the sleeping dogmas without pausing to
    enumerate their heads ...

JA: But I will need to introduce the technical distinctions and relations, deployed in PTOS,
    of terms like "sign" (the genus), in relation to "icon", "index", "symbol" (the species):

JA, quoting and correcting JA, outlining and interpreting CSP:

  | For future reference, here is a primer for the
  | classification of signs in Peircean semiotics:
  |
  |.Sign
  |....Icon
  |....Index
  |....Symbol
  |.......Term
  |.......Proposition
  |.......Argument
  |..........Abduction
  |..........Induction
  |..........Deduction
  |
  | Cf. Max Fisch, "Introduction", page xxxii, in C.S. Peirce,
  |'Writings of Charles S. Peirce: A Chronological Edition',
  |'Volume 1, 1857-1866', Peirce Edition Project,
  | Indiana University Press, Bloomington, IN, 1982.
  |
  | By "primer", of course, you may catch my drift
  | that the whole scheme of classification is set
  | to "blow up" from this point on, but this much
  | will do for a start, & for my present purposes.
  |
  | It needs to be understood that this scheme classifies
  | the aspects of functioning or the modes of being that
  | any sign may have to some degree, and that almost any
  | concrete token of a truly effective sign is likely to
  | have in a significant measure.  So let us not jump to
  | the facile conclusion that this scheme, or any of the
  | many schemes that develop, expand, and refine it, are
  | meant to be taken as mutually exclusive categories of
  | the signs themselves, even if the whole array of them
  | aspires, perhaps, to a certain form of exhaustiveness.
  |
  | My immediate purpose, on the present occasion, is to
  | begin pinning down the slippery concept of a concept,
  | in other words, to provide our notions of a notion
  | with a provisional placement in the semiotic plan.
  |
  | The way I see it (TWISI), a concept is just a sign
  | in the mind, in particular, a symbol, which is the
  | kind of a sign that depends for its interpretation
  | in an especially integral way on the sign relation
  | as a whole, which whole sign relation is typically
  | personified in the hypostasis of an "interpreter".
  |
  | This means that a concept has a significant portion
  | of its properties accounted for by its standing as
  | a symbol, by the mere fact of its membership among
  | that non-exclusive tribe of signs called "symbols",
  | which it only partly derives from its mental locus,
  | and this aside from the manifest aspects of an index
  | or the manifold attributes of an icon that it has by
  | dint of being an "affection or impression of the soul".
  |
  | http://suo.ieee.org/email/msg01111.html

HP: For example, in mathematics we have the noun symbols, x, y, etc.
    and the verb signs, +, =, etc.  We speak of the "plus sign" because
    it is an operation (that must be performed where and when indicated),
    and the "symbol, x," because it stands, passively, wherever and whenever
    we write it, for whatever we choose.  We also speak of a "STOP sign" because
    in this case the symbol "STOP" is functioning as a verb, a non-displaceable
    operation (actually, it stands for an elliptical imperative sentence:
    "You STOP here and now.").  I won't go into Peirce's other numerous
    eccentric terminologies.

JA: That's okay, I probably will.

HP: As a non-logician, it seems to me Jon is just inquiring
    into Peirce and logical strings and graphs.  If this is
    Peirce's main contribution I can understand why scientists
    do not pay him much attention.  Inquiry to most scientists
    does not really depend on this type of logical analysis,
    but on imagination and observation.  I don't know of any
    cases of discovery in science, or even mathematics, where
    logical analysis played the creative role.  Of course, in
    math proofs require logic, but rarely is logic the source
    of the inquiry.

JA: I am guessing then that you are one of those who does not consider
    this art that we call "computer science" to be a "real" science?

HP: Again, if you don't want to make finer distinctions, then science can mean
    any form of knowledge, just like sign can mean any interaction with an agent.
    I think it is conceptually useful to make a distinction between formal, or
    purely syntactical activities, and activities that require observation or
    measurement. I think most mathematicians and computer theorists strive
    for purely formal systems that can be operated measurement-free and
    semantics-free.  I'm not sure about logicians.  Mostly they try to
    be formalists, but because they often use natural language, they
    cannot prevent tacit semantic biases from slipping in.  I think
    it is an open question whether complete formalism is possible,
    even in mathematics.  I doubt it.  But nevertheless, the ideal
    is worth imagining.

HP: I think for most scientists "inquiry" means exploration
    or looking for something entirely new in our experience.
    After all, modern scientific inquiry did not begin with
    logic but with the extension of our natural senses by
    instruments and by the extension of our natural imagination
    by mathematics.  Modern biology began with the microscope,
    chemistry with the analytic balance and chemical indicators,
    and physics with the telescope, theodolite, and mathematics.

JA: Ah, the "2001: A Space Oddity" picture of science!
    These instruments just fell from the sky one day,
    and science began.  It would explain a lot of
    this cargo cultism that I see about me today,
    but I have another picture of the motion.

HP: I don't appreciate the point of your sarcasm.  What did I actually say that you dispute?
    I did not mean to imply that instruments are sufficient for science, but I think they
    are necessary.  The naked eye sees very little of the universe, large and small.
    As an old instrument-maker myself (I designed and constructed the first compound
    x-ray optics the likes of which are used in the Chandra telescope:

    http://chandra.harvard.edu/

    I can assure you that instruments do not "just fall from the sky"
    (although Chandra will, literally, only too soon.)

HP: Chronometers, galvanometers, spectroscope, mass spectrometers, centrifuges,
    chromatography, radioactive tracers, particle accelerators, and especially
    mathematics, are the essential prostheses for our senses and brains without
    which scientific inquiry would have come to a dead end like scholasticism.

JA: Yes, I came to the university as a post-sputnik era math and physics major,
    and so I heard all the same stories of history, read all the same romantic
    accounts of our noble climb from pre-historical slime (=< 1901), but then
    I made the "experiment" of actually going out and "observing" what was
    actually laid down in some of the old "fossil pits", and lo and behold
    I discovered that our "ascent" was far more gradual and rule-governed
    than all these romantic novel-ists had been catechizing me to believe.

HP: I agree that too many intelligent students like you received a very bad education.
    I am glad you have learned to observe and inquire for yourself.

HP: The real problem for scientific inquiry is:  How do we know what are we looking for?
    This is an old problem.  Meno asked Socrates, "But how will you look for something
    when you don't in the least know what it is?  How on earth are you going to set up
    something you don't know as the object of your search?  To put it another way, even
    if you come right up against it, how will you know that what you have found is the
    thing you didn't know?"  This is the big question, but Socrates gives one of his
    sillier answers:  "The soul, since it is immortal and has been born many times,
    and has seen all things both here and in the other world, has learned everything
    that there is."  Therefore, he concludes:  "learning is nothing but recollection."

JA: Here, now, Howard, you have, in your own inimitable way, a way that I would not even
    dare to attempt to imitate, brought us to the very hub and nub of the Big Question.
    So I will fortify myself with another cup of coffee, and return with anticipation.

HP: I will also temporarily break off here and take a nap.

JA: Yes, logic, by any other name, is known for its dormitive virtues.

I'm back ...

On my application to graduate school the last time around, in Systems Engineering,
I was requested to submit a few written pages by way of an "Interest Statement".
I probably don't have to tell you what happened next.  Here is an excerpt
from the little essay that issued forth:

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Inquiring Minds,

This selection explains the notion of a "knowledge field" (KF) and
brings us back through the point where we first came in, with the
problematics that are classically illustrated in Plato's 'Meno'.

| Document History:
|
| Project:  Intelligent Dynamic Systems Engineering
| Heading:  Systems Engineering: Interest Statement
| Contact:  Jon Awbrey
| Version:  Draft 5.0
| Created:  1991-Nov-12
| Revised:  1992-Sep-01
| Revised:  2001-Jan-06
| Setting:  Oakland University, Rochester, Michigan, USA
| Excerpt:  Pages 4-7

1.1.2.1  Vector Field & Control System

Dynamically, as in a control system, intelligence is a decision process that
selects an indicator of a tangent vector to follow at a point or a descriptor
of a corresponding operator to apply at a point.  The pointwise indicators
or descriptors can be any relevant signs or symbolic expressions:  names,
code numbers, address pointers, or quoted phrases.  A "vector field" attaches
to each point of phase space a single tangent vector or differential operator.
The "control system" is viewed as a ready generalization of a vector field, in
which whole sets of tangent vectors or differential operators are attached to
each point of phase space.  The "strategy" or "policy problem" of a controller
is to pick out one of these vectors to actualize at each point in accord with
reaching a given target or satisfying a given property.  An individual control
system is specified by information attached to each dynamic point that defines
a subset of the tangent space at that point.  This pointwise defined subset is
called "the indicatrix of permissible velocities" by (Arnold, 1986, ch. 11).

In the usage needed for combining AI and control systems to obtain
autonomous intelligent systems, it is important to recognize that the
pointwise indicators and descriptors must eventually have the character
of symbolic expressions existing in a language of non-trivial complexity.
Relating to this purpose, it does not really matter if their information
is viewed as represented in the states of discrete machines or in the
states of physical systems to which real and complex valued measurements
are attributed.  What makes the system of indications and descriptions
into a language is that its elements obey specific sets of axioms that
come to be recognized as characterizing interesting classes of symbol
systems.  Later on I will indicate one very broad definition of signs 
and symbol systems that I favor.  I find that this conception of signs
and languages equips the discussion of intelligent systems with an
indispensable handle on the levels of complexity that arise in their
description, analysis, and clarification.

1.1.2.2  Fields of Information & Knowledge

Successive extensions of the vector field concept can be achieved by 
generalizing the form of pointwise information defined on a phase space.
A subset of a tangent space at a point can be viewed as a boolean-valued
function there, and as such can be generalized to a probability distribution
that is defined on the tangent space at that point.  This type of probabilistic
vector field or "information field" founds the subject of stochastic differential
geometry and its associated dynamic systems.  An alternate development in this
spirit might embody pointwise information about tangent vectors in the form of
linguistic expressions and ultimately in knowledge bases with the character of
empirical summaries or logical theories attached to each point of a phase space.

It is convenient to bring together under the heading of a "knowledge field" any
form of pointwise information, symbolic or numerical, concrete or theoretical,
that constrains the set of pointwise tangent vectors defined on a phase space.
In computational settings this information can be procedural and declarative
program code augmented by statistical and qualitative data.  In computing
applications a knowledge field acquires an aptly suggestive visual image:
bits and pieces of code and data elements sprinkled on a dynamic surface,
like bread crumbs to be followed through a forest.  The rewards and dangers
of so literally a "distributed" manner of information storage are extremely
well-documented (Hansel & Gretel, n.d.), but there are times when it provides
the only means available.

1.1.2.3  The Trees & The Forest

A sticking point of the whole discussion has just been
reached.  In the idyllic setting of a knowledge field the
question of systematic inquiry takes on the following form:

What piece of code should be followed in order to discover that code?

It is a classic catch, whose pattern was traced out long ago in the paradox
of Plato's 'Meno'.  Discussion of this dialogue and of the task it sets for
AI, cognitive science, education, including the design of intelligent tutoring
systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86),
(Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991).
Though it appears to mask a legion of diversions, this text will present itself at
least twice more in the current engagement, both on the horizon and at the gates
of the project to fathom and to build intelligent systems.  Therefore, it is
worth recalling how this inquiry begins.  The interlocutor Meno asks:

| Can you tell me, Socrates, whether virtue can be taught,
| or is acquired by practice, not teaching?  Or if neither
| by practice nor by learning, whether it comes to mankind
| by nature or in some other way?  (Plato, 'Meno', p. 265).

Whether the word "virtue" (arete) is interpreted to mean virtuosity
in some special skill or a more general excellence of conduct, it is
evidently easy, in the understandable rush to "knowledge", to forget
or to ignore what the primary subject of this dialogue is.  Only when
the difficulties of the original question, whether virtue is teachable,
have been moderated by a tentative analysis does knowledge itself become
a topic of the conversation.  This hypothetical mediation of the problem
takes the following tack:  If virtue were a kind of knowledge, and if
every kind of knowledge could be taught, would it not follow that
virtue could be taught?

For the present purpose, it should be recognized that this "trial factorization"
of a problem space or phenomenal field is an important intellectual act in itself,
one that deserves attention in the effort to understand the competencies that
support intelligent functioning.  It is a good question to ask just what sort
of reasoning processes might be involved in the ability to find such a middle
term, as is served by "knowledge" in the example at hand.  Generally speaking,
interest will reside in a whole system of middle terms, which might be called
a "medium" of the problem domain or the field of phenomena.  This usage makes
plain the circumstance that the very recognition and expression of a problem
or phenomenon is already contingent upon and complicit with a particular set
of hypotheses that will inform the direction of its resolution or explanation.

One of the chief theoretical difficulties that obstructs the unification of
logic and dynamics in the study of intelligent systems can be seen in relation
to this question of how an intelligent agent might generate tentative but plausible
analyses of problems that confront it.  As described here, this requires a capacity
for identifying middle grounds that ameliorate or mollify a problem.  This facile
ability does not render any kind of demonstrative argument to be trusted in the
end and for all time, but is a temporizing measure, a way of locating test media
and of trying cases in the media selected.  It is easy to criticize such practices,
to say that every argument should be finally cast into a deductively canonized form,
harder to figure out how to live in the mean time without using such half-measures
of reasoning.  There is a line of thinking, extending from this reference point
in Plato through a glancing remark by Aristotle to the notice of C.S. Peirce,
which holds that the form of reasoning required to accomplish this feat is
neither inductive nor deductive and reduces to no combination of the two,
but is an independent type.

Aristotle called this form of reasoning "apagogy" ('Prior Analytics', 2.25)
and it was variously translated throughout the Middle Ages as "reduction" or
"abduction".  The sense of "reduction" here is just that by which one question
or problem is said to reduce to another, as in the AI strategy of goal reduction.
Abductive reasoning is also involved in the initial creation or apt generation of
hypotheses, as in diagnostic reasoning.  Thus, it is natural that abductive reasoning
has periodically become a topic of interest in AI and cognitive modeling, especially
in the effort to build expert systems that simulate and assist diagnosis, whether in
human medicine, auto mechanics, or electronic trouble-shooting.  Recent explorations
in this vein are exemplified by (Peng & Reggia, 1990) and (O'Rorke, 1990).

But there is another reason why the factorization problem presents an especially
acute obstacle to progress in the system-theoretic approach to AI.  When the states
of a system are viewed as a manifold it is usual to imagine that everything factors
nicely into a base manifold and a remainder.  Smooth surfaces come to mind, a single
clear picture of a system that is immanently good for all time.  But this is how an
outside observer might see it, not how it appears to the inquiring system that is
located in a single point and has to discover, starting from there, the most fitting
description of its own space.  The proper division of a state vector into basic and
derivative factors is itself an item of knowledge to be discovered.  It constitutes
a piece of interpretive knowledge that has a large part in determining exactly how
an agent behaves.  The tentative hypotheses that an agent spins out with respect to
this issue will themselves need to be accommodated in a component of free space that
is well under control.  Without a stable theater of action for entertaining hypotheses,
an agent finds it difficult to sustain interest in the kinds of speculative bets that
are required to fund a complex inquiry.

States of information with respect to the placement of this fret or fulcrum can
vary with time.  Indeed, it is a goal of the knowledge directed system to leverage
this chordal node toward optimal possibilities, and this normally requires a continuing
interplay of experimental variations with attunement to the results.  Therefore it seems
necessary to develop a view of manifolds in which the location or depth of the primary
division that is effective in explaining behavior can vary from moment to moment.
The total phenomenal state of a system is its most fundamental reality, but the
way in which these states are connected to make a space, with information that
metes out distances, portrays curvatures, and binds fibers into bundles --
all this is an illusion projected onto the mist of individual states
from items of code in the knowledge component of the current state.

The mathematical and computational tools needed to implement such a perspective
goes beyond the understanding of systems and their spaces that I currently have
in my command.  It is considered bad form for a workman to blame his tools, but
in practical terms there continues to be room for better design.  The languages
and media that are made available do, indeed, make some things easier to see,
to say, and to do than others, whether it is English, Pascal (Wirth, 1976),
or Hopi (Whorf, 1956) that is being spoken.  A persistent attention to this
pragmatic factor in epistemology will be necessary to implement the brands
of knowledge-directed systems whose intelligence can function in real time.
To provide a computational language that can help to clarify these problems
is one of the chief theoretical tasks that I see for myself in the work ahead.

A system moving through a knowledge field would ideally be equipped with
a strategy for discovering the structure of that field to the greatest extent
possible.  That ideal strategy is a piece of knowledge, a segment of code existing
in the knowledge space of every point that has this option within its potential.
Does discovery mark only a different awareness of something that already exists,
a changed attitude toward a piece of knowledge already possessed?  Or can it be
something more substantial?  Are genuine invention and proper extensions of the
shared code possible?  Can intelligent systems acquire pieces of knowledge that
are not already in their possession, or in their potential to know?

If a piece of code is near at hand, within a small neighborhood of a system's place in
a knowledge field, then it is easy to see a relationship between adherence and discovery.
It is possible to picture how crumbs of code could be traced back, accumulated, and gradually
reassembled into whole slices of the desired program.  But what if the required code is more
distant?  If a system is observed in fact to drift toward increasing states of knowledge,
does its disposition toward knowledge as a goal need to be explained by some inherent
attraction of knowledge?  Do potential fields and propagating influences have to be
imagined in order to explain the apparent action at a distance?  Do massive bodies
of knowledge then naturally form, and eventually come to dominate whole knowledge
fields?  Are some bodies of knowledge intrinsically more attractive than others?
Can inquiries get so serious that they start to radiate gravity?

Questions like these are only ways of probing the range of possible systems that
are implied by the definition of a knowledge field.  What abstract possibility best
describes a given concrete system is a separate, empirical question.  With luck, the
human situation will be found among the reasonably learnable universes, but before that
hope can be evaluated a lot remains to be discovered about what, in fact, may be learnable
and reasonable.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

HP: It is not the metaphysics of reincarnation that is silly here (I'm in favor of it).
    It is Socrates' lack of understanding of problem identification.  As we are all too
    well aware today, if you don't know what you are looking for, access to an infinite
    database (no matter how well indexed, and whether it is in an immortal soul or in an
    infinitely fast computer) is not a solution.  In fact, the more the data, the worse
    the problem.  You still don't know what you are looking for.  I think Peirce worried
    about this problem too, but I don't think he found an adequate answer.  Jon may have
    another opinion.

HP: There have been two extreme approaches to this problem.
    At one extreme is the assumption of initial total ignorance.
    Then blind search and natural selection is the only hope.
    Of course, this requires many trials and memory of failures
    and successes (i.e., the Darwinian solution:  replication,
    heritable variation, and natural selection, also assumed by
    evolutionary epistemologists, a la Campbell, Popper, et al.).

HP: The other extreme, a physical equivalent of Socrates omniscient soul,
    is a Laplacean omnipotent determinism where free will and ignorance are
    just illusions and have nothing to do with the inexorable course of events.
    Neither of these extremes alone makes much sense in terms of current physics
    and biology.  Today the active controversy in evolution is over finding a suitable
    balance between chance and determinism, that is, between Darwinian blind search and
    selection and non-selective self-organizing (dynamic) processes.

HP: I think there are two misconceptions of the search problem.
    The first is that the search space it too large.  The main
    criticism of the creationists, intelligent design theists,
    and even the self-organizing anti-Darwinians, is that the
    search space for the totally ignorant is so large that
    successful blind search is too improbable.  But the
    evidence is clear that in the course of evolution
    organisms have greatly increased their searchable
    domains by adding more sensors and motor controls;
    and as I pointed out above, science also depends for
    its progress on greatly increasing its searchable domains
    by instrumentation.  Enlarging the searchable domain is not
    the problem, it is part of the answer to evolution and learning.
    What would be the evolutionary future of organisms if their inquiries
    were restricted to a fixed set of sensors (or a fixed logic)?

HP: The second misconception is that "blind" applies to the entire search process.
    But "blind" applies only to a simple initial event in a highly organized living
    system that has adapted to a highly ordered environment.  This is a genetic form
    or analog of intelligence.  Similarly, there is at some level in every creative
    idea a blind search, but usually in the context of highly developed problem domain.

HP: I think the most significant change in attitudes towards this balance between
    determinism and chance in the last 20 years has been the loss of dominance of
    logic-based, hard-programmed problem-solving, as in GOFAI (good old fashioned AI)
    and the renewed appreciation of the power of biological analogs like neural nets
    and genetic algorithms to discover solutions and integrate behaviors.

HP: Most important, however, has been the realization that blind search
    and selection requires strong, open-ended interactions with a rich,
    highly-ordered (i.e., descriptively compressible) environment (as has
    been partially simulated by environmentally "embedded autonomous robots")
    What is still missing in these robots is the open-ended ability to construct
    new sensors.  It appears that only with this unrestricted "sensing" of a rich,
    ordered environment does a balanced coupling of self-organization and blind search
    and natural selection become effective.

HP: Here are a few references on these points:

    Brooks, R., "Intelligence without reason."  In 12th Int. Conf. on AI, Morgan Kauffman, 1991.

    Campbell, D., "Evolutionary epistemology." In The Philosophy of Karl Popper, Schilpp, ed.,
    Open Court, 1974.

    Cariani, P. "Some epistemological implications of devices that construct their own sensors
    and effectors."  In Artificial Life II, Langton, et al, eds., Addison-Wesley, 1992.
    
    Clark, A., "Being there." MIT Press, 1997.

    Conrad, M., "The geometry of evolution." BioSystems 24, 61-81, 1990.

    Dawkins, R., "The evolution of evolution." Artificial life I, Langton, ed.,
    Addison-Wesley, 1989, p.201.

HP: This is one view of inquiry.  I suspect I am missing something about Jon's view.

31 Jul 2001 • 17:02 • Inquiry Into Models

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: OCA: Re: Inquiry Into Models
Date: Tue, 31 Jul 2001 17:02:42 -0400
From: H H Pattee
  To: Organization Complexity Autonomy

I would like to wind up a hanging tail or thread
that Jon finds "too long to pursue now." 

At 11:33 AM 7/31/01 -0400, Jon wrote:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

At this point, [defining sign as a triad:of 3-tuples of the 

form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign"] I personally 
find the comparsion with group theory to be compelling.

  As it happens, one of my many "returns" to mathematics,
  after a time in the wilds of philosophy and psychology,
  was through the slits of "group representation theory",
  but the tale thereby hanging is too long to pursue now.

Let me pursue it briefly because it relates closely to what science
is all about.  Group representation theory is a theory of homomorphisms,
or how one formal structure can be mapped into another formal structure
so that interesting or significant properties are preserved.  If the
mapping (image, observation, projection, coding, measurement) is from
a physical system (i.e., matter and energy in space and time) to a formal
system then we have an physical model. Here is Hertz's statement
of this epistemic homomorphism (formally a commutation relation):

"We form for ourselves images or symbols of external objects; and the form which we give them is such that the logically
necessary (denknotwendigen) consequents of the images in thought are always the images of the necessary natural
(naturnotwendigen) consequents of the thing pictured."

"For our purpose it is not necessary that they [the images] should be in conformity with the [external] things in any other
respect whatever. As a matter of fact, we do not know, nor have we any means of knowing, whether our conception of
things [our models] are in conformity with them [external things] in any other than this one fundamental respect." [H.
Hertz (1857-1894), The Principles of Mechanics, Dover, NY, 1984, pp.1-2; orig. German ed., Prinzipien Mechanik,
1894]

This is a terse statement. A commutation diagram makes it clearer:

EXTERNAL   _____ WE FORM FOR _____IMAGES OR SYMBOLS,  PICTURES                        
OBJECTS                   OURSELVES . . .         [SIGNS, BRAIN STATES, WHATEVER]
      |                                                               /                            |
      |                                                             /                              |
[NATURAL LAWS]    . . . SUCH THAT . . .     [LOGIC, MATHEMATICAL MODEL]    
      |                              /                                                             |
NECESSARY           /                                                               |
NATURAL             /                                                                  |                                                                        
CONSEQUENTS ____ARE THE SAME AS____THE LOGICALLY NECESSARY 
                                                                               CONSEQUENTS OF THE MODEL

"WE FORM FOR OURSELVES . . ." includes all forms of sensing, perception observation, measurement, coding, etc.
which must be initiated by an agent or organism. In physics, this is the essential cut between the world and the observer
that is necessary whenever a measurement is made. It cannot be considered as resulting from natural laws. That is why
there is a "measurement problem" in physics.

Jon's (Peirce's?) definition of sign as a triad, <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" might corresponds
to the first line of the above diagram, but there is no model or homomorphism, which is why I find it epistemologically
inadequate. Peirce's definition of sign is too vague and ambiguous for me to unravel. When he has more time, perhaps Jon
could diagram it, and say what "determined or created by" constructively entails. And what implements the "sort of
correspondence" that Peirce has in mind? Peirce's definition:

| A sign is something, 'A', 
| which brings something, 'B', 
| its 'interpretant' sign 
| determined or created by it, 
| into the same sort of correspondence 
| with something, 'C', its 'object', 
| as that in which itself stands to 'C'. 

Howard

31 Jul 2001 • 21:33 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Tue, 31 Jul 2001 21:33:46 -0400
From: Jon Awbrey
  To: Sam Hunting
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Sam Hunting wrote (SH):
Jon Awbrey wrote (JA):

JA: Here is one quick link on the "Definition Of A Sign":

    http://suo.ieee.org/ontology/msg02034.html

SH: A question from the peanut gallery:

    What is a relational property?

    Thanks!  (No need for one of your wonderful punning extended essays -- KISS.)

SH, quoting LW:

  | "To imagine a language is to imagine a form of life."
  |  Ludwig Wittgenstein, Philosophical Investigations

A relational property is just a property that something has
by virtue of being in a relation at the moment in question.
In effect, this is really just another way of saying that
something is related to something in the specified way.

For example, "mi" is a name I call myself, that is to say,
a sign that reminds me of me, at the moment when somebody
while singing a song has led me to interpret "mi" as "me".
In this moment is actualized the sign relational 3-tuple
<me, "mi", "me"> of the form <object, sign, interpretant>.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Incidental Musement:

http://www.stratfordfestival.ca/2001/playbill/soundofmusic.html

01 Aug 2001 • 01:11 • Inquiry Into Models

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Models
Date: Wed, 01 Aug 2001 01:11:32 -0400
From: Jon Awbrey
  To: Arisbe, Organization Complexity Autonomy
  CC: SemioCom, Standard Upper Ontology, Topic Map Mail

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Jon Awbrey wrote (JA):
Howard Pattee wrote (HP):
Heinrich Hertz wrote (HH):
Jon Awbrey did not write (~JA):
Charles Sanders Peirce wrote (CSP):

HP: I would like to wind up a hanging tail or thread
    that Jon finds "too long to pursue now."

JA: Doleful experience has taught me that it is best to expand our focus a bit
    to compass "sign relations", taken as wholes, over and above just isolated
    signs, and taken at least at first in extension as sets of 3-tuples of the
    form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" of
    the "elementary sign relation" (ESR) <o, s, i>.

JA: At this point, I personally find the comparsion with group theory to be compelling.
    A "group" is another sort of set of 3-tuples that is subject to a terse definition,
    and yet the theory of groups encompasses a wealth of imaginative possibilities and
    utilitarian potentials that can scarcely be con-&-sur-veyed in any finite lifetime.

JA: As it happens, one of my many "returns" to mathematics,
    after a time in the wilds of philosophy and psychology,
    was through the slits of "group representation theory",
    but the tale thereby hanging is too long to pursue now.

~JA: defining sign as a triad: of 3-tuples of the form <o, s, i>,
     with o, s, i the "object", "sign", "interpretant sign"

HP: Let me pursue it briefly because it relates closely to what science is
    all about.  Group representation theory is a theory of homomorphisms, or
    how one formal structure can be mapped into another formal structure so
    that interesting or significant properties are preserved.  If the mapping
    (image, observation, projection, coding, measurement) is from a physical
    system (i.e., matter and energy in space and time) to a formal system
    then we have a physical model.  Here is Hertz's statement of this
    epistemic homomorphism (formally a commutation relation):

HH: | We form for ourselves images or symbols of external objects;
    | and the form which we give them is such that the logically
    | necessary (denknotwendigen) consequents of the images in
    | thought are always the images of the necessary natural
    | (naturnotwendigen) consequents of the thing pictured.
    |
    | For our purpose it is not necessary that they [the images] should be
    | in conformity with the [external] things in any other respect whatever.
    | As a matter of fact, we do not know, nor have we any means of knowing,
    | whether our conception of things [our models] are in conformity with
    | them [external things] in any other than this one fundamental respect.
    |
    | H. Hertz (1857-1894),
    |'The Principles of Mechanics', Dover, NY, 1984, pp. 1-2;
    | orig. German ed., 'Prinzipien Mechanik', 1894.

HP: This is a terse statement.  A commutation diagram makes it clearer:

Howard, this diagram seems to have been messed up by your line wrap.

> EXTERNAL   _____ WE FORM FOR _____ IMAGES OR SYMBOLS,  PICTURES
> OBJECTS          OURSELVES   . . . [SIGNS, BRAIN STATES, WHATEVER]
>       |                                                               /
> |
>       |                                                             /
> |
> [NATURAL LAWS]    . . . SUCH THAT . . .     [LOGIC, MATHEMATICAL MODEL]
>       |                              /
> |
> NECESSARY           /                                              |
> NATURAL             /
> |
> CONSEQUENTS ____ARE THE SAME AS____THE LOGICALLY NECESSARY CONSEQUENTS OF THE MODEL

HP: "WE FORM FOR OURSELVES ..." includes all forms of sensing, perception,
    observation, measurement, coding, etc. which must be initiated by an
    agent or organism.  In physics, this is the essential cut between the
    world and the observer that is necessary whenever a measurement is made.
    It cannot be considered as resulting from natural laws.  That is why there
    is a "measurement problem" in physics.

HP: Jon's (Peirce's?) definition of sign as a triad, <o, s, i>, with
    o, s, i the "object", "sign", "interpretant sign" might correspond
    to the first line of the above diagram, but there is no model or
    homomorphism, which is why I find it epistemologically inadequate.
    Peirce's definition of sign is too vague and ambiguous for me to
    unravel.  When he has more time, perhaps Jon could diagram it,
    and say what "determined or created by" constructively entails.
    And what implements the "sort of correspondence" that Peirce
    has in mind?  Peirce's definition:

CSP: | A sign is something, 'A',
     | which brings something, 'B',
     | its 'interpretant' sign
     | determined or created by it,
     | into the same sort of correspondence
     | with something, 'C', its 'object',
     | as that in which itself stands to 'C'.
     |
     | CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
     | http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm

Howard, please excuse me if I wax a bit tetchy at this point --
as nobody knows the troubles I've seen over this one scruple --
and not all of the obscurities that one finds being credited
to Peirce are really the obscurities of Peirce, nor even due
to his way of writing, which I think is admirably clear here.

This is a perfectly good -- ok, a nearly perfectly good -- mathematical definition
of a particular family of combinatorial structures, that I know as "sign relations".

A sign relation L is a SET of 3-tuples of the form <o, s, i>,
where o is an element of the set O, called the "object domain",
where s is an element of the set S, called the "sign domain", and
where i is an element of the set I, called the "interpretant domain".

In other words, a sign relation L is a SUBSET of the cartesian product OxSxI,
a circumstance which Asciians write as "L c OxSxI".

Thus CSP did not say, and JA will not say, assertively, what JA mentions here
in the form of a statement that says "a sign is a triad of the form <o, s, i>",
nor any such thing as that.

Many of these further issues are tackled in the running accumulation of links
that I have already posted, but I will admit that the dialogical organization
of some of these sub-sutras is not always the best for finding quick answers,
and so I will work on extracting some more caustically focused e-lucidations.

The link-o-rama that I started on the topic of "Determination" is meant to begin
addressing what Peirce meant by "determined or created" in this sign definition,
and also elsewhere, in general.

To make a long story short, what Peirce means by "correspondence" in this definition
is just the whole 3-adic sign relation itself, which he occasionally describes as
a "triple correspondence".  He does not mean to suggest any sort of pallid 2-adic
"imaging" or "mirrortying" as implicated in a "correspondence notion of truth".

The issues that you raise at the end of your note are related to those
that I tried to raise once in the SUO Forum, without much success, but
hope springs eternal and all that, so here is how I tried to spring it:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Computable Manifolds & Discrete Topologies

http://suo.ieee.org/ontology/msg01383.html
http://suo.ieee.org/ontology/msg01405.html
http://suo.ieee.org/ontology/msg01440.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Manifolds Of Sensuous Impressions (MOSI's)

http://suo.ieee.org/ontology/msg01392.html
http://suo.ieee.org/ontology/msg01397.html
http://suo.ieee.org/ontology/msg01399.html
http://suo.ieee.org/ontology/msg01422.html
http://suo.ieee.org/ontology/msg01461.html
http://suo.ieee.org/ontology/msg01476.html
http://suo.ieee.org/ontology/msg01490.html
http://suo.ieee.org/ontology/msg01579.html

Alternates --

http://stderr.org/pipermail/arisbe/2001-March/000341.html
http://stderr.org/pipermail/arisbe/2001-March/000342.html
http://stderr.org/pipermail/arisbe/2001-March/000343.html
http://stderr.org/pipermail/arisbe/2001-March/000344.html
http://stderr.org/pipermail/arisbe/2001-March/000349.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Reference Material --

Sign Relations, Extensional Style

http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg01224.html
http://suo.ieee.org/email/msg01233.html
http://suo.ieee.org/email/msg03111.html
http://suo.ieee.org/email/msg04807.html

Higher Order Sign Relations, Quotation, Reflection

http://suo.ieee.org/ontology/msg00625.html
http://suo.ieee.org/ontology/msg00703.html
http://suo.ieee.org/ontology/msg00973.html

01 Aug 2001 • 10:42 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Wed, 01 Aug 2001 10:42:04 -0400
From: Jon Awbrey
  To: Sam Hunting
  CC: Arisbe, Organization Complexity Autonomy,
      SemioCom, Standard Upper Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Sam,

This topic has been de-topicalized
by the Topic Map Mail List Manager.

Vide:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: Topic Map Mailing list
Date: Wed, 01 Aug 2001 09:12:57 -0400
From: Jon Awbrey
  To: Michel Biezunski
  CC: W.M. Jaworski, Topic Map Mail

Michel,

I will comply.

Jon

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Michel Biezunski wrote:
> 
> Jon, WMJ
> 
> The discussions you are having on the topic map mailing
> list are quite fascinating and enlightening, but the problem
> is that they are not really centered on what makes the core
> interest for topic map users.
> 
> Can you please have this discussion on another mailing forum
> or mailing list? Once this will have been setup send a message
> to the topic map mailing list to indicate where to find this discussion,
> so that interested parties can join.
> 
> Thank you in advance for your cooperation.
> 
> Michel
> 
> ==========================================
> Michel Biezunski, InfoLoom
> ==========================================
> 
> > -----Original Message-----
> > Subj: Re: Working Or Talking (WOT)
> > From: Topic Map Mail
> > Sent: Sunday, July 29, 2001 8:40 PM
> >   To: W.M. Jaworski
> >   Cc: Topic Map Mail
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > W.M. Jaworski wrote:
> > >
> > > wmj: If you prefer only talking, sorry I am not the partner.
> > >      If you are able to recover from your document the initial
> > >      (draft) versions of the set table, please do.  Why?  This
> > >      will allow me to offer you (constructive?) comments and
> > >      move to the next step.
> > >
> > > Regards
> > >
> > > WMJ
> >
> > I do not know what you mean by "the set table".
> > When I do not know what you mean I will say so.
> > When I do know what you mean I will say so.
> > If you think this can be done by telepathy,
> > then I am not your medium.
> >
> > Jon Awbrey
> >

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

You might look into joining the Arisbe, OCA, or IEEE Ontology Groups.
I am appending their addresses and subscription information here:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Arisbe

http://stderr.org/cgi-bin/mailman/listinfo/arisbe
http://stderr.org/pipermail/arisbe/

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Ontology Sublist of the IEEE Standard Upper Ontology (SUO) Forum

http://suo.ieee.org
http://suo.ieee.org/refs.html
http://suo.ieee.org/links.html

http://suo.ieee.org/email
http://suo.ieee.org/ontology   <<<---<<<
http://suo.ieee.org/suo-ce
http://suo.ieee.org/suo-kif

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Organization Complexity Autonomy (OCA) List

Contact John Collier:

John Collier
Department of Philosophy               fax: +61 2 4921 6928
University of Newcastle, NSW 2308                 AUSTRALIA
http://www.newcastle.edu.au/department/pl/Staff/JohnCollier/

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Sam Hunting wrote:
> 
> Are all properties intrinsically relational?
> 
> --- Jon Awbrey wrote:
> >
> > Sam Hunting wrote (SH):
> > Jon Awbrey wrote (JA):
> >
> > JA: Here is one quick link on the "Definition Of A Sign":
> >
> >     http://suo.ieee.org/ontology/msg02034.html
> >
> > SH: A question from the peanut gallery:
> >
> >     What is a relational property?
> >
> >     Thanks!  (No need for one of your wonderful punning extended essays -- KISS.)
> >
> > SH, quoting LW:
> >
> >   | "To imagine a language is to imagine a form of life."
> >   |  Ludwig Wittgenstein, Philosophical Investigations
> >
> > A relational property is just a property that something has
> > by virtue of being in a relation at the moment in question.
> > In effect, this is really just another way of saying that
> > something is related to something in the specified way.
> >
> > For example, "mi" is a name I call myself, that is to say,
> > a sign that reminds me of me, at the moment when somebody
> > while singing a song has led me to interpret "mi" as "me".
> > In this moment is actualized the sign relational 3-tuple
> > <me, "mi", "me"> of the form <object, sign, interpretant>.
> >
> > Jon Awbrey
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> >
> > Incidental Musement:
> >
> > http://www.stratfordfestival.ca/2001/playbill/soundofmusic.html
> >
> > o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Where Were We (WWW)?

Oh yes, "Are all properties intrinsically relational?"

I don't know.

I suppose it depends on what you mean by "intrinsic".
It might also depend on what you mean by "all".

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

01 Aug 2001 • 17:20 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Wed, 01 Aug 2001 17:20:15 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology, SemioCom

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: Our discussion appears to be diverging, so let me try to refocus my problem.
    You are working on inquiry.  This is a big word.  I would say you can inquire
    about anything imaginable, but I am assuming you are focusing on what we call
    scientific inquiry, since I thought that was Peirce's focus.  What I am trying
    to discern is what is fundamentally different in Peirce's (and your own view)
    of scientific inquiry from a typical physicist's (e.g., Hertz's) view.

Ok, let me see if I can restate the focus that I will be
trying to maintain over the next academic year, at least.

| Inquiry Driven Systems:  An Inquiry Into Inquiry
|
| Contact: Jon Awbrey
| Version: Draft 8.4
| Created: 23 Jun 1996
| Revised: 04 Jun 2001
| Advisor: M.A. Zohdy
| Faculty: Lipman, Mili, Windeknecht
| Setting: Oakland University, Rochester, Michigan
| Excerpt: Section 1.1.1. "Problem"
|
| 1.  Research Proposal
|
| 1.1.  Outline of the Project:  Inquiry Driven Systems
|
| 1.1.1.  Problem
|
| This research is oriented toward a single problem:  What is the nature of inquiry?
| I intend to address crucial questions about the operation, the organization, and
| the computational facilitation of inquiry, taking inquiry to encompass the general
| trend of all forms of reasoning that lead to the features of scientific investigation
| as their ultimate development.

Now, it took me three of four drafts of my dissertation proposal to get this one little
paragraph written as it is, so I know that I must have put a modicum of thought into it.

I think of "inquiry" as naming a generic class of "forms of conduct" (FOC's).
The species that many of us call "scientific inquiry" is perhaps the current
paragon of this genus, but that does not mean that its evolution is complete.

How might it be possible for us to improve our ability to do the best sorts of inquiry?
Hint:  People frequently mention the importance of "organa" (instruments) for science.
Years ago, all too many years ago, I pursued this question under the banner and the
charge of building an "Intelliscope" for inquiry, an instrument to augment, extend,
leverage, and magnify our powers to carry out effective inquiries in optimal ways.

And it still sounds like a good plan to me.

But what would it take to build such an instrument?

AI, there's the rub.

The only kind of AI worth having, from my POV.

At present I do not understand some of the distinctions that you draw,
and this makes it difficult for me to chart my course in relation to
your coordinate system.  I do not understand the contrasts that you
draw between "physicist" and "pragmatist", "logic" and "math", and
I do have much feeling for the way that you appear to be employing
the contrast between "formal" and "material"(?).  I realize that
these words are sometimes used as labels for bits of turf, but
I no longer have much stake in that.  So I think it might help
to reach an understanding on the use of these axes before we
attempt to plot our explorations any further into this space.

HP: Specifically, in the previous post, I asked whether Peircean logic is formal.
    You sound like the sign relation is entirely formal:

    | JA: A sign relation L is a SET of 3-tuples of the form <o, s, i>,
    |     where o is an element of the set O, called the "object domain",
    |     where s is an element of the set S, called the "sign domain", and
    |     where i is an element of the set I, called the "interpretant domain".
    |
    | JA: In other words, a sign relation L is a SUBSET of the cartesian product OxSxI,
    | a circumstance that Asciians write as "L c OxSxI".

HP: You also sound like Peirce's "correspondence" is also formal, in which case the
    sign relation would not in itself be an adequate model of scientific inquiry.
    That is, as a formal system, it does not address the problem of observation
    and measurement.

I guess I just do not understand the use of the word "formal"
as you appear to be using it in several of the above statements.
I grasp "formal" as meaning something like "concerned with form"
or "pertaining to form".  To my way of thinking, this contains
no implication of "being limited exclusively to form", since
form and matter are just two diverse aspects of being.

JA: To make a long story short, what Peirce means by "correspondence"
    in this definition is just the whole 3-adic sign relation itself,
    which he occasionally describes as a "triple correspondence".

HP: But then the last sentence sounds like this formal system is intended
    as an alternate to a theory of truth often used in science:

JA: He does not mean to suggest any sort of pallid 2-adic "imaging" or "mirrortying"
    as implicated in a "correspondence notion of truth".

As I understand it, a notion of truth is ever contained within
and never makes sense beyond the bounds of a notion of inquiry.

HP: The Hertz's modelling relation is instructive because:

HP: (1) it clearly separates the formal logical syntax of our models (laws)
        from the empirical observational semantics (initial conditions),
        which is essential for physics, and

HP: (2) it emphasizes the limits of scientific knowledge:
        "We do not know, nor have we any means of knowing,
        whether our conception of things are in conformity
        with [external reality] in any other than this one
        fundamental respect."

HP: So, to restate my main question:

HP: Does Peircean inquiry strictly separate
    the logical syntax of signs from
    the semantics of observation?

I do not know what you mean by "strictly separate" in this context.
I understand the relations among objects, signs, and ideas to make
sense only within the context of one or another 3-adic sign relation.
I've been told that Peirce seldom if ever used the term "semantics" --
no matter, he recognized the denotative or the referential relation
of signs and ideas to actual, imaginary, or intentional objects,
so that is what we may call his sense of "semantics".  Are you
asking whether objects and signs, as absolute categories, are
mutually exclusive?

Jon Awbrey

01 Aug 2001 • 20:30 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Wed, 01 Aug 2001 20:30:20 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology, SemioCom

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: What I am trying to discern is what is fundamentally different in
    Peirce's (and your own view) of scientific inquiry from a typical
    physicist's (e.g., Hertz's) view.  Specifically, in the previous
    post, I asked whether Peircean logic is formal.  You sound like
    the sign relation is entirely formal:

JA: A sign relation L is a SET of 3-tuples of the form <o, s, i>,
    where o is an element of the set O, called the "object domain",
    where s is an element of the set S, called the "sign domain", and
    where i is an element of the set I, called the "interpretant domain".
    In other words, a sign relation L is a SUBSET of the cartesian product
    OxSxI, a circumstance that Asciians write as "L c OxSxI".

HP: You also sound like Peirce's "correspondence" is also formal, in which case the
    sign relation would not in itself be an adequate model of scientific inquiry.
    That is, as a formal system, it does not address the problem of observation
    and measurement.

JA: To make a long story short, what Peirce means by "correspondence" in
    this definition is just the whole 3-adic sign relation itself, which
    he occasionally describes as a "triple correspondence".

HP: But then the last sentence sounds like
    this formal system is intended as an
    alternate to a theory of truth often
    used in science:

JA: He does not mean to suggest any sort of pallid 2-adic "imaging" or
    "mirrortying" as implicated in a "correspondence notion of truth".

HP: The Hertz's modelling relation is instructive because
   (1) it clearly separates the formal logical syntax of
       our models (laws) from the empirical observational
       semantics (initial conditions), which is essential
       for physics, and
   (2) it emphasizes the limits of scientific knowledge:
       "We do not know, nor have we any means of knowing,
       whether our conception of things are in conformity
       with [external reality] in any other than this one
       fundamental respect."

HP: So, to restate my main question:
    Does Peircean inquiry strictly separate
    the logical syntax of signs from the
    semantics of observation?

SS: Perhaps I could clarify things a bit by noting that o-s-i involves an elsion concerning i.

I did not understand that last sentence.

SS: The object can be taken to exist "out there".

Yes, it can.

SS: The sign is a construction contributed to by both the object (its counterstructures - Uexküll)
    and -- what?  Some semioticians have supplied for this 'what', a system of interpretance (SI).

In my work I speak of a "system of interpretation" (SOI) -- excuse my French.

SS: This system not only co-constructs the sign, but fully, by (or within) itself,
    constructs the interpretant(s).  In this light, we can assign the formality to
    the SI, AS WELL AS a complex of sensation -> feedback --> perception, which
    make up measurement.

I might, perhaps, prefer to say that the connotative aspect of a SOI
is constituted of signs, interpretant signs, and their relationship.

But "affects and impressions" (the Greek "pathemata"), the "data of the senses" (DOTS),
measurements, perceptions, and intelligible conceptions are all just special types of
signs, all with their own interpretant signs in the minds of ensouled creatures.

SS: So, the SI is responsible for both the formalisms and the measurements.

I believe that Nature, the ever pressent object reality,
has its share of responsibility for our impressions and
perforce must be assigned a part in the cosmic dialogue.

SS: Yet they are separate actvities.

I would not say "separate", not if I was being careful,
neither one being autonomous with respect to the other.
I prefer "moderately or relatively independent" (MORI).

SS: Without the predicament of the SI, with its needs and desires,
    there is no semiosis in this more restricted sense (which is
    approprate to Howard's questions).  Measurement and formal
    manipulations would, then, not be separated in one sense
    because they are linked through the needs of the SI,
    and so interpenetrate in one way or another.

Yes, I think that says it very admirably.

Jon Awbrey

02 Aug 2001 • 01:23 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 02 Aug 2001 01:23:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology, SemioCom

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: I guess I just do not understand the use of the word "formal"
    as you appear to be using it in several of the above statements.
    I grasp "formal" as meaning something like "concerned with form"
    or "pertaining to form".  To my way of thinking, this contains
    no implication of "being limited exclusively to form", since
    form and matter are just two diverse aspects of being.

HP: I am using "formal" in the mathematician's sense where it just means those
    axiomatic symbolic sets and their manipulations that are performed by rules
    that do not require assigning extrinsic meaning to the symbols or rules for
    their manipulation (like adding a column of numbers).  Such intrinsically
    meaningless systems (fun for mathematicians) often exhibit structures that
    later, when given observational interpretations, turn out to be excellent
    models of the physical world (e.g., matrices, differentiable manifolds,
    group theory, etc.).  Wigner famously called this the "unreasonable
    effectiveness" of mathematics for modelling physical systems.

I was afraid of that, but did not want to be charged with pushing you to it.
In spite of your next disclaimer, you have just given the usual description
and the stereotypical rationalization of the point of view that is commonly
called "formalism".  As a reformed formalist, I know all too well how this
story goes, but it no longer has  much to do with the way that I now use
the words "form" and "matter", having traced their meanings as far back
as Aristotle to pick up the uncut stuff.  And though it's been a while
since I encountered Wigner's motto in context, I am pretty sure that
I always felt he was hinting at a form of pythagorean realism here,
though I may well have guessed his meaning wrong both then and now.

As it happens, I recently wrote a narrative about my conversion
in response to a series of questions from another correspondent:

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj: Re: I am astonished by mathematicians' reluctance/refusal to consider seriously Gödel's Platonism
Date: Fri, 08 Jun 2001 18:50:59 -0400
From: Jon Awbrey
  To: Reader X

Reader X wrote (RX):
Jon Awbrey wrote (JA):

RX: I am astonished by mathematicians' reluctance/refusal
    to consider seriously Godel's Platonism ...

JA: From my experience, I think the truth is more that they
    simply take it for granted, but have heard that it is
    unfashionable, and so they keep quiet about it ...

JA: Just from the characters that I have known in mathematics when I was passing through
    their neighborhood, I would guess that it is purely a matter of economy of effort.
    Someone pegs you in the hall and asks you about your "philosophy of math" -- you
    are itching to get back to your office where you can write down the latest idea
    about some problem that has passionately engaged your every free moment for all
    the last year or decade or three, so you tell 'em the short answer that you are
    guessing they'll be the happiest to hear -- "Oh, it's just a meaningless formal
    game played with glass beads according to rules that we make up as we go along",
    chuckle sagely, and race off up the stairs to your secret lair.  It's not like
    you were going to change any minds, anyway, and years of futile wrangling in
    your undergrad years have taught you that this is the most practical strategy.
    It is only on the very rare occasion, every now and then, when someone like
    Gödel gets provoked enough by the village idiocies of someone like Russell
    that they will interrupt their main affairs to try and stem the tides of
    fashion.  But the popular lunacy goes on anyway, acting as if it has
    absorbed the result into whatever system of preveilng belief they
    had before you bothered to raise the curtain.  And so it goes.

HP: I am not referring to the philosophical and psychological disputes over ontology
    or the sources of mathematical creativity (formalists, intuitionists, logicists,
    platonists, etc.).  Most un-programmed calculation is formal.  (One can argue
    about memory-stored-program computers).

In the context of mathematics and the theory of computation, I mostly understand
the word "formal" in the adjectiveal senses of formal grammars, formal languages,
and formal systems.  In this case I hear it to mean something roughly synonymous
with "explicit".  For example, the grammar rules, the sentences, or the axioms
and inference rules are explicitly enumerated in a finitary fashion, but this
aspect of form can be featured in relief without any prejudice that requires
its formalities to be meaningless, perfunctory, or, if you will, pro forma.

HP: The Hertz's modelling relation is instructive because:

HP: (1) it clearly separates the formal logical syntax of our models (laws)
        from the empirical observational semantics (initial conditions),
        which is essential for physics, and

HP: (2) it emphasizes the limits of scientific knowledge:
        "We do not know, nor have we any means of knowing,
        whether our conception of things are in conformity
        with [external reality] in any other than this one
        fundamental respect."

JA: I do not know what you mean by "strictly separate" in this context.
    I understand the relations among objects, signs, and ideas to make
    sense only within the context of one or another 3-adic sign relation.

HP: Hertz's epistemic condition is also irreducibly triadic with the same
    terms (object, image/sign, observer/interpreter), but he goes on to
    explain the necessary conditions for a good model, a homomorphism.

But an arrow or morphism is a 2-adic artifact.  Sure, its categorical context
exhibits a couple of salient 3-adic structures, the composition operation and
the anchoring of natural transformations, but the map itself is a very special
sort of 2-adic relation.  In PTOS (the pragmatic theory of signs), it would be
classified as an "iconic notation".  An icon is a sign that denotes its object
by virtue of a property that it shares with it.  For a "structure-preserving"
mapping, this property is clearly just the structure that is being preserved.

But iconic notations and indexical notations imply very special types
of sign relations, being almost "degenerate" in view of the fact that
they are "nearly 2-adic".  "Symbolic notations", in the PTOS sense of
sense of the term "symbolic", constitute sign relations that are more
generic and more genuine, in a sense, than iconic and indexical kinds.

HP: When we want to use a formal symbol system to model a physical system ...

There it is!  I spy the crux of our misunderstanding ...

The formal symbol system may be iconic of the object system,
but it does not have to be, nor does its virtue of denoting
have to be exhausted by whatever iconic powers it does have.

The rationalization that you have so far given of how a symbol system can achieve
its "unreasonable effectiveness" in relating us to real pragmata fails to capture
the effective ingredient of the generic phenomenon by which symbols acquire their
natures and effect the conveyance of their meanings.  When it comes to accounting
for the conditions of possibility that explain how symbols motivate interpretants
with regard to an object, there is a deficit, a shortfall here that the exchequer
of the 2-dim map just cannot cover.

HP: When we want to use a formal symbol system to model a physical system we have to
    assign observable qualities to some of the otherwise meaningless symbols and then
    provide initial conditions for them by measurement.  If you do not make a strict
    distinction between the formal rule-system that represent universal, inexorable
    laws and the initial conditions which may be different for every observer, the
    model no longer makes sense.  To survive, inquiring physicists (bacteria and
    all living systems) want to know what they cannot influence and what they
    can change.

HP: So, to restate my main question:

HP: Are Peircean rules of inquiry formal?

When I am able to use my sense of "formal", and my sense of "logic",
then I am able to say that logic is the formal and normative branch
of semiotics, where semiotics is the general study of sign relations.

And yet my sense of "formal" does not seem to be your sense of "formal".
For now I can only anticipate that we may agree on the gloss "explicit".
But now you have, quite aptly I think, broadened your sense of "logic"
from a sense that appeared limited to deduction to include the whole
of "inquiry", of which we might say with Dewey-eyed enthusiasm that
logic is the theory thereof.  And this brings us to the hard part
of one definition of pragmatic thinking, to wit, the tenet that
makes it out au fond to be the "logic of abduction".

HP: They appear to be formal and therefore
    to apply universally for all inquiry
    conditions, like "laws of inquiry".

There may be such laws.
There may be such rules.
They may turn out formal.
But I don't know that yet.

HP: How, then, do the unique conditions of a specific observer or system under study
    enter the formal inquiry?  How is this different from normal physicist's inquiry?

I think that this sounds very similar to a question that I ask in my dissertation:

| 1.2.2  A Fugitive Canon
|
| The principal difficulties associated with this task appear to spring from two roots.
|
| First, there is the issue of "computational mediation".  In using the sorts of sequences
| that computers go through to mediate discussion of the sorts of sequences that people
| go through, it becomes necessary to re-examine all of the facilitating assumptions
| that are commonly taken for granted in relating one human experience to another,
| that is, in describing and building structural relationships among the
| experiences of human agents.
|
| Second, there is the problem of "representing the general in the particular".
| How is it possible for the most particular imaginable things, namely, the
| transient experiential states of agents, to represent the most general
| imaginable things, namely, the agents' own conceptions of the abstract
| categories of experience?
|
| Finally, not altogether as an afterthought, there is a question
| that binds these issues together.  How does it make sense to
| apply one's individual conceptions of the abstract categories
| of experience, not only to the experiences of oneself and
| others, but in points of form to compare them with the
| structures present in mathematical models?
|
| http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm

Jon Awbrey

02 Aug 2001 • 18:00 • Manifolds Of Sensuous Impressions

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Manifolds Of Sensuous Impressions (MOSIs)
Date: Thu, 02 Aug 2001 18:00:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology, SemioCom

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Manifolds Of Sensuous Impressions (MOSIs)

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| This paper is based upon the theory already established, that the function of
| conceptions is to reduce the manifold of sensuous impressions to unity, and that
| the validity of a conception consists in the impossibility of reducing the content
| of consciousness to unity without the introduction of it.  (CSP, CP 1.545, CE 2.49).

Let me read you a story from one of my favorite books of manifolds:

| Serge Lang,
|'Differential & Riemannian Manifolds',
| Springer-Verlag, New York, NY, 1995.

But first, a message from our medium:

o~~~~~~~~~o~~~NOTATIONATE~NOTEFACTION~~~o~~~~~~~~~o

In presenting this text I am obligated to change
many Greek characters into Latin letters, and so
by way of a slightly skewed form of compensation,
I will convert Roman numerals to Arabic decimals.
Notes from the translator (me) will be placed in
square brackets, to ease the transits to English.

Let "|_|", interfixed with extra space around it,
or else "|_|<i>", antefixed, signify the union
of two sets, or of the many sets indexed by i,
respectively.

Let "|^|", interfixed with extra space on either side,
or else "|^|<i>", antefixed, signify the intersection
of two sets, or of a family of many sets indexed by i,
respectively.

Let "o", interfixed with extra space around it,
signify functional composition, interpreted in
the sense that (f o g)(x) = f(g(x)).

Note to critics who may happen to follow the style sheet
of the APA ("American Pedantical Association").  The "we"
that you see prevailing in this mannerism of mathematical
writing is not of necessity the "we" of plural authorship,
and of necessity not the "we" of birth through royal blood,
as it was discovered years ago that there is no royal robe
to mathematics, but it is the very democratic "we" of the
participatory demonstracy, and it begins to lose its title
to that with every citizen of this res publica who demurs
from their reponsibility and their right to follow along.

o~~~~~~~~~o~~~~~~~~~o~RECITATIVE~o~~~~~~~~~o~~~~~~~~~o

Chapt 2.  Manifolds

Starting with open subsets of Banach spaces [think R^n for the moment],
one can glue them together with 'C^p'-isomorphisms [bijective mappings
that are continuously differentiable up to at least as far as order p].
The result is called a manifold.  We begin by giving the formal definition.
We then make manifolds into a category, and discuss special types of morphisms.
We define the tangent space at each point, and apply the criteria following
the inverse function theorem to get a local splitting of a manifold when
the tangent space splits at a point.
 
We shall wait until the next chapter to give a manifold structure
to the union of all the tangent spaces.

2.1.  Atlases, Charts, Morphisms

Let X be a set.  An "atlas" of class C^p (p >= 0) on X is a collection
of pairs (U<i>, q<i>) (i ranging in some indexing set), satisfying the
following conditions:

AT 1.  Each U<i> is a subset of X and the U<i> cover X.

AT 2.  Each q<i> is a bijection of U<i> onto an open subset q<i>U<i>
       of some Banach space E<i> and for any i, j, [it is true that]
       q<i>(U<i> |^| U<j>) is open in E<i>.

AT 3.  The map

       q<j> o q<i>^-1  :  q<i>(U<i> |^| U<j>)  ->  q<j>(U<i> |^| U<j>)

       is a 'C^p'-isomorphism for each pair of indices i, j.

It is a trivial exercise in point set topology to prove that one
can give X a topology in a unique way such that each U<i> is open,
and the q<i> are topological isomorphisms.  (Lang, DARM, 20-21).

| Serge Lang,
|'Differential And Riemannian Manifolds' (DARM),
| Springer-Verlag, New York, NY, 1995, pp. 20-21.

o~~~~~~~~~o~~~~~~~~~o~EVITATICER~o~~~~~~~~~o~~~~~~~~~o

To be continued, and I dare say it, to be differentiated,
up to some order as yet to be predestinately determinate.

Jon Awbrey

03 Aug 2001 • 02:00 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Fri, 03 Aug 2001 02:00:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology, SemioCom

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: I was afraid of that, but did not want to be charged with pushing you to it.
    In spite of your next disclaimer, you have just given the usual description
    and the stereotypical rationalization of the point of view that is commonly
    called "formalism".

HP: Fear not!  Push on!  But what rule of logic, polemics,
    or ethics allows you to disclaim my disclaimer?

No rule of logic.  I am making an empirical observation.
I am merely setting out a rough description of a sample
of behavior, as I observe its effects from my point of
view, and making a hypothesis, informed by my previous
experience, about a form of conduct that may plausibly
be guessed to underlie it.  It's an extremely fallible
process.

HP: As I warned, I'm not talking stereotypic rationalizations.
    I'm simply defining my usage by stating a simple, empirically
    testable condition for a formal process.  Just follow the rules.
    Adding a column of numbers can be accomplished whether or not
    the numbers refer to apples, bytes, or nothing but number.
    It's called calculating.

Oh, you mean an algorithm?
Id est, an effective procedure?
To wit, an effective description
of a particular pattern of behavior?
You regard this as empirically testable?
I worry about that.  Some things I know of
say yes, okay.  Other things say no, no way.
I will have to think about this for a while.

But I still perceive a residue of the attitude called "formalist" in this seemingly,
all too seemingly innocent definition of "formal".  It shows up in the tendency to
use qualifiers like "just", "merely", "nothing but" in the invitation to follow.

JA: As a reformed formalist, I know all too well how this story goes,
    but it no longer has  much to do with the way that I now use the
    words "form" and "matter", having traced their meanings as far
    back as Aristotle to pick up the uncut stuff.

HP: How you and Aristotle choose to use words is fine, but for this discussion
    I chose to use "formal" to indicate just following rules.  In my usage,
    either you follow the rules, or you don't.

Okay, this is something that I have at least thought about.
Because I have had this same discussion many times before,
and that is just in this lifetime.  In fact, we were just
talking about this same problem the other day, perhaps in
slightly different words.  It's the very same boggle that
I ran into way back then, when I was just a poor innocent
mathematics and physics student, who would have scoffed --
who recursively scoffed -- at the very idea of reading up
on what such Ancients as Plato and Aristotle wrote.  But,
willy nilly, pursuing a course of inquiry more nilly than
willy, at least, at first, in those dim initial conditions
that I half-deplored, half-explored at the time, following
my own gnosis where it led, and executing, or so I thought,
a plan not a whit more sophisticated than a simple backtrack
algorithm, I found myself running backwards evermore and again
recursively to the timeworn topoi where the knot was first tied.

> If you don't, you get the wrong answer.  Of course I use the word
> more broadly in other contexts, but if you want to understand me
> in this context you have to listen to how I use it.

When I say I do not understand your usage, I really mean it.
Oh, it's not like I never heard this way of talking before,
or even that I did not speak this way for years and years.
No, I mean that I do not understand this form of talking
in the way that I no longer understand expressions that
I am beginning to suspect are irreducibly ambiguous
or even irredeemably inconsistent.  It's still just
a suspicion at this point, but it grows stronger.

Example of a false 2-chotomy:  Particle Versus Wave.
For pragmatic thinkers, conceptual distinctions are
only tools, and some just do not do the job anymore.

These (com)putative concepts of "following a rule" (FAR) or "following a set of rules" (FASOR),
that you seem to regard as being so clear, so consistent, so unambiguous, just do not strike me
as being that way at all.  And this is exactly why I found myself forced back to the Ancients to
locate the urliest manifestation of the anomaly, and why I tried to introduce a 3-fold staple to
mend the rent of these faulty 2-chotomies, between FAR and ~FAR, or else betwixt FASOR and ~FASOR.
So my best guess about how to clear this up is to acknowledge a 3-fold spectrum of models, to wit:

1.  "Models of Potential" (MOP's)
2.  "Models of Execution" (MOE's)
3.  "Models of Criticism" (MOC's)

For instance, I am probably following all sorts of rules right now that I know not of.
For me to follow up on even a little bit of all of this following would require me to
take up a "form of reflective critique" (FORC) on my own polydidactic followings that
I can but anticipate the due bifurcations of my unitary, all too unitary self thereof.

And then there is a theorem of Rice ...

JA: And though it's been a while since I encountered Wigner's motto
    in context, I am pretty sure that I always felt he was hinting
    at a form of pythagorean realism here, though I may well have
    guessed his meaning wrong both then and now.

HP: You guessed wrong.  Wigner is as open-minded and puzzled as
    Peirce whom, as a prolusion to his paper, he quotes thus:
    "... and it is probable that there is some secret here
    which remains to be discovered."  Wigner also means
    what he says in conclusion:  "... fundamentally,
    we do not know why our theories work so well."

Okay, I guess I will leave it until I get a chance to read this stuff again,
but I do not see how being an open-minded, puzzled, wondering spirit weighs
against acquiring a sense of pragmatic, platonic, and pythagorean realities.

HP: Incidentally, just to see more how you think about mathematics,
    what is your guess on the ultimate source of complex Hilbert spaces?

Oh, it's always a toothache or something.
I worry about the impact of modern dentistry
on the health in future of modern mathematics.

And, by way of definition:
1.  General Relativity =>
2.  Pythagorean Realism =>
3.  Equation: Form = Matter.
Just blame it on my toothache.

HP: Hertz's epistemic condition is also irreducibly triadic with
    the same terms (object, image/sign, observer/interpreter), but
    he goes on to explain the necessary conditions for a good model,
    a homomorphism.

JA: But an arrow or morphism is a 2-adic artifact ... etc., etc.
 
HP: I don't know the definition of a "2-adic artifactual arrow" ...

The series of terms, "homomorphism", "morphism", "arrow",
following a gradient from more concrete to more abstract,
are used by category theorists to refer to basically the
same entity, but when they want to emphasize the nuances
of concrete existence versus abstract axiomatic sketches.
The monicker "arrow" falls out of the picture f : X -> Y.
A function is, of course, just a brand of 2-adic relation.

HP: I don't know the definition of a "2-adic artifactual arrow",
    but neither Hertz nor I drew any arrows.  I drew some edges,
    as I've caught you and Peirce doing often enough, to indicate
    some kind of relation.  Hertz's statement is only 40 words.
    It is an elegantly phrased, general statement in the introduction
    of a long book. I am sure, like Peirce, he would not have wished
    to restrict the skill and ingenuity of the observer in choosing
    the types of phenomena, the types of symbols or signs, and the
    n-adicity of relations that might help integrate experience
    into a model.  You have no justification for imposing the
    elaborate, idiosyncratic Percean distinctions on Hertz's
    mere 40 words.

The only question of interest to me here is whether a given statement
about the subject in question -- in so many words, or more, or less --
is adequate to the subject in question, that is, whether the words
are assembled in such a way that they describe the subject, being
general enough to capture the theme of its protean variations.

The Erlangen Programme was a very pretty picture of all possible geometry,
but it turned out to be just a little bit too pretty to be truly complete.

I have good reasons to say that any notion of how signs relate to objects
that is limited to commutative diagrams and linear (homomorphic) mappings
is just not general enough to cover all of the conceivable and all of the
observable cases of sign relations that are useful in adapting to reality.

JA: The rationalization that you have so far given of how a symbol system can achieve
    its "unreasonable effectiveness" in relating us to real pragmata fails to capture
    the effective ingredient of the generic phenomenon by which symbols acquire their
    natures and effect the conveyance of their meanings.  When it comes to accounting
    for the conditions of possibility that explain how symbols motivate interpretants
    with regard to an object, there is a deficit, a shortfall here that the exchequer
    of the 2-dim map just cannot cover.

HP: An impressive 85 big words of indisputable discourse --
    unless, of course, you claim to have the answers.

I am pretty much just footnoting CSP.

HP: When we want to use a formal symbol system to model a physical system we have to
    assign observable qualities to some of the otherwise meaningless symbols and then
    provide initial conditions for them by measurement.  If you do not make a strict
    distinction between the formal rule-system that represent universal, inexorable
    laws and the initial conditions which may be different for every observer, the
    model no longer makes sense.  To survive, inquiring physicists (bacteria and
    all living systems) want to know what they cannot influence and what they
    can change.

HP: So, to restate my main question:

HP: Are Peircean rules of inquiry formal?

JA: When I am able to use my sense of "formal", and my sense of "logic",
    then I am able to say that logic is the formal and normative branch
    of semiotics, where semiotics is the general study of sign relations.

HP: You are able to say whatever you say,
    but if you use my definition of formal,
    may I put you down for a, "No"?

You may put me down any way that pleases you.
I have told you that I do not think in these
terms that you seem to think that no one can
possibly think and do without.  I do without.

HP: Final question:  Can you say how Percean inquiry fundamentally differs from
    processes of physical or mathematical inquiry as introspectively described by,
    say, Faraday, Maxwell, Hertz, Boltzmann, Hadamard, Poincare, Heisenberg,
    Einstein, Turing, Wigner, and von Neumann?

I have learned that introspection is very often a form of self-deception.
It is just about as useful and as fallible as every other human faculty.

JA: I think that this sounds very similar to a question that I ask in my dissertation.

HP: No, I don't think your dissertation task list would answer my question.
    I have some idea of how the above scientists went about their inquiries,
    because they wrote about it.  I do not yet know enough about how you or
    Peirce would go about scientific inquiry to know how you would do it,
    or think about it, differently.  That is my question.

My chosen task is to figure out the conditions affording the possibility of inquiry,
where "inquiry" is just a convenient name for a process, both dynamic and symbolic,
by which an agent transits from a state of doubt, ignorance, obscurity, uncertainty, ...,
about a phenomenon or a problem to a state of belief, knowledge, clarity, certainty, ...,
about the same issue.  Why would I begin an inquiry into inquiry if I already knew
the answer well enough to write out the code for a universal program of inquiry?

Jon Awbrey

03 Aug 2001 • 09:04 • What Is Pragmatic Thinking?

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: What Is Pragmatic Thinking?
Date: Fri, 03 Aug 2001 09:04:19 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

I sense that one of our difficulties understanding each other may involve
a question of just what a pragmatic philosophy of the Peircean persuasion
actually is.  For instance, I have noted, but do not yet quite understand,
a contrast that you make to pose between the way that a typical physicist
thinks, or perhaps is supposed to think, and the way that one I typically
call a "pragmatician" thinks, or ought to think.  In an effort to clarify
that aspect of the problem, I will try to set out a more positive account
of what it is, as exactly as my rough and ready description can render it,
that constitutes "pragmatic thinking", that is, of this particular stripe.

If you seek the rule that a pragmatic thinker follows, then the name for
that would be the "Pragmatic Maxim".  Now this maxim is an abstract rule,
and so there are, and will be more, many splintry ways of formulating it.
Peirce gave five or six among the set that I have studied most carefully,
but I think that it satisfices to begin with this, my own favorite motto:

| Consider what effects that might conceivably
| have practical bearings you conceive the
| objects of your conception to have.  Then,
| your conception of those effects is the
| whole of your conception of the object.
|
| Charles Sanders Peirce, 'The Maxim of Pragmatism', CP 5.438

Here is the context of this version, which also gives another variant:

| Pragmaticism was originally enounced in the form of a maxim, as follows:
| Consider what effects that might 'conceivably' have practical bearings you 'conceive'
| the objects of your 'conception' to have.  Then, your 'conception' of those effects
| is the whole of your 'conception' of the object.
|
| I will restate this in other words, since ofttimes one can thus eliminate
| some unsuspected source of perplexity to the reader.  This time it shall be
| in the indicative mood, as follows:  The entire intellectual purport of any
| symbol consists in the total of all general modes of rational conduct which,
| conditionally upon all the possible different circumstances and desires,
| would ensue upon the acceptance of the symbol.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.438

Here is an incidental exegesis that I rendered on this maxim on another occasion:

| It is common to miss the indexical character of the pronouns
| in this statement, and to think that he said something about
| "the conception" rather than something about "thy conception".
| There is another version that speaks of "we" and "us", but it
| changes only the poignancy, and not the point of this address.
|
| Whether this currently most popular misreading arises from the
| horror of relativism that most of us learned in the Academy --
| a force apparently so overpowering that it leads us to deny,
| formally speaking, the role of interpretive communities in the
| very pictures of "what is" that they themselves will formulate --
| and whether or not that was actually the lesson that any of us
| was supposed to derive from obeying the dictum to "know thyself" --
| I just hope that it will not be the ultimately persistent message.
|
| The world did not go away when relativity came to physics,
| and I do not believe we need to have fears about ontology.
|
| I bring this up now, not just because it is a recurrent issue, anyway,
| but because it is relevant to the nature of the interpreter that makes
| judgments about category assignments in formulating and implementing
| an ontology, and also to the quality of the inquiry that ensues when
| there emerges a lack of consensus about them.
|
| For this audience, it can be noted that the pragmatic maxim
| is basically a "principle of representation", logically akin
| to the "regular representations" and the "term models" of all
| sorts of algebraic structures, from groups to lambda calculi.
| My memory is dim, but I believe that theorems on the subject
| of "Peirce Representations" are some of the few for which
| the Peirces, B. or C., still retain credit in mathematics.
|
| http://suo.ieee.org/email/msg00645.html

To avert a host of other potential misreadings,
it might be noted that, for Peirce, a 'concept'
or a 'conception' is a special type of 'symbol'.

I will discuss a few of the logical implications
and practical consequences of this maxim as we go.

Jon Awbrey

03 Aug 2001 • 17:17 • Inquiry Into Models

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Subj: OCA: Re: Inquiry Into Models
Date: Fri, 03 Aug 2001 17:17:16 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

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Jon Awbrey wrote (JA):
C.S. Peirce wrote (CSP):
Howard Pattee wrote (HP):
Heinrich Hertz wrote (HH):

HP: I would like to wind up a hanging tail or thread that Jon finds "too long to pursue now."

I guess I should not have put my tale out there if I did not want to be forced to chase it.

JA: Doleful experience has taught me that it is best to expand our focus a bit
    to compass "sign relations", taken as wholes, over and above just isolated
    signs, and taken at least at first in extension as sets of 3-tuples of the
    form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" of
    the "elementary sign relation" (ESR) <o, s, i>.

JA: At this point, I personally find the comparsion with group theory to be compelling.
    A "group" is another sort of set of 3-tuples that is subject to a terse definition,
    and yet the theory of groups encompasses a wealth of imaginative possibilities and
    utilitarian potentials that can scarcely be con-&-sur-veyed in any finite lifetime.

JA: As it happens, one of my many "returns" to mathematics,
    after a time in the wilds of philosophy and psychology,
    was through the slits of "group representation theory",
    but the tale thereby hanging is too long to pursue now.

HP: Let me pursue it briefly because it relates closely to what science is
    all about.  Group representation theory is a theory of homomorphisms, or
    how one formal structure can be mapped into another formal structure so
    that interesting or significant properties are preserved.  If the mapping
    (image, observation, projection, coding, measurement) is from a physical
    system (i.e., matter and energy in space and time) to a formal system
    then we have a physical model.  Here is Hertz's statement of this
    epistemic homomorphism (formally a commutation relation):

HH: | We form for ourselves images or symbols of external objects;
    | and the form which we give them is such that the logically
    | necessary (denknotwendigen) consequents of the images in
    | thought are always the images of the necessary natural
    | (naturnotwendigen) consequents of the thing pictured.
    |
    | For our purpose it is not necessary that they [the images] should be
    | in conformity with the [external] things in any other respect whatever.
    | As a matter of fact, we do not know, nor have we any means of knowing,
    | whether our conception of things [our models] are in conformity with
    | them [external things] in any other than this one fundamental respect.
    |
    | H. Hertz (1857-1894),
    |'The Principles of Mechanics', Dover, NY, 1984, pp. 1-2.
    | Original German Edition:  'Prinzipien Mechanik', 1894.

HP: This is a terse statement.  A commutation diagram makes it clearer:

Howard, this diagram appears to have been messed up by your line wrap.
I am going to make an attempt to reconstruct your commutative diagram.
Let me know if I get it right or not.  I always have to switch to
a fixed width font when I try to do this sort of ASCII-glyphics.

|   EXTERNAL OBJECTS ____ WE FORM FOR OURSELVES ____ IMAGES, SYMBOLS, OR PICTURES
|         |                                        / [SIGNS, BRAIN STATES, WHATEVER]
|         |                                       /                  |
|         |                                      /                   |
|   [NATURAL LAWS]        . . . SUCH THAT . . . /    [LOGICAL, MATHEMATICAL MODEL]
|         |              /                                           |
|         |             /                                            |
|         |            /                                             |
|   NECESSARY NATURAL /___ ARE THE SAME AS THE _____ LOGICALLY NECESSARY
|   CONSEQUENTS                                      CONSEQUENTS OF THE MODEL

HP: "WE FORM FOR OURSELVES ..." includes all forms of sensing, perception, observation,
    measurement, coding, etc. which must be initiated by an agent or organism.  In physics,
    this is the essential cut between the world and the observer that is necessary whenever
    a measurement is made.  It cannot be considered as resulting from natural laws.  That is
    why there is a "measurement problem" in physics.

Okay, now there is a big problem here, one that I noticed quite a while back,
and one to which I have returned on a periodic basis whenever I try to think
very seriously about the puzzles of causality, on those increasingly sparse
occasions when I trick myself into supposing that causality is a sensible
or a solvable problem.  The contretemps this time is not with Peirce but
with his formidable precursor Duns Scotus, at least, as he was read by
W.S. McCulloch.  I have cited this passage numerous times, but the bit
that I think should give readers pause, hopefully of the reflective
variety, appears instead to pass under their gnosis without so much
as a moment of notice, or else to 'sink beneath their wisdom like
a stone'.  So I think, perhaps, that it may now be time to call
e-special attention to the underlying incongruities of views.
Many people just blithely assume that the arrow of causality
and the arrow of implication just naturally must run in the
same direction, but it ain't necessarily so, nor has it
always been taken for granted by thoughtful thinkers on
the binding contract between eternality and secularity.

Here is the theme of my pandoric gloss:

| Please remember that we are not now concerned with
| the physics and chemistry, the anatomy and physiology,
| of man.  They are my daily business.  They do not contribute
| to the logic of our problem.  Despite Ramon Lull's combinatorial
| analysis of logic and all of his followers, including Leibnitz with
| his universal characteristic and his persistent effort to build logical
| computing machines, from the death of William of Ockham logic decayed.
| There were, of course, teachers of logic.  The forms of the syllogism
| and the logic of classes were taught, and we shall use some of their
| devices, but there was a general recognition of their inadequacy to
| the problems in hand.  Russell says it was Jevons -- and Feibleman,
| that it was DeMorgan -- who said, "The logic of Aristotle is inadequate,
| for it does not show that if a horse is an animal then the head of the horse
| is the head of an animal."  To which Russell replies, "Fortunate Aristotle,
| for if a horse were a clam or a hydra it would not be so."  The difficulty
| is that they had no knowledge of the logic of relations, and almost none
| of the logic of propositions.  These logics really began in the latter
| part of the last century with Charles Peirce as their great pioneer.
| As with most pioneers, many of the trails he blazed were not followed
| for a score of years.  For example, he discovered the amphecks -- that
| is, "not both ... and ..." and "neither ... nor ...", which Sheffer
| rediscovered and are called by his name for them, "stroke functions".
| It was Peirce who broke the ice with his logic of relatives, from
| which springs the pitiful beginnings of our logic of relations of
| two and more than two arguments.  So completely had the traditional
| Aristotelian logic been lost that Peirce remarks that when he wrote
| the 'Century Dictionary' he was so confused concerning abduction, or
| apagoge, and induction that he wrote nonsense.  Thus Aristotelian logic,
| like the skeleton of Tom Paine, was lost to us from the world that it
| had engendered.  Peirce had to go back to Duns Scotus to start again
| the realistic logic of science.  Pragmatism took hold, despite its
| misinterpretation by William James.  The world was ripe for it.
| Frege, Peano, Whitehead, Russell, Wittgenstein, followed by a
| host of lesser lights, but sparked by many a strange character
| like Schroeder, Sheffer, Gödel, and company, gave us a working
| logic of propositions.  By the time I had sunk my teeth into
| these questions, the Polish school was well on its way to glory.
| In 1923 I gave up the attempt to write a logic of transitive verbs
| and began to see what I could do with the logic of propositions.
| My object, as a psychologist, was to invent a kind of least psychic
| event, or "psychon", that would have the following properties:  First,
| it was to be so simple an event that it either happened or else it did
| not happen.  Second, it was to happen only if its bound cause had happened --
| shades of Duns Scotus! -- that is, it was to imply its temporal antecedent.
| Third, it was to propose this to subsequent psychons.  Fourth, these were
| to be compounded to produce the equivalents of more complicated propositions
| concerning their antecedents.  (McCulloch, WIANTAMMKIAAMTHMKAN?, EOM, pages 7-8).
|
| Warren S. McCulloch,
|"What Is a Number that a Man May Know It,
| and a Man, that He May Know a Number",
| The Ninth Alfred Korzybski Memorial Lecture,
|'General Semantics Bulletin', Numbers 26 & 27,
| Institute of General Semantics, Lakeville, CT, 1961.
|'Embodiments of Mind', MIT Press, Cambridge, MA, 1965.

I have to break here.  Maybe we can discuss the problem next time.

Jon Awbrey

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HP: Jon's (Peirce's?) definition of sign as a triad, <o, s, i>, with
    o, s, i the "object", "sign", "interpretant sign" might correspond
    to the first line of the above diagram, but there is no model or
    homomorphism, which is why I find it epistemologically inadequate.
    Peirce's definition of sign is too vague and ambiguous for me to
    unravel.  When he has more time, perhaps Jon could diagram it,
    and say what "determined or created by" constructively entails.
    And what implements the "sort of correspondence" that Peirce
    has in mind?  Peirce's definition:

CSP: | A sign is something, 'A',
     | which brings something, 'B',
     | its 'interpretant' sign
     | determined or created by it,
     | into the same sort of correspondence
     | with something, 'C', its 'object',
     | as that in which itself stands to 'C'.
     |
     | CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
     | http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm

JA: Howard, please excuse me if I wax a bit tetchy at this point --
    as nobody knows the troubles I've seen over this one scruple --
    and not all of the obscurities that one finds being credited
    to Peirce are really the obscurities of Peirce, nor even due
    to his way of writing, which I think is admirably clear here.

JA: This is a perfectly good -- ok, a nearly perfectly good -- mathematical definition
    of a particular family of combinatorial structures, that I know as "sign relations".

JA: A sign relation L is a SET of 3-tuples of the form <o, s, i>,
    where o is an element of the set O, called the "object domain",
    where s is an element of the set S, called the "sign domain", and
    where i is an element of the set I, called the "interpretant domain".

JA: In other words, a sign relation L is a SUBSET of the cartesian product OxSxI,
    a circumstance which Asciians write as "L c OxSxI".

JA: Thus CSP did not say, and JA will not say, assertively, what JA mentions here
    in the form of a statement that says "a sign is a triad of the form <o, s, i>",
    nor any such thing as that.

JA: Many of these further issues are tackled in the running accumulation of links
    that I have already posted, but I will admit that the dialogical organization
    of some of these sub-sutras is not always the best for finding quick answers,
    and so I will work on extracting some more caustically focused e-lucidations.

JA: The link-o-rama that I started on the topic of "Determination" is meant to begin
    addressing what Peirce meant by "determined or created" in this sign definition,
    and also elsewhere, in general.

JA: To make a long story short, what Peirce means by "correspondence" in this definition
    is just the whole 3-adic sign relation itself, which he occasionally describes as
    a "triple correspondence".  He does not mean to suggest any sort of pallid 2-adic
    "imaging" or "mirrortying" as implicated in a "correspondence notion of truth".

04 Aug 2001 • 01:20 • Laws And Models

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Subj: OCA: Laws And Models
Date: Sat, 04 Aug 2001 01:20:22 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

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Subject: Laws And Models, Erstwhile Known As:

| Abstraction, Analogy, Arrow, Epitome, Example,
| Icon, Law, Metaphor, Model, Morphism, Paradigm,
| Prototype, Rule, Simulacra, Simulation, Theory

Arisbeans, OCAsionals, Brand X Ontologists ...

While reviewing a few of the SUO discussions
in which I participated during the last year,
I noticed a topic that strikes me as salient
with respect to questions about the relation
of pragmatic thinking to natural science, to
be specific, in regard to their perspectives
on the nature of laws and the uses of models.

For the sake of recovering the context of my own share in this discussion,
I am appending an extended list of links as they fell out along this line,
teasing out also the more timely of these threads and reweaving them here.

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Note 1

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Subj: Triadically Irreducible Relations And Teridentity
Date: Thu, 05 Oct 2000 11:11:49 -0400
From: Jon Awbrey
  To: Peirce Subgroup

Abstractions are just partial descriptions,
descriptions that leave out a lot of detail.

It is our bound fate as human narrators that
all of our descriptions will be abstractions,
as long as we talk about anything significant,
extractions from the wealth of possible detail
that are likely to be partial in both of these
senses, incomplete and biased, and hence they
will be samples, selections, simplifications,
specimens, symptoms, ..., and thus to make
a long story short, signs, just signs.

So the question is not really whether there is something more
to the subject after we have finished with our partial account --
if the subject was interesting, there will always be more to say.
The question is just whether certain sorts of partial description
can be useful in understanding a vastly more complex reality.
And classifying the patterns in "how we think" according to
your favorite system of logical forms can indeed be useful,
depending on your favorite system, of course.

| Digression
|
| This makes it sound like logic is a descriptive science,
| just another branch of psychology, and, of course, we all
| know that this particular idea is just not sound.  Perhaps
| it always begins as a descriptive description of language,
| like noticing the tautology in "descriptive description",
| but then it becomes a prescriptive doctrine that says,
| in the same instance, "Quit saying stuff like that!",
| or a normative science that says, more contingently,
| "If you are interested in achieving a certain economy,
| effectiveness, and efficiency in your communication,
| then you will want to avoid the use of such redundant,
| repetitive, and needless to say 'pleonastic' phrasing".
| And you probably have heard about how Peirce championed
| what he called a "non-psychological" account of logic,
| with respect to which I have explained the funny way
| that mathematically trained people then and now still
| use the prefix "non" in such cases, almost an acronym
| for "not of necessity", to widen a subject beyond its
| initial domain by dropping one or more of the initial
| axioms.  What this means is that we can still regard
| the descriptive study of "how we think" as providing
| data, and some of the most fascinating data, indeed,
| considering who we are and all, but still just grist
| for the mill of a normative study.  But I digress ...

That seems simple enough, but you know there is more to be said.
There are in the idioms of ordinary discussion about these matters
just one or two or three things that are likely to cause confusion.

I called your attention to this overcharged property of -ionized words,
like "abstraction", that they equivocally denote both process and result,
both conduct and product, if you will.  So we have a picture like this:

|                   Abstraction
|    Abstractee    (the process)    Abstraction
|   (the object) o------->-------o (description)

But as you well know, or have come to accept, it gets worse.
Having invested so much in their partial descriptions, people
will tend to become, well, 'partial' to them.  And, human nature
being what it is, it seems to be something of a sore annoyance to
keep thinking about something that you love so much as imperfect,
so people will come to imagine that there really is some object
that is perfectly described by their favorite description.
Comes the dawn of the hypostasis, the imaginary substance
that we shove under our abstraction to shore it up.

|                   Abstraction
|    Abstractee    (the process)    Abstraction
|   (the object) o------->-------o (description)
|                 \             ^
|                  \           /
|                   \         /
|                    \       /
|                     \     /
|                      \   /
|                       v /
|                        o
|                   Abstraction
|                  (hypo-stasis)

And with this form of triple equivocality in the word "abstraction"
I think that the mathematician in all of us thinks to have achieved
a "form of perfection" (FOP).

And with that, I think that perhaps I should quit
while I still have my head, and take up the rest
of your note at a later time.

I leave you to contemplate the charge of our champion.

Jon Awbrey

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Note 2 -- http://suo.ieee.org/email/msg01293.html

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Subj: Abstraction, Analogy, Example, Icon,
      Metaphor, Model, Morphism, Paradigm,
      Prototype, Simulation

Date: Thu, 05 Oct 2000 14:14:05 -0400
From: Jon Awbrey
  To: John F Sowa
  CC: Standard Upper Ontology

John,

No sweat about exiling all the poets from this
or any other Re:Public -- I gather that they
have become quite accustomed to it by now,
and I tend to suspect that they would not
have it any other way.  It gives them all
a well-deserved holiday from the likes
of us straight-latticed types.

I have changed the title of this discussion as a way
of attempting to bring out the more positive aspects
of what I see as a complex of many underlying topics.

The notion of "abstraction", of course, becomes associated
with this list of concepts for a significantly distinctive
reason than the notions that fall into the other slots, and
so I will take it up first, though by no means finish with it.

By way of establishing immediate relevance to ontologies,
I will just remind people of the important distinction
that you make between 'axiomatic' and 'prototypic'
ontologies:

http://www.bestweb.net/~sowa/ontology/
http://www.bestweb.net/~sowa/ontology/gloss.htm

I have recently been instructed, by folks who ought to know,
that a presentation of any research topic ought to begin with
a historical introduction and a review of the literature, so,
in a token gesture to that type of advice, I was planning to
go back to Aristotle and tell you how he would tell us that
this all got started, but, on second thought, I think that
I will begin with something out of a more recent exchange
that I had with one of the habitués of the Peirce Forum,
on this very topic of "abstraction".

My reasons for interjecting this particular exchange
into the present context are twofold:

1.  I think that our ambivalent, nay, "amtrivalent" usage
    of the term "abstraction" amply illustrates one of the
    significant types of ambiguity that still prevails in
    both our casual and our formal idioms, and that will
    prove recalcitrant to being "managed" without losing
    touch with the way that the rest of the world speaks --
    perhaps not entirely a bad thing, still, it's not so
    easy being an exile if you have not got used to it,
    yet.

2.  I think that everyone will immediately recognize the
    abstract similarity that exists between the diagram
    that I draw below and the one that I drew a couple
    of days ago in my conversation with Chris Menzel
    about assertions and propositions in sentential
    calculus or "zeroth order logic" (ZOL), to wit:

                        f
                  X o------>o B
                     \     ^
     <x_1, ..., x_n>  \   /  f'
                       v /
                        o
                       B^n

    You may remember that this was supposed to illustrate
    the "factoring" of a proposition f : X -> B = {0, 1}
    into the composition f'(c(x)), where c : X -> B^n is
    the "coding" of each x in X as an n-bit string in B^n,
    and where f' is the mapping of codes into a co-domain
    that we interpret as t-f-values, B = {0, 1} = {F, T}.

    The full discussion can be found in the SUO archive at:

    http://suo.ieee.org/email/msg01251.html

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Note 3 -- http://suo.ieee.org/email/msg01350.html

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Subj: Abstraction, Analogy, Example, Icon,
      Metaphor, Model, Morphism, Paradigm,
      Prototype, Simulation

Date: Sun, 08 Oct 2000 21:48:14 -0400
From: Jon Awbrey
  To: John F Sowa
  CC: Standard Upper Ontology

SUO Group:

Here is the historical introduction that I promised you last time.

I start as near to the beginning as I can get and present Aristotle's
original account of the form of reasoning that he called "paradeigma".
The name suggests a "side-show", or a parallel comparison of cases, and
it is usually translated as reasoning by analogy, example, or paradigm.

In this context, it is useful to revisit once again the story
of a simple instance of inquiry that I presented a while back:

http://suo.ieee.org/email/msg00676.html

It is interesting to note that this story is really a narrative cycle
in miniature, with the cycle of inquiry proceeding through all of its
typical phases in the typical order:  Abduction, Deduction, Induction.

Regarding the two examples together in this way, one can make make the
curious observation that the first two steps of inquiry, taken in tandem,
present a type of lattice-theoretic dual to the two steps that are spanned
in reasoning by analogy.  I don't really know what to make of this yet --
I just think that it's curious.

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Complex and Mixed Forms of Reasoning (CAMFOR's)

In discussing complex and mixed forms of reasoning,
like those that are typically involved in forming
analogies and conducting inquiries, it helps to
begin with some maximally simple examples, and
this will lead us to look under the lamp-post
of "apophantic" reasoning, that is, among
propositional, sentential, or syllogistic
styles of reasoning.  This is alright,
so long as we do not imagine that we
can remain in this charmed circle
forever.

Examples of Cyclic, Parallel, & Serial Syllogisms

The discussion of analogy and inquiry cries out for a couple
of good examples -- models of inference that will be concrete,
intuitive, simple enough to cut our teeth on at the early phases
of our reflective meta-morphosis, but solid enough to also serve
in sharpening the tools of our meta-logical reasoning capacities.

Along these lines, the best points of departure that I have yet
encountered are:

1.  For analogy, Aristotle's incipient but incisive account
    of its anatomy and function, treating it as a species
    of hybrid inference.

2.  For inquiry, John Dewey's deceptively simple but
    richly suggestive story of inquiry activities in
    everyday life.

In order to allow readers an opportunity to contemplate these
examples on their own, before I truck up the grounds with my
own way of laying out their constructions, I will cite them
here first, then set out a traditional array of terminology
that I will need, and then proceed to the dissecting room.

Aristotle's "War Against Neighbors" Example

| Let A be "bad", B "to make war on neighbors",
| C "Athens against Thebes", and D "Thebes against Phocis".
| Then if we require to prove that war against Thebes is bad,
| we must be satisfied that war against neighbors is bad.
| Evidence of this can be drawn from similar examples,
| e.g., that war by Thebes against Phocis is bad. 
| Then since war against neighbors is bad, and
| war against Thebes is against neighbors,
| it is evident that war against Thebes is bad.
|
| Aristotle, 'Prior Analytics', 2.24

John Dewey's "Sign of Rain" Example

| A man is walking on a warm day.  The sky was clear the
| last time he observed it;  but presently he notes, while
| occupied primarily with other things, that the air is cooler.
| It occurs to him that it is probably going to rain;  looking up,
| he sees a dark cloud between him and the sun, and he then quickens
| his steps.  What, if anything, in such a situation can be called
| thought?  Neither the act of walking nor the noting of the cold
| is a thought.  Walking is one direction of activity;  looking and
| noting are other modes of activity.  The likelihood that it will
| rain is, however, something 'suggested'.  The pedestrian 'feels'
| the cold;  he 'thinks of' clouds and a coming shower.
|
| John Dewey, 'How We Think', 1910, pages 6-7

A good start at analyzing these examples, surprisingly enough,
can be made within a primitive propositional and syllogistic
framework.  In order to carry this out, I will first outline
a few terms of art from classical logic that can be used to
articulate the procedural stages of a generic inquiry process,
and then I will present my analysis of what is taking place,
logically speaking, to move this particular inquiry forward.

Basic Terminology

In the case of propositional logic, deduction comes down to an
application of the transitive law for conditional implications.
Contemplated on the scheme of Figure 1, deduction takes
a Case, the minor premiss X => Y, and puts it with
a Rule, the major premiss Y => Z, to arrive at
a Fact, the demonstrative conclusion X => Z.

Contrasted with this pattern, induction takes
a Fact of the form X => Z and matches it with
a Case of the form X => Y to guess that
a Rule of the form Y => Z is possibly in play.

Cast on this same template, abduction takes
a Fact of the form X => Z and matches it with
a Rule of the form Y => Z to guess that
a Case of the form X => Y is presently in view.

In its original usage a statement of Fact has to do with
a deed done or a record made, that is, a type of event that
is openly observable and not riddled with speculation as to
its very occurrence.  In contrast, a statement of Case may
refer to a hidden or a hypothetical cause, that is, a type
of event that is not immediately observable to all concerned.
Obviously, the distinction is a rough one and the question
of which mode applies can depend on the points of view that
different observers adopt over time.  Finally, a statement
of a Rule is called that because it states a regularity or
a regulation that governs a whole class of situations, and
not because of its syntactic form.  So far in this discussion,
all three types of constraint are expressed in the form of
conditional propositions, but this is not a fixed requirement.
In practice, these modes of statement are distinguished by
the roles that they play within an argument, not by their
style of expression.  When the time comes to branch out from
the syllogistic framework, we will find that propositional
constraints can be discovered and represented in arbitrary
syntactic forms.

In the normal course of a typical inquiry, the three basic types of
inference proceed in the order:  Abduction, Deduction, Induction.
However, the same building blocks can be assembled in other ways
to yield different kinds of complex inferences.  Of particular
importance for our purposes, reasoning by analogy is analyzed
as a combination of induction and deduction, in other words,
as the abstraction and application of a Rule.

For ease of reference, Figure 1 and
the Legend beneath it summarize the
classical terminology for the three
types of inference and the relations
that can be observed among them.

|          Z
|          o
|          |\
|          | \
|          |  \
|          |   \
|          |    \  Rule
|          |     \
|          |      \
|          | A   > \
|          |  \ /   \
|    Fact  | <-@-D   o Y
|          |  / \   /
|          | I   > /
|          |      /
|          |     /
|          |    /  Case
|          |   /
|          |  /
|          | /
|          |/
|          o
|          X
|
| Figure 1.  Basic Structure & Terminology
|
| Deduction takes a Case, the minor premiss of the form X => Y,
| matches it with a Rule, the major premiss of the form Y => Z,
| then adverts to a Fact, the bound outcome of the form X => Z.
|
| Induction takes a Case of the form X => Y,
| matches it with a Fact of the form X => Z,
| then adverts to a Rule of the form Y => Z.
|
| Abduction takes a Fact of the form X => Z,
| matches it with a Rule of the form Y => Z,
| then adverts to a Case of the form X => Y.
|
| Even more succinctly:
|
|           Abduction  Deduction  Induction
|
| Premiss:     Fact       Rule       Case
| Premiss:     Rule       Case       Fact
| Outcome:     Case       Fact       Rule

Aristotle's Illustration of Reasoning by Analogy, Example, Paradigm

Here is the original statement again:

| Let A be "bad", B "to make war on neighbors",
| C "Athens against Thebes", and D "Thebes against Phocis".
| Then if we require to prove that war against Thebes is bad,
| we must be satisfied that war against neighbors is bad.
| Evidence of this can be drawn from similar examples,
| e.g., that war by Thebes against Phocis is bad. 
| Then since war against neighbors is bad, and
| war against Thebes is against neighbors,
| it is evident that war against Thebes is bad.
|
| Aristotle, 'Prior Analytics', 2.24

Figure 2 gives a graphical illustration of Aristotle's
example of "Example", that is, the form of reasoning
that proceeds by Analogy or according to a Paradigm.

|                                  A
|                                  o
|                                 /*\
|                                / * \
|                               /  *  \
|                              /   *   \
|                             /    *    \
|                            /     *     \
|                           /   R u l e   \
|                          /       *       \
|                         /        *        \
|                        /         *         \
|                       /          *          \
|                   F a c t        B        F a c t
|                     /          *   *          \
|                    /         *       *         \
|                   /        *           *        \
|                  /       *               *       \
|                 /   C a s e            C a s e    \
|                /     *                       *     \
|               /    *                           *    \
|              /   *                               *   \
|             /  *                                   *  \
|            / *                                       * \
|           o                                             o
|          C                                               D
|
| Figure 2.  Aristotle's "War Against Neighbors" Example
|
| A  =  Atrocious, Adverse to All, A bad thing.
| B  =  Belligerent Battle Between Brethren.
| C  =  Contest of Athens against Thebes.
| D  =  Debacle of Thebes against Phocis.
|
| A is a major term,
| B is a middle term,
| C is a minor term,
| D is a minor term, similar to C.

In this analysis of reasoning by Analogy,
it is a complex or a mixed form of inference
that can be seen as taking place in two steps:

1.  The first step is an Induction that abstracts a Rule
    from a Case and a Fact.

(Case)   D => B,   Thebes vs Phocis is a battle between neighbors.
(Fact)   D => A,   Thebes vs Phocis is adverse to all.
(Rule)   B => A,   A battle between neighbors is adverse to all.

2.  The final step is a Deduction that applies this Rule
    to a Case to arrive at a Fact.

(Case)   C => B,   Athens vs Thebes is a battle between neighbors.
(Rule)   B => A,   A battle between neighbors is adverse to all.
(Fact)   C => A,   Athens vs Thebes is adverse to all.

Analysis of Dewey's Example of Inquiry

Returning to the "Rainy Day" story, we find our peripatetic
hero presented with a surprising Fact:

(Fact)   C => A,   "in the Current situation the Air is cool".

Responding to an intellectual reflex of puzzlement about the
situation, his resource of common knowledge about the world
is impelled to seize on an approximate Rule:

(Rule)   B => A,   "just Before it rains, the Air is cool".     

This Rule can be recognized as having a potential relevance to
the situation because it matches the surprising Fact, C => A,
in its consequential feature A.  All of this suggests that the
present Case may be one in which it is just about to rain:

(Case)   C => B,   "the Current situation is just Before it rains".

The whole mental performance, however automatic and semi-conscious
it may be, that leads from a problematic Fact and a knowledge base
of Rules to the plausible suggestion of a Case description, is what
is usually called an abductive inference.

The next phase of inquiry uses deductive inference to expand
the implied consequences of the abductive hypothesis, with the
aim of testing its truth.  For this purpose, the inquirer needs
to think of other things that would follow from the consequence
of his precipitate explanation.  Thus, he now reflects on the
Case just assumed:

(Case)   C => B,   "the Current situation is just Before it rains".

He looks up to scan the sky, perhaps in a random search for
further information, but since the sky is a logical place to
look for details of an imminent rainstorm, symbolized in our
story by the letter B, we may safely suppose that our reasoner
has already detached the consequence of the abduced Case, C => B,
and has begun to expand on its further implications.  So let us
imagine that our up-looker has a more deliberate purpose in mind,
and that his search for additional data is driven by the new-found,
determinate Rule:

(Rule)   B => D,   "just Before it rains, Dark clouds appear".

Contemplating the assumed Case in combination with this new Rule
leads him by an immediate deduction to predict an additional Fact:

(Fact)   C => D,   "in the Current situation Dark clouds appear".

The reconstructed picture of reasoning assembled in this second phase
of inquiry is true to the pattern of deductive inference.

Whatever the case, our subject observes a Dark cloud, just as he would
expect on the basis of the new hypothesis.  The explanation of imminent
rain removes the discrepancy between observations and expectations and
thereby reduces the shock of surprise that made this inquiry necessary.

Figure 3 gives a graphical illustration of Dewey's example of inquiry,
isolating for the purposes of the present analysis the first two steps
in the more extended proceedings that go to make up the whole inquiry.

|          A                                               D
|           o                                             o
|            \ *                                       * /
|             \  *                                   *  /
|              \   *                               *   /
|               \    *                           *    /
|                \     *                       *     /
|                 \   R u l e             R u l e   /
|                  \       *               *       /
|                   \        *           *        /
|                    \         *       *         /
|                     \          *   *          /
|                   F a c t        B        F a c t
|                       \          *          /
|                        \         *         /
|                         \        *        /
|                          \       *       /
|                           \   C a s e   /
|                            \     *     /
|                             \    *    /
|                              \   *   /
|                               \  *  /
|                                \ * /
|                                 \*/
|                                  o
|                                  C
|
| Figure 3.  Dewey's "Rainy Day" Inquiry
|
| A  =  the Air is cool,
| B  =  just Before it rains,
| C  =  the Current situation,
| D  =  a Dark cloud appears.
|
| A is a major term,
| B is a middle term,
| C is a minor term,
| D is a major term, associated with A.

In this analysis of the first steps of Inquiry,
we have a complex or a mixed form of inference
that can be noted as taking place in two steps:

1.  The first step is an Abduction that abstracts a Case
    from the consideration of a Fact and a Rule.

(Fact)   C => A,   In the Current situation the Air is cool.
(Rule)   B => A,   Just Before it rains, the Air is cool.
(Case)   C => B,   The Current situation is just Before it rains.

2.  The next step is a Deduction that admits this Case
    to another Rule and so arrives at a novel Fact.

(Case)   C => B,   The Current situation is just Before it rains.
(Rule)   B => D,   Just Before it rains, a Dark cloud will appear.
(Fact)   C => D,   In the Current situation, a Dark cloud will appear.

This is nowhere near a complete analysis of the Rainy Day inquiry,
even insofar as it might be carried out within the constraints of
the syllogistic framework, and it covers only the first two steps
of the relevant inquiry process, but maybe it will do for a start.

o~~~~~~~~~o~~~~~~~~~o~REVIEW~o~~~~~~~~~o~~~~~~~~~o

Abstraction, Analogy, Model, Morphism

http://suo.ieee.org/email/msg01246.html
http://suo.ieee.org/email/msg01251.html
http://suo.ieee.org/email/msg01293.html
http://suo.ieee.org/email/msg01350.html
http://suo.ieee.org/email/msg01772.html
http://suo.ieee.org/email/msg01812.html
http://suo.ieee.org/email/msg01824.html
http://suo.ieee.org/email/msg01910.html
http://suo.ieee.org/email/msg04768.html
http://suo.ieee.org/email/msg04770.html

Alternates --

http://suo.ieee.org/ontology/msg02361.html
http://suo.ieee.org/ontology/msg02363.html

http://stderr.org/pipermail/arisbe/2001-May/000481.html
http://stderr.org/pipermail/arisbe/2001-May/000482.html

o~~~~~~~~~o~~~~~~~~~o~WEIVER~o~~~~~~~~~o~~~~~~~~~o

04 Aug 2001 • 11:11 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sat, 04 Aug 2001 11:11:34 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard, I continue to be at a loss for how to interpret many
of the technical terms and phrases that you use in this text.
I do not know what else to do but keep pressing for clarity.
Many of my most familiar terms and phrases are being used in
ways the meaning of which to you I can neither grasp, guess,
nor for which invent any consistent sense.  Most of these
problematic themes appear to arise in the neighborhood of
the rootword "forma" -- which to me is an old Latin word
for "beauty", and so not a conceit that I would gladly
let go.  I have had some training in what are commonly
called the "formal sciences".  But the way that you
treat the word "formal" and many of the predicates
in which you wrap the phrase "formal system" are
all against the grain of that training for me,
or else contain a hint of some novel subject
altogether.  You have written out some lines
that you call "definitions" of these items,
but so far I do not see that they bound.
I am afraid that there is nothing for
it but just to keep inquiring into
their purports of meaningfulness.

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: As I warned, I'm not talking stereotypic rationalizations.
    I'm simply defining my usage [of "formal"] by stating a simple,
    empirically testable condition for a formal process.
    Just follow the rules.

I guess that the trouble starts right at the very beginning, but
I did not realize before that you meant this as formal definition.
Are you then saying that you're saying:

|
| Definition.  A "formal process" is "just follow the rules".
|

HP: Adding a column of numbers can be accomplished whether or
    not the numbers refer to apples, bytes, or nothing but number.
    It's called calculating.

I see an act of abstraction, and then I see an activity of calculation.

JA: Oh, you mean an algorithm?
    Id est, an effective procedure?
    To wit, an effective description
    of a particular pattern of behavior?
    You regard this as empirically testable?
    I worry about that.  Some things I know of
    say yes, okay.  Other things say no, no way.
    I will have to think about this for a while.

HP: Within the limits of error a formal system
    is probably more empirically testable than
    any other empirically testable system.  But,
    you are well-justified in worrying about that,
    since all empirical tests are noisy and have
    some error.  Therefore, on this general ground
    alone we never can verify with certainty that
    a "formal system" is more than just very good
    statistics.

Again, I see that you are using this phrase "formal system" in a way
that I cannot unify with the long-accustomed uses that I know for it --
id est, I can see that you are enclausing it in express predications
in which it would never occur to me to enclose it, and so this tends
to make me suspect that you are using it to describe a subject other
than those that I have formerly described, expressed, or known by it.

Just by way of seeking a point of common origin and reference, the first things
that pop into my mind when I see "formal system" are things that by other names
many call "axiom systems", "formal grammars", "formal languages", and their ilk.
Is that anything like what you intend to indicate here?

JA: But I still perceive a residue of the attitude called "formalist"
    in this seemingly, all too seemingly innocent definition of "formal".
    It shows up in the tendency to use qualifiers like "just", "merely",
    "nothing but" in the invitation to follow.

HP: Your perception of my attitude is incorrect.  You are mistaking my attempt
    to clearly communicate (by defining my words) with what I actually believe
    about formal systems.  While you are thinking about this, I will summarize
    what I think about the physics of symbols.

HP: http://www.c3.lanl.gov/~rocha/pattee/

I started reading this a while back.
And I was once a heavy consumer of
that Santa Fe strain of semiotics.

HP: The conceptual problem with formal systems is worse than simply the 
    fact that we cannot, with certainty, empirically verify their existence.

Now here is an example of what I mean, a "formal system"-related sentence
that gives me such a jolt when I read it that I do a double take and then
conclude for the moment that we must be using radically diverse languages.

Can you elaborate on what this sentence means?

HP: The deeper problem from the physicist's view is that every single step
    of a formal [process?] is subject to empirical error.  This is assuming
    measurement and control are irreversible events, hence dissipative and
    noisy. (I'm ignoring Landauer, Bennett, et al. who claim "in principle"
    reversibility because nobody has done it.)  In this view, a mathematical
    proof is nothing more than a series of noisy empirical measurement
    (recognizing symbol vehicles) controlled by noisy rules (rewriting,
    storing, etc.).  This holds for all reading and writing of symbols
    (symbol vehicles being in part defined as arbitrary coded physical
    structures).

Okay, this more like stuff that I have at least thought about a little.

HP: The fact that the accumulated statistical errors may be very small is an
    important practical fact, but that would not satisfy Platonic formalism.

But now you are jolting me again.  "Platonic formalism" clangs like
a contradiction in terms to my mind's ear -- of course, if you were
to capitalize the pun in the form "Platonic Formalism" then perhaps
that would have telegraphed the punchline in a way that you thought
was just too easy.  If this be not a joke, then can you tell me
what it means?

HP: There is also the related Lakatos-type problem that we cannot completely
    define sets, rules, and domains of applicability leaving no ambiguity.
    The "formal" logic problems of infinite sets, consistency and completeness
    are also real, but ignored by most physicists as "just formal."  They have
    more pragmatic problems.

And thereby hangs a tale.  Let me try pull it through the form of a riddle:
Can you tell me what was the first widely-used "Virtual Reality" system in
the field of computer science?

JA: When I say I do not understand your usage, I really mean it.
    Oh, it's not like I never heard this way of talking before,
    or even that I did not speak this way for years and years.
    No, I mean that I do not understand this form of talking
    in the way that I no longer understand expressions that
    I am beginning to suspect are irreducibly ambiguous
    or even irredeemably inconsistent.  It's still just
    a suspicion at this point, but it grows stronger.

HP: So we appear to agree about the inadequacy of formal systems, ...

We might, just perhaps, but we would first have to arrive at
an accommodation as to what the phrase "formal system" names.

HP: So we appear to agree about the inadequacy of formal systems,
    if perhaps for different reasons.  And yet, we all continue
    to use formal systems.  Why is this?  Well, it's because we
    have nothing better.  Noise is built in to the universe.
    It is everywhere, and the ideal of formal systems is not
    only to reduce noise to the minimum, it also frees us from
    the bounds of everyday experience.  How else but by formal
    systems could the imagination unambiguously manipulate (and
    communicate) imaginary numbers in infinite dimensional spaces?
    (That was the reason for my Hilbert space question.) Galileo and
    all physicists thereafter have followed Nicholas Cusanus's advice
    with unreasonable success:  "If the transcendental is accessible to
    us only through the medium of images and symbols, let the symbols at
    least be as distinct and unambiguous as mathematics will permit."

Well, now I am getting the sense that you are posing all symbol systems
to fall out under the banner of "formal systems".  Is that a good guess?
If so, then I can almost see a connection with the pragmatic picture of
logic as "formal and normative semiotic", but there would be a twist or
two before the tie could be made tight, if at all.

HP: It is also wise to remember that evolution by natural selection requires noise
    in the genetic symbol system.  There is good evidence that creative thought, and
    therefore inquiry, also require some noise.  As Spinoza and Martha Stewart always
    say, sub specie aeternitatis, a little noise is a good thing.  The greatest danger
    of formal language, as Stan would agree, is its premature or inappropriate application
    to imaginative, vague, or creative thought.

Okay, I can warm to this a little, as it was always less the noise factor,
the big hullaballo over ambiguity and all that -- than the sampling ratio,
all the stuff that gets left out of our formal acounts, that brings me to
the point, almost, of decrying how "inadequate" formal systems always are,
though, on reflection, I'm apt to back off pressing this point when I wit
of how "adequacy" is adequately judged only relative to an intendable aim.

JA: I have good reasons to say that any notion of how signs relate to objects
    that is limited to commutative diagrams and linear (homomorphic) mappings
    is just not general enough to cover all of the conceivable and all of the
    observable cases of sign relations that are useful in adapting to reality.

HP: I agree, although I would like to hear your good reasons.

When you think on this, and you will ... [standard joke follows].

HP: My point about Hertz's 40 words was just that it was not a formal statement, and
    therefore should not be limited by your characterization of it in formal terms.
    This is why physicists often reject logic in the formative stages of inquiry.

Who doesn't?

Jon Awbrey

04 Aug 2001 • 23:45 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sat, 04 Aug 2001 23:45:02 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: Howard, I continue to be at a loss for how to interpret many
    of the technical terms and phrases that you use in this text.
    I do not know what else to do but keep pressing for clarity.
    Many of my most familiar terms and phrases are being used in
    ways the meaning of which to you I can neither grasp, guess,
    nor for which invent any consistent sense.  Most of these
    problematic themes appear to arise in the neighborhood of
    the rootword "forma" -- which to me is an old Latin word
    for "beauty", and so not a conceit that I would gladly
    let go.

HP: I am using the concept of 'formal" only in the sense used in the areas you mention,
    formal math, formal logic, formal language.  I'm using the standard meaning found
    in any math dictionary:  "An uninterpreted symbolic system including non-logical
    axioms on which there is a relation of deducibility in purely syntactic terms."
    Hermann Weyl, more metaphorically, calls a formal system: "... a game of symbols
    played according fixed rules [where] the symbols are not meant to be symbols for
    something."

I believe that many different issues are being confounded here under the same name.
This is very typical of what happens when a good idea, like "let's pay attention to
the forms of what's happening here", gets turned into an "-ism", like "nothing but
the forms of what's happening here matters very much at all".  I understand about
uninterpreted formal systems, and I do a large part of my basic logical work with
abstract calculi that are even more uninterpreted than most you will typically see.
But not all formal systems are uninterpreted, nor meant to be valued most highly in
that very abstract form.  I tend to use the word "abstract" when I want to emphasize
the circumstance that the form of the proceedings is being emphasized almost to the
exclusion of interest in anything else, as in the phrase "pro forma", but neither
the word "abstract" nor the word "formal" implies that the concrete material has
somehow gone away.  The way I see it, the only sense of "formal" worth having
is one that highlights the facets of form without deluding us into thinking
that no other aspect matters, that is, up until we reach that pythagorean
perspective where we can truly see exactly how form and matter are one.

Your line from Weyl is typical of the formalist line.
What I did not find out for many years is that nobody,
especially no real mathematician, as Weyl most surely
was, ever really lives by that line.  Some of this is
very personal to me, as I bought this line for a very
long time, and only gradually came to the realization,
and with not just a little sense of personal betrayal
and deep intellectual disillusionment, that this line
is just a red herring that your average mathematician
will tend to hand a pesky student in order to get him
out of his office, to avoid a dreaded "philosophical"
discussion, or else that a famous virtuoso will hand
a tedious reporter in order to give her a nice story.
It is a convenient line in a certain type of social
situation, and maybe it is their idea of a harmless
joke or a pacifying fiction, but if I ever run into
a mathematician who says that he or she really and
truly buys it, then my initial hypothesis will have
be that the person is a victim of a self-deception.
 
HP: As I warned, I'm not talking stereotypic rationalizations.

HP: I'm simply defining my usage [of "formal"] by stating a simple,
    empirically testable condition for a formal process.
    Just follow the rules.

JA: I guess that the trouble starts right at the very beginning, but
    I did not realize before that you meant this as formal definition.
    Are you then saying that you're saying:
    |
    | Definition.  A "formal process" is "just follow the rules".
    |

HP: The class of formal system cannot be formally defined.
    "Just follow the rules" was as short a description
    as I could imagine that expresses the key idea
    that interpretation of the symbols (other than
    just following the rules) is not relevant in
    formal manipulations.

I am trying to point out the fact that this is not any kind of definition,
whether casual or formal, because the predicates "following a rule" (FAR)
and "following a set (sequence, series, system) of rules" (FASOR) are way
too ambiguous as casually used and way too far from being empirical ideas.

HP: Adding a column of numbers can be accomplished whether or
    not the numbers refer to apples, bytes, or nothing but number.
    It's called calculating.

JA: I see an act of abstraction, and then I see an activity of calculation.

HP: You see too much.  To add, a calculator does not have to abstract anything.
    It just follows the rules.

Normally speaking, we do the abstraction before we go to the calculator.
Then the calculator does the calculation?  You could say that, I guess,
but then you would be saying too much.  More carefully speaking, you'd
be nearer the truth to say that the calculator goes through the motion
that we interpret as being a calculation.  And then we do the reverse
of the initial abstraction step, to wit, we interpret the patterns of
colored lights, in order to make use of the whole operation.  I think
that it is necessary to see all of this in order to understand why in
the heck we bother to do it, to wit, to know the pragma of the conduct.

JA: Oh, you mean an algorithm?
    Id est, an effective procedure?

HP: Yes and Yes.  These are special cases of formal procedures.

JA: To wit, an effective description
    of a particular pattern of behavior?
    You regard this as empirically testable?

HP: Yes.  The test for formal operations (quoting Kleene):
    "It must me possible to perform the deductions treating
    the symbols as words without meaning.  For to say they
    have meaning necessary to the deductions ... amounts
    to saying that not all of the properties necessary
    for deduction have been expressed in the axioms."
    In other words, if you can't find a necessary rule,
    or you do have to act without a rule, then you don't
    have a formal system.

You must be aware of the circumstance that there are different
dispositions, inclinations, persuasions, and personal styles of
thinking even in the formal sciences like logic and mathematics.
For instance, there are model-theoretically inclined folks and
there are proof-theoretically bent folks, and all of the lines
that you are citing in this connection are skewed to the sorts
of things that the "proof and syntax is all" (PASIA) school is
very well known for preaching.  But not everybody attends that
particular Church.

JA: I worry about that.  Some things I know of
    say yes, okay.  Other things say no, no way.
    I will have to think about this for a while.

HP: Within the limits of error a formal system
    is probably more empirically testable than
    any other empirically testable system. But
    you are well-justified in worrying about that,
    since all empirical tests are noisy and have
    some error.  Therefore, on this general ground
    alone we never can verify with certainty that
    a "formal system" is more than just very good
    statistics.

JA: Again, I see that you are using this phrase "formal system" in a way
    that I cannot unify with the long-accustomed uses that I know for it --
    id est, I can see that you are enclausing it in express predications
    in which it would never occur to me to enclose it, and so this tends
    to make me suspect that you are using it to describe a subject other
    than those that I have formerly described, expressed, or known by it.

HP: Perhaps that is because I am pointing out the physical limitations
    of formal systems that nobody likes to mention.

In Classical AI, it used to be discussed much and mentioned almost to tears
in the hushed tones of the "Physical Symbol System Hypothesis" (PSSH), still
another of the annoying truths that Peirce used to mention, and more, to use.

But now I am guessing that you are speaking of the implementation
or the realization of an abstractly specified formal system, which
is certainly fine by me, but the properties of control, information,
or the lacks thereof, of which you are speaking, I am still guessing,
are only properly predicable of the total system, from which the form
is solely in our imaginations abstracted.

JA: Just by way of seeking a point of common origin and reference, the first things
    that pop into my mind when I see "formal system" are things that by other names
    many call "axiom systems", "formal grammars", "formal languages", and their ilk.
    Is that anything like what you intend to indicate here?

HP: That is exactly the way I have been thinking of "formal" all along.

JA: But I still perceive a residue of the attitude called "formalist"
    in this seemingly, all too seemingly innocent definition of "formal".
    It shows up in the tendency to use qualifiers like "just", "merely",
    "nothing but" in the invitation to follow.

HP: You are too suspicious.  I said I did not want to get involved here
    with the metaphysics of the "formalists" (versus "intuitionists",
    "logicists", Platonists") on the foundations of mathematics.
    To work with a formal system (math, logic, language, whatever)
    does not need a commitment to any philosophy.  You don't even
    have to like it.  Just follow the rules.

But you are the one who keeps quoting the formalist bible as if they
were the only ones who can speak for the one true teaching about form.
I already know -- that if you ask them -- they'll tell that this is so.

HP: Your perception of my attitude is incorrect.  You are mistaking my attempt
    to clearly communicate (by defining my words) with what I actually believe
    about formal systems.

Again, you are mistaking the teachings of formalists
with the truth, the whole truth, and nothing but the
truth about form.  You are using a particular school's
characterization of what constitutes the formal aspect,
and their doctrine, or fiction, or joke, about what it
all means to them, as if there were no other view of it.

There other ways of looking at form,
not to mention its relation to matters
of dynamics and styles of interpretation.

HP: I believe formal systems are an ideal that cannot be met in principle,
    but that can can be made to work well enough to safely bet on their
    results.  While you are thinking about this, I will summarize what
    I think about the physics of symbols.

HP: http://www.c3.lanl.gov/~rocha/pattee/

HP: The conceptual problem with formal systems is worse than simply the 
    fact that we cannot, with certainty, empirically verify their existence.

JA: Now here is an example of what I mean, a "formal system"-related sentence
    that gives me such a jolt when I read it that I do a double take and then
    conclude for the moment that we must be using radically diverse languages.
    Can you elaborate on what this sentence means?

HP: The only formal tests for a formal system are for its completeness and its consistency.
    But any formal test assumes that all the symbols are read and written correctly and that
    all the rules have been followed correctly.  This requires the informal observation and
    recognition of symbols which are only assumed to be error free, but which cannot be proved
    to be error free (since proof is only a formal concept).  Since physically all observations
    are noisy, there is always a finite probability of error.  But as I said, the recognition of
    symbols and rules is less noisy than most measurements (that is why we use bits and binary
    switches in computers).

This is the same problem that people get into when they confound logic and psychology.
I believe that it is a bad idea to confound the level of the implementation with the
level of the abstractly specified formal system, as you do when you say stuff like:

| HP: The conceptual problem with formal systems
|     is worse than simply the fact that we cannot,
|     with certainty, empirically verify their existence.

The first time that I read this I naturally parsed the substantive "existence" at the end
with an inflection that semantically agreed with the adjectives "conceptual" and "formal"
up front, but now I am getting the drift that you meant "existence" in a physical sense.
And that just mixes the levels.  The reason we abstract the form is to attend away from
the implementation.  It is fine and dandy to engineer the reverse of this abstraction --
I recommend it on a periodic basis -- but when one goes through the trouble to ginger
the inverse step, stepping down in the direction of the ground, then the predicates
that one hauls in are no longer the predicaments of the form.

HP: The deeper problem from the physicist's view is that every single step
    of a formal [process] is subject to empirical error.  This is assuming
    measurement and control are irreversible events, hence dissipative and
    noisy.  I'm ignoring Landauer, Bennett, et al. who claim "in principle"
    reversibility because nobody has done it.)  In this view, a mathematical
    proof is nothing more than a series of noisy empirical measurement
    (recognizing symbol vehicles) controlled by noisy rules (rewriting,
    storing, etc.).  This holds for all reading and writing of symbols
    (symbol vehicles being in part defined as arbitrary coded physical
    structures).

I would just prefer to say:

| The deeper problem from the physicist's view is that every single step
| of an actualized, implemented, or realized formal process is subject
| to empirical error.

Does that make sense to you?

JA: Okay, this more like stuff that I have at least thought about a little.

HP: The fact that the accumulated statistical errors may be very small is an
    important practical fact, but that would not satisfy Platonic formalism.

JA: But now you are jolting me again.  "Platonic formalism" clangs like
    a contradiction in terms to my mind's ear -- of course, if you were
    to capitalize the pun in the form "Platonic Formalism" then perhaps
    that would have telegraphed the punchline in a way that you thought
    was just too easy.  If this be not a joke, then can you tell me
    what it means?

HP: I meant only to contrast Platonic forms which are imagined to be "perfect forms"
    with physically realizable forms that are imperfect and statistical.  There is
    an "unbridgeable gulf" (Planck) between a probability, however small, and
    perfect determinism.

Okay, but I do not see a connection between platonic ideas and perfect determinism.

HP: There is also the related Lakatos-type problem that we cannot completely define sets,
    rules, and domains of applicability leaving no ambiguity.  The "formal" logic problems
    of infinite sets, consistency, and completeness are also real, but ignored by most
    physicists as "just formal."  They have  more pragmatic problems.

JA: And thereby hangs a tale.  Let me try pull it through the form of a riddle:
    Can you tell me what was the first widely-used "Virtual Reality" system in
    the field of computer science?

HP: Turing's original machine was a virtual reality model
    formalizing the brain trying to do arithmetic, but
    maybe Pythagorus was using numbers to make virtual
    models of God.

Good guess, but I was thinking "FORTRAN".

It was implemented by people who had to attend to the realities
of the information dimension so that physicists could forestall
by a few more years the need to do so and to keep on pretending
that they operated in a world of infinite precision arithmetic.

JA: When I say I do not understand your usage, I really mean it.
    Oh, it's not like I never heard this way of talking before,
    or even that I did not speak this way for years and years.
    No, I mean that I do not understand this form of talking
    in the way that I no longer understand expressions that
    I am beginning to suspect are irreducibly ambiguous
    or even irredeemably inconsistent.  It's still just
    a suspicion at this point, but it grows stronger.

HP: So we appear to agree about the inadequacy of formal systems, ...

JA: We might, just perhaps, but we would first have to arrive at
    an accommodation as to what the phrase "formal system" names.

HP: So we appear to agree about the inadequacy of formal systems,
    if perhaps for different reasons.  And yet, we all continue
    to use formal systems.  Why is this?  Well, it's because we
    have nothing better.  Noise is built in to the universe.
    It is everywhere, and the ideal of formal systems is not
    only to reduce noise to the minimum, it also frees us from
    the bounds of everyday experience.  How else but by formal
    systems could the imagination unambiguously manipulate (and
    communicate) imaginary numbers in infinite dimensional spaces?
    (That was the reason for my Hilbert space question.) Galileo and
    all physicists thereafter have followed Nicholas Cusanus's advice
    with unreasonable success:  "If the transcendental is accessible to
    us only through the medium of images and symbols, let the symbols at
    least be as distinct and unambiguous as mathematics will permit."

My new guess is that when you say "formal system" you mean the type of object system
that I would consider as an augmented system or a compound object under the formulas
of an "implemented formal system" or maybe a "formal system + concrete realization".

JA: Well, now I am getting the sense that you are posing all symbol systems
    to fall out under the banner of "formal systems".  Is that a good guess?

HP: Certainly not!  Almost all symbol systems, all semiotic systems,
    are usually thought of as interpreted systems.  You know that.
    Formal systems are rare just because all extrinsic meaning, all
    semantic reference, has been eliminated (as far as possible).

No, I am pretty sure that I would never say it that way.
You simply must realize that the particular description
of "What Is And What Should Be The Formal" that you are
using in all of these statements is only the picture of
a single historically circumscribed and situated school
of thought.  I personally think that the entire picture
is a well-intentioned joke that just got out of control,
like certain computer viruses that we have came to know
and to hate.

I really see no need to "eliminate" the meaning of a form of conduct
in order to arrive at an appreciation of its form, and I have worked
on formal semantics as well as on formal pragmatics.  I believe that
the adjective "formal" can have a focusing effect on the mind, while
remaining neutral with respect to many details of matter and meaning.

To use an analogy that I have put into practice in a very real way,
formal structure is derived from concrete conduct much in the same
way that tangents and normals are derived and produced from curves.

HP: It is also wise to remember that evolution by natural selection requires noise
    in the genetic symbol system.  There is good evidence that creative thought, and
    therefore inquiry, also require some noise.  As Spinoza and Martha Stewart always
    say, sub specie aeternitatis, a little noise is a good thing.  The greatest danger
    of formal language, as Stan would agree, is its premature or inappropriate application
    to imaginative, vague, or creative thought.

JA: Okay, I can warm to this a little, as it was always less the noise factor,
    the big hullaballo over ambiguity and all that -- than the sampling ratio,
    all the stuff that gets left out of our formal acounts, that brings me to
    the point, almost, of decrying how "inadequate" formal systems always are,
    though, on reflection, I'm apt to back off pressing this point when I wit
    of how "adequacy" is adequately judged only relative to an intendable aim.

HP: I agree.  As I said, you try to use formal systems
    all the time because they are much less noisy and
    ambiguous than natural language.

Perhaps, but does not formal abstraction involve a certain amount
of what is often so euphemystically called "systematic ambiguity"?

I guess if I tried to sum up what I have been trying to say in this cycle,
it would be that I view the point of view that we describe as the "formal"
as a way of looking at an object system and not as its exhaustive essence.

Jon Awbrey

05 Aug 2001 • 09:14 • Reflective Interpretive Frameworks

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Subj: OCA: Reflective Interpretive Frameworks (RIFs)
Date: Sun, 05 Aug 2001 09:14:12 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

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| Die unbegreiflich hohen Werke
| Sind herrlich wie am ersten Tag.
|
| The world's unwithered countenance
| Is bright as on the earliest day.
|
| Goethe, 'Faust',
| Quoted in Weyl, 'The Open World', (Weyl, 29)

The straightforward way of Aristotle is a turn that I can admire,
but not quite achieve;  he writes it straight out:  soul is form.

| Tell me, good Brutus, can you see your face?
|
| No, Cassius, for the eye sees not itself
| But by reflection, by some other things.
|
| 'Tis just;
| And it is very much lamented, Brutus,
| That you have no such mirrors as will turn
| Your hidden worthiness into your eye,
| That you might see your shadow.  ...
|
| Into what dangers would you lead me, Cassius,
| That you would have me seek into myself
| For that which is not in me?
|
| Therefor, good Brutus, be prepared to hear.
| And since you know you cannot see yourself
| So well as by reflection, I, your glass,
| Will modestly discover to yourself
| That of yourself which you yet know not of.
|
| William Shakespeare, 'Julius Caesar', 1.2.53-72

The rest of this section, continuing the discussion of formalization
in terms of concrete examples and extending over the next 50 subsections,
details the construction of a "reflective interpretive framework" (RIF).
This is a special type of sign-theoretic setting, illustrated in the
present case as based on the sign relations A and B, but intended
more generally to constitute a fully developed environment of
objective and interpretive resources, in the likes of which
an "inquiry into inquiry" can reasonably be expected to
find its home.

An inquiry into inquiry necessarily involves itself in various forms of self-application
and self-reference.  Even when the "inquiree" and the "inquirer", the operand inquiry and
the operant inquiry, are conceived to be separately instituted and disjointly embodied in
material activity, they still must share a common form and enjoy a collection of definitive
characteristics, or else the use of a common term for both sides of the application is
equivocal and hardly justified.  But this depiction of an inquiry into inquiry, if it
is imagined to be valid, raises a couple of difficult issues, of how a form of activity
like inquiry can be said to apply and to refer to itself, and of how a general form of
activity can be materialized in concretely different processes, that is, represented
in the parametrically diverse instantiations of its own generic principles.  Before
these problems can be clarified to any degree it is necessary to develop a suitable
framework of discussion, along with a requisite array of conceptual tools.  This is
where the construction of a RIF comes in.

| And now the investigation itself is under investigation.
|
| President Clinton, August 17, 1998

The task of building a RIF is here approached on two fronts, structural and functional.
The structural approach looks to the formal constitution of the framework itself, with
an eye to the static logical relationships that potentially exist among its objective
and its interpretive elements, that is, the abstract relations that can be permitted
through the medium of its use to be brought to light, to be recognized on future
occasions, and to be signified to a community of observant and interpretive agents.
The functional approach looks to the dynamic and effective conduct of a typical
reflective interpreter, with an eye to the medium of operational resources that
support its activity, and it seeks to discover amid this defrayal the workings
of the act of reflection that makes it all possible.

| I was, at that time, in Germany, whither the wars, which have not yet finished there,
| had called me, and as I was returning from the coronation of the Emperor to join the army,
| the onset of winter held me up in quarters in which, finding no company to distract me, and
| having, fortunately, no cares or passions to disturb me, I spent the whole day shut up in a
| room heated by an enclosed stove, where I had complete leisure to meditate on my own thoughts.
|
| Rene Descartes, 'Discourse on Method', (Des1, 35)

On the manifest I can see the ostenciled mark --
a reputed distinction?  a travel destination? --
let us inspect the credential of the customed
stamp, collected at the border: "Ego-Non-Ego".

| A child hears it said that the stove is hot.  But it is not, he says;  and, indeed,
| that central body is not touching it, and only what that touches is hot or cold.
| But he touches it, and finds the testimony confirmed in a striking way.  Thus,
| he becomes aware of ignorance, and it is necessary to suppose a self in which
| this ignorance can inhere.  ...
|
| In short, error appears, and it can be explained only by supposing a self
| which is fallible.
|
| Ignorance and error are all that distinguish our private selves
| from the absolute ego of pure apperception.
|
| Charles Sanders Peirce, 'Collected Papers', (CP 5.233-235)

Peirce makes the point that one's first awareness of a personal existence arises in reaction to
the brute impact of experience and is ultimately compounded by way of reflection on its imports.
Taking this to echo the exchange between Brutus and Cassius, I have the points that I need to
stake out and to sound out a significant portion of the RIF that I intend to discuss.

Jon Awbrey

05 Aug 2001 • 12:20 • Inquiry Into Models

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Subj: OCA: Re: Inquiry Into Models
Date: Sun, 05 Aug 2001 12:20:15 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: Your diagram is near enough to the way I meant it,
    but it was not meant as a formalization, but as a
    clarification, as in diagramming a sentence.

|   EXTERNAL OBJECTS ____ WE FORM FOR OURSELVES ____ IMAGES, SYMBOLS, OR PICTURES
|         |                                        / [SIGNS, BRAIN STATES, WHATEVER]
|         |                                       /                  |
|         |                                      /                   |
|   [NATURAL LAWS]        . . . SUCH THAT . . . /    [LOGICAL, MATHEMATICAL MODEL]
|         |              /                                           |
|         |             /                                            |
|         |            /                                             |
|   NECESSARY NATURAL /___ ARE THE SAME AS THE _____ LOGICALLY NECESSARY
|   CONSEQUENTS                                      CONSEQUENTS OF THE MODEL

HP: Let me elaborate.  The only formal part is in the right vertical column.
    All the rest is a kind of epistemological diagram indicating the necessary
    conditions for an empirically verifiable formal model to successfully represent
    our experience.  An important aspect of the Hertz's statement, emphasized by the
    diagram, is that the horizontal lines represent the observer's (or agent's) semantic
    interaction with the world (i.e., detection, pattern recognition, observation, measurement),
    the right vertical column represents the syntactic or formal (usually sequential) manipulations
    of the observer, and the left vertical column represents the part of the world (space, time, energy,
    and matter) that we choose to model.  The separation of semantics (measurement of particular events)
    from syntax (the formal model of universal laws) is essential for physical theory.

HP: I often quote von Neumann, although there is general consensus in physics:

    | That is, we must always divide the world into two parts, the one being the observed system,
    | the other the observer.  In the former, we can follow up all physical processes (in principle
    | at least) arbitrarily precisely.  In the latter, this is meaningless.  The boundary between
    | the two is arbitrary to a very large extent.  ...  -- but this does not change the fact
    | that in each method of description the boundary must be placed somewhere, if the method
    | is not to proceed vacuously, i.e., if a comparison with experiment is to be possible.
    |
    | John von Neumann,
    |'Mathematical Foundations of Quantum Mechanics',
    | Translated from the German edition by Robert T. Beyer,
    | Princeton University Press, Princeton, NJ, 1955, 1983.
    | Princeton Landmarks in Physics Series, 1996, page 420.

The paragraph concludes:

| Indeed experience only makes statements of this type:
| an observer has made a certain (subjective) observation;
| and never any like this:  a physical quantity has a certain value.
|
| JvN, MFOQM, page 420.

HP: The most difficult column is the middle vertical column that is often called
    the "epistemic cut" because it separates the subject and object, or better,
    the knower from the known.  This can never be formalized without losing
    its essential function which is to provide the initial conditions for
    the formal model.  As von Neumann has made clear, if you try to move
    the cut left to include the measurement process in the model, then
    you must create a new measurement for new initial condition for
    the new model now including the old measuring device as part
    of the model -- an infinite regress. 

HP: This is summary and consequently it is oversimplified.
    Before saying more, I would like to know if Peirce makes
    a clear distinction or defines an epistemic cut between
    the world and the inquirer.

Howard,

I think that it would be fair to say -- in fifty words or less, but who's counting? --
that Peirce treats the lines that we draw between self and other as any other brand
of hypothetical construction, to wit, lines of whose positions we are bound to draw
the consequence of their supposed truth, whereon to abandon, defend, or redraw them.

I have strung a few beads, reflective of
this "particular line of thought" (PLOT),
on the random sampler of threads from my
dissertation that I e-nounced under that
mot "Reflective Interpretive Frameworks".

Jon Awbrey

05 Aug 2001 • 15:00 • Laws And Models

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Subj: OCA: Re: Laws And Models
Date: Sun, 05 Aug 2001 15:00:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subject:  "Laws And Models", Erstwhile Known As:

| Abstraction, Analogy, Arrow, Epitome, Example,
| Icon, Law, Metaphor, Model, Morphism, Paradigm,
| Prototype, Rule, Simulacrum, Simulation, Theory.

Exercise for the reader.
Divide the congeries of terms in the extended title above into a couple of
subtitles, consisting of terms that are more consistently alike each other.

I see myself getting into another discussion of laws, models, paradigms, and theories,
but before I dare to do that, rational procedure dictates that I do a duty of autopsy
on the lingering discourse of a previous discussation in the very same topics as this,
that I was shocked to discover in which I persisted through a sevenmonth of last year.

Perhaps some observer here can help me
to sort out exactly where I went wrong.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Note 4

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Abstraction, Analogy, Example, Icon,
      Metaphor, Model, Morphism, Paradigm,
      Prototype, Simulation

Date: Wed, 25 Oct 2000 14:56:03 -0400
From: Jon Awbrey
  To: Standard Upper Ontology
  CC: Conceptual Graphs

I keep coming back to the following two pictures or configurations:

1.  There is that A-frame construction in Aristotle's discussion
    of reasoning by way of Analogy, Example, or Paradigm, which
    he articulates as a combination of Induction and Deduction.

|                           Atrocious Adversity
|                                    A
|                                    o
|                                   /*\
|                                  / * \
|                                 /  *  \
|                                /   *   \
|                               /    *    \
|                              /     *     \
|                             /   R u l e   \
|                            /       *       \
|                           /        *        \
|                          /     Bellicose     \
|                         /       Battles       \
|                     F a c t        B        F a c t
|                       /         Between         \
|                      /        Bordermates        \
|                     /        *           *        \
|                    /       *               *       \
|                   /   C a s e             C a s e   \
|                  /     *                       *     \
|                 /    *                           *    \
|                /   *                               *   \
|               /  *                                   *  \
|              / *                                       * \
|             o                                             o
|            C                                               D
|         Contest:                                        Debacle:
|   Athens versus Thebes                            Thebes versus Phocis
|
| Figure 2.  Aristotle's "War Against Neighbors" Example
|
| A  =  Atrocious, Adverse to All, A bad thing.
| B  =  Belligerent Battle Between Brethren.
| C  =  Contest of Athens against Thebes.
| D  =  Debacle of Thebes against Phocis.
|
| A is a major term,
| B is a middle term,
| C is a minor term,
| D is a minor term, similar to C.

Note on Terminology:  I am using the terms "Case", "Fact", "Rule"
in the medieval manner that was added to the classical treatment
of syllogism at a somewhat later time, but predating our present
usage by several hundered years.  Under this schematization, one
enumerates the following three forms of reasoning:

Abduction:  Fact + Rule ---> Case,
Deduction:  Case + Rule ---> Fact,
Induction:  Case + Fact ---> Rule.

The cardinal- or hinge-point to note about Aristotle's example
of reasoning by example is that the middle term B serves as an
explanation of 'why' the major term A should be considered as
applicable to the contemplated instances of conflict, C and D,
instance C a future contingent whose advisability of rendering
actual was presently, at that time in Athens, being disputed,
instance D already a part of the discussants' previous history,
from which they might reasonably be expected to have learned.

2.  The other picture is John Sowa's World-Model-Theory Triptych:

http://www.bestweb.net/~sowa/ontology/mthworld.gif

Well, it took me so much time to find the loose ends of this thread
that I have plumb forgot what I was going to say, but I remember
that I saw some kind of analogy between these two pictures --
(Between Analogy Analogy Triptych)? -- and so I am sure that
if I take a little break it will all come back to me, soon.

http://suo.ieee.org/email/msg01772.html

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Note 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: Abstraction, Analogy, Example, Icon,
      Metaphor, Model, Morphism, Paradigm,
      Prototype, Simulation

Date: Fri, 27 Oct 2000 12:48:13 -0400
From: Jon Awbrey
  To: Philip Jackson
  CC: Conceptual Graphs, Standard Upper Ontology

Philip Jackson wrote (PJ):
Jon Awbrey wrote (JA):

JA: Abduction:  Fact + Rule ---> Case,
    Deduction:  Case + Rule ---> Fact,
    Induction:  Case + Fact ---> Rule.

JA: The cardinal- or hinge-point to note about Aristotle's example
    of reasoning by example is that the middle term B serves as an
    explanation of 'why' the major term A should be considered as
    applicable to the contemplated instances of conflict, C and D,
    instance C a future contingent whose advisability of rendering
    actual was presently, at that time in Athens, being disputed,
    instance D already a part of the discussants' previous history,
    from which they might reasonably be expected to have learned.

JA: The other picture is John Sowa's World-Model-Theory Triptych:

JS: http://www.bestweb.net/~sowa/ontology/mthworld.gif

JA: Well, it took me so much time to find the loose ends of this thread
    that I have plumb forgot what I was going to say, but I remember
    that I saw some kind of analogy between these two pictures --
    (Between Analogy Analogy Triptych)? -- and so I am sure that
    if I take a little break it will all come back to me, soon.

PJ: One way to construct an analogy might be along the lines:

    "The world is all that is the case",
    as Wittgenstein said at one time.

JA: I am taking a bit of a risk trying to preserve these antic notions
    of "Case", "Fact", "Rule", and their relationships to various forms
    of inference, both demonstrative and otherwise, especially alongside
    of the more finely geared up and more sharply tooled up instrumental
    senses that we have become accustomed, in modern times, to be using --
    and so I genuinely fear exceeding my margin of tolerance by trying
    to bring that "Master of those Games that are Played with Stones",
    Ludovico Wittgenstein, into the mix of my concrete foundations.

JA: If you wish to do this, then we will have to make sure that
    we carefully examine the assembled tokens and playing pieces,
    for instance, these little bitty words, "case", "fact", "rule",
    to see if all of the puzzle pieces really do belong in, or even
    ever came from, the same box, otherwise I fear that we will soon
    become the mercilessly strained victims of a hopelessly scrambled
    and inescapably dis-integral picture.

PJ: A model (of a theory) may be considered as a collection of facts.

JA: Well, you are stealing some of my most portentous rumbling here,
    but one of my aims in stringing out this thread is to introduce
    a "trial" notion of what constitutes a "model".  Up until a few
    days ago, I would have said "dual" notion, but as every good
    Peircean (and every good Freudian) eventually must, I am
    beginning to e-spy the spectre of thirdness raising its
    three urly heads.

JA: I used to think that a "model" was "anything about which
    a statement or a theory holds", thereby putting it into
    close relationship with the notion of a semantic object,
    that is, anything that a sign denotes.  Moreover, I was
    used to thinking -- or was that just my imagination? --
    that this was the sense of it that currently prevailed
    in the logical subject that we know as "model theory",
    and yet, I am beginning to have my doubts about that.

JA: So let me distinguish this sense of the word "model" from
    whatever it is that does presently dominate the thinking
    of those who currently practice this "theory of models",
    and let me give it a name, that nobody else will desire,
    dubbing it the "naive" or the "natural" sense of "model".

JA: Let me re-capitulate the triune heads of this dogma:

    1.  The naive meaning or the natural sense of the term "model".

    2.  The logical meaning of "model" that we find, or hope to find,
        in the customary conduct and the standard practices of that
        formal subject that is called, by convention, "model theory".

    3.  The analogical meaning of "model", wherein it is related to
        a whole host of notions like "analogue", "avatar", "copy",
        "facsimile", "icon", "image", "likeness", "representation",
        "reproduction", "simulacre", "simulation", and so on.

PJ: A theory may be considered as a collection of rules.

JA: Well, I usually consider a theory to be a collection of sentences,
    or, perhaps, the abstract propositions, the hypostatic statements,
    or the "logical equivalence classes" (LEC's) of signs that may be
    thought to correspond with these expressions, formulae, sentences.

PJ: These statements are open to further discussion, of course.

PJ: Patrick Grim's book "The Incomplete Universe" presents a collection of arguments
    against "The world is all that is the case".  We could (indeed, must) accept
    incompleteness and talk in terms of "everything we know that is the case",
    while granting that the world is larger than what we know.

PJ: Viewing a model as a collection of facts which satisfies a theory,
    is not the same as viewing a model as something that explains or
    emulates some phenomenon or situation.  This second concept of
    model is closer to the concept of a scientific theory ...

http://suo.ieee.org/email/msg01812.html

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Notes 6, 7, 8, 9, 10, 11

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

http://suo.ieee.org/email/msg01824.html
http://suo.ieee.org/email/msg01830.html
http://suo.ieee.org/email/msg01854.html
http://suo.ieee.org/email/msg01863.html
http://suo.ieee.org/email/msg01910.html
http://suo.ieee.org/email/msg01917.html

05 Aug 2001 • 21:00 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Sun, 05 Aug 2001 21:00:00 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote:
> 
> Jon,
> Our discussion is diverging into too many issues.  I began this discussion because I wanted to know
> how Peirce's methods of inquiry fundamentally differed from the types of inquiry I know in physics.
> Specifically, I asked,first, if Peirce's logic was treated as a formal logic, ...

Peirce defines "logic" as "formal semiotic".
In this he uses his definition of "formal".

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

In this connection, I personally prefer the definitions that appear
in 'The New Elements of Mathematics', a set of volumes of Peirce's
largely unpublished mathematical work, edited by Carolyn Eisele
(who passed away at the age of 98 just last January).

Here Peirce defines "logic" as "formal semiotic" and gives
one of his clearest definitions of the concept of a "sign".
The way I read it, this definition places the being of
a sign within a relational context, as a pragmatic role,
not as an essential attribute of the thing that takes up
that role.  I will quote two versions of the definition
from NEM 4, pp. 20-21 and 54, nearly the same in both
locations but with a few interesting variations.

[Here, I will use single quotes for Peirce's italics.]

o~~~~~~~~~o~~~~~~~~~o~CITATION~o~~~~~~~~~o~~~~~~~~~o

Version 1.

| No. 12.  'On the Definition of Logic'.
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time.  Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'.  It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized.  (CSP, NEM 4, 20-21).

Version 2.

| No. 12.  'On the Definition of Logic'.
|
| Logic is 'formal semiotic'.  A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'.  This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM, 54).

o~~~~~~~~~o~~~~~~~~~o~NOITATIC~o~~~~~~~~~o~~~~~~~~~o

http://suo.ieee.org/email/msg00829.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

> ... and second, if his method of inquiry tries to separate the syntax of logic
> from the semantics (i.e., the interpretations of the logical signs).  This seems
> to me to be necessary, but I do not understand Peirce.  Maybe he has other ideas.

You asked:

HP: Does Peircean inquiry strictly separate
    the logical syntax of signs from
    the semantics of observation?

I replied:

JA: I do not know what you mean by "strictly separate" in this context.
    I understand the relations among objects, signs, and ideas to make
    sense only within the context of one or another 3-adic sign relation.
    I've been told that Peirce seldom if ever used the term "semantics" --
    no matter, he recognized the denotative or the referential relation
    of signs and ideas to actual, imaginary, or intentional objects,
    so that is what we may call his sense of "semantics".  Are you
    asking whether objects and signs, as absolute categories, are
    mutually exclusive?

You responded:

HP: Hertz's epistemic condition is also irreducibly triadic with
    the same terms (object, image/sign, observer/interpreter), but
    he goes on to explain the necessary conditions for a good model,
    a homomorphism.  When we want to use a formal symbol system to
    model a physical system we have to assign observable qualities
    to some of the otherwise meaningless symbols and then provide
    initial conditions for them by measurement. If you do not make a
    strict distinction between the formal rule-system that represent 
    universal, inexorable laws and the initial conditions which may
    be different for every observer, the model no longer makes sense.
    To survive, inquiring physicists (bacteria and all living systems)
    want to know what they cannot influence and what they can change.

This led to many interesting further discussions, but I am still waiting for you to tell me
what you mean by "strictly separate".  Perhaps you think that this phrase is monosemic, but
it is not.  I know of very many radically different possible meanings, myself.  Chomsky once
described syntax as an "independent component", using these words in the mathematical sense.
Some people read "independent" as "autonomous", which he never said, but now there is this
entire cottage industry obliterature devoted to mining the maps their own mis-readings.
So I have learned that it pays to be careful in these things.

HP: To answer this question you needed to understand what I meant by a "formal system",
    but in spite of my identification of formal with standard definitions and my agreeing
    with your own suggestions (axiomatic systems, formal logic, formal languages, algorithm,
    effective procedure, etc.) you still say you are at a loss to understand.  You appear to
    evade my questions by saying you can't think that way.  I also do not understand why you
    are impervious to my repeated denials that I am promoting a philosophical "line" that
    you don't like and that I have stated I don't like either.  You appear to be looking
    for monsters under the bed.  So, only for purposes of answering my questions, not
    promotion, I will try again to identify what I mean by "formal system."

I know about axiom systems, formal grammars, formal languages, formal logics,
algorithms, effective descriptions, etc.  But what I know tells me that your
notion of "just follow the rules" is not well-defined in any empirical or
formal sense, as best as my fuzzy recall can remind me.  I pointed to
intuitive examples and theorems of recursion theory that I remember
as once impressing this impression on me.  I could be wrong about
the theorems -- I will have to go check my old textbooks -- but
I think that my concrete counter-examples are fairly clear.

HP: But before that, let me say why I am not promoting formal systems
    over any other system or aspect of inquiry, and why my meaning of
    formal procedure has no relation to the metaphysical view of some
    mathematicians often called formalists.  I regard formal procedures
    as just one of many essential tools or techniques of scientific inquiry,
    and as I emphasized in my first comment on this thread, it is almost never
    the first tool used in creative inquiry, but rather is useful only after
    playing with many vague, ambiguous images that have no formal expression.

Howard, I gather that your working method is quite practical and reasonable,
but the question that you keep asking me strikes me like a line from a movie:

| I am not a racist, just tell me
| if it's true what they say that
| white guys can't jump.

Just because some folks are called "Formalists"
does not mean that they hold the patent on the
definition of "Form".  If that was all it took,
all religions would dub themselves "Truism" and
be done with it.  You are viewing the scene the
way that the formalists have formerly painted it.
One of the chief difficulties that I have telling
people what Peirce said is getting it through to
them that he did not just check a different foil
on what they cannot seem to help thinking is the
"all-purpose universal multiple choice exam".

HP: There are an unlimited number of possible formal systems.

Actually, they are countable.

HP: The basic elements are a finite, fixed sets of symbols, axioms, and rules
    for reading and writing these symbols.  The basic restriction is that the
    reading and writing of the symbols is determined only by the axioms and rules
    and depends on the symbol vehicles alone (this is sometimes called syntax), and
    not on any referents or meanings or interpretations (sometimes called semantics).
    In other words, whether they have interpretation or not is irrelevant to their
    formal manipulation.  Formal languages, formal logics, algorithms, and mechanical
    procedures are common names for types of formal processes.

HP: I am feel sure you know what I'm talking about.
    I am puzzled by why my questions are so difficult
    for you to discuss.

The formal arena, to wit, the rational domain, is one thing.
The bearing of the conceivable tests in experience upon it
is a whole nuther question, and right at the moment it is
my impression that you are confounding the two reigns.
I believe in trying to integrate the empirical domain
and the rational realm, but that is not the same as
confounding them.

Jon Awbrey

06 Aug 2001 • 01:11 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 06 Aug 2001 01:11:47 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

Here is a type of chart or diagram that I use
to keep track of the various sorts of domains
that I have to think about in my logical work.
To extent that most of this work derives from
basically Peircean ideas, maybe it will serve
to address your questions about the ways that
the various aspects of sign relations -- what
folks have come to call "syntax", "semantics,
"semiotics", and "pragmatics" -- are related
to one another.

--------------------------------///--------------------------------------
    Objective Framework (OF)            Interpretive Framework (IF)
--------------------------------///--------------------------------------
 Formal or Mathematical Objects     Formal or Mathematical Signs & Texts
--------------------------------///--------------------------------------

          Propositions                          Expressions
           (Logical)                          (Propositional)
               o                                     o
               |                                     |
               |                                     |
               o                                     o
              / \                                   / \
             /   \                                 /   \
            o     o                               o     o
        Sets       Maps                  Set Names       Map Names
  (Geometric)     (Functional)          (Geometric)     (Functional)

--------------------------------///--------------------------------------

I am always working within a suitable sign relation, say L c OxSxI, where O, S, I
are the pertinent domains of objects, signs, and interpretant signs, respectively.

The objects are the things that I have to mention, to talk and to think about.
The signs and the interpretants are what I use to talk and to think about them.

Let me restrict my attention for now to that part of my work where I spend most of my time
exploiting certain analogies between logic and real analysis, that is to say, between sets
of type B^k and (B^k -> B) and sets of type R^k and (R^k -> R), with B = {0, 1}, R = Reals.

The "formal objects" are the elements, sets, and functions that go with this set-up.
The "formal signs" are the expressions that are available to indicate these objects.

The word "formal" here means that I am concerned with their form,
and also that their place within the setting is formally declared.
It is considered "good form" to see how far you can get this way,
but everybody knows that you just can't have it all this way.

In computational work, which is what I am almost always working toward these days,
one is primarily concerned with public signs, and so it is convenient to let the
domain of signs and the domain of interpretant signs be the same domain, S = I.
In such a setting, I will typically refer to this as the "syntactic domain",
in part because it will always be formalized as a formal language, with
a formal grammar that defines its membership, and maybe a parser, too.

Now, at this point it may sound almost as if all we need to worry about is the
two sets O and S = I, plus the 2-adic relation of denotation that connects them.
But that would be ignoring the realities of computation, which can be described
as the job of taking obscure signs (like "5+7") for a formal object (a number)
and transforming it somehow into a clear sign (like "12") for the same object.
This process of passing from an initial sign s to an interpretant sign s' to
another interpretant sign s", ..., and eventually to a canonical or a normal
sign for the same object is a special case of a "sign process" or "semiosis".

The full pragmatic sign relation is L c OxSxI.
Syntax is the business of defining S as a set.
Semantics is the 2-dim projection of L on OxS.
Semiotic transitions are certain pairs in SxI.

When the setting is very rich, with many types of objects,
typically organized into an "ontological hierarchy" (OH),
along with all of their corresponding sign classes, then
I will try to organize the whole panoply of objects and
signs into an "objective framework" (OF), on one side,
and an "interpretive framework", on the other side.
Now this works well enough as long as these sides
do not overlap too much, but when you begin to
need to start talking and thinking about your
own syntax, that is, to make pieces of the
IF into objects of discussion and thought,
and thus to push them into the OF, then
you have to become more sophisticated,
and to need a structure that I call a
"reflective interpretive framework",
or a RIF.

Jon Awbrey

06 Aug 2001 • 11:44 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry (All Flesh Is Kreas)
Date: Mon, 06 Aug 2001 11:44:00 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

Let me continue with this "concrete" example -- yes, it's also "abstract",
but abstract and concrete, artificial and natural, formal and material,
like most other dimensions of variation in the world, are "relative",
and yes, the line between absolute and relative is also relative --
where was I?  Oh yes, the example of "zeroth order logic" (ZOL),
and all of the various sorts of things, "objective" things and
"interpretive" things, that I have been having to think about
in order to implement a computational instrument for working
ZOL at a level beyond the levels of our meagre former powers.

JA: Here is a type of chart or diagram that I use
    to keep track of the various sorts of domains
    that I have to think about in my logical work.
    To extent that most of this work derives from
    basically Peircean ideas, maybe it will serve
    to address your questions about the ways that
    the various aspects of sign relations -- what
    folks have come to call "syntax", "semantics",
    "semiotics", and "pragmatics" -- are related
    to one another.

o---------------------------------///--------------------------------------o
|    Objective Framework (OF)             Interpretive Framework (IF)      |
o---------------------------------///--------------------------------------o
| Formal or Mathematical Objects      Formal or Mathematical Signs & Texts |
o---------------------------------///--------------------------------------o
|                                                                          |
|          Propositions                           Expressions              |
|           (Logical)                              (Logical)               |
|               o                  ^                   o                   |
|               |                  |                   |                   |
|               |             Abstraction              |                   |
|               |                  |                   |                   |
|               o     <-Denotation-@-Annotation->      o                   |
|              / \                 |                  / \                  |
|             /   \           Concreation            /   \                 |
|            /     \               |                /     \                |
|           o       o              v               o       o               |
|        Sets       Maps                   Set Names       Map Names       |
|  (Geometric)     (Functional)           (Geometric)     (Functional)     |
|                                                                          |
o---------------------------------///--------------------------------------o
|   Q c  X          q :  X  -> B           "Q"             "q"             |
|   F c K^k         f : K^k -> B           "F"             "f"             |
|   G c B^k         g : B^k -> B           "G"             "g"             |
|   H c R^k         h : R^k -> B           "H"             "h"             |
o---------------------------------///--------------------------------------o

The vertical dimension of my framèd landscape is one of increasing abstraction
among the forms of things-become as one ascends toward the summit of the scene,
and, diversely, one of increasing concrescence in the matters that fill in the
forms as one drifts toward the base of the frame to which I'm working interior.

JA: I am always working within a suitable sign relation, say L c OxSxI, where O, S, I
    are the pertinent domains of objects, signs, and interpretant signs, respectively.

JA: The objects are the things that I have to mention, to talk and to think about.
    The signs and the interpretants are what I use to talk and to think about them.

JA: Let me restrict my attention for now to that part of my work where I spend most of my time
    exploiting certain analogies between logic and real analysis, that is to say, between sets
    of type B^k and (B^k -> B) and sets of type R^k and (R^k -> R), with B = {0, 1}, R = Reals.

JA: The "formal objects" are the elements, sets, and functions that go with this set-up.
    The "formal signs" are the expressions that are available to indicate these objects.

JA: The word "formal" here means that I am concerned with their form,
    and also that their place within the setting is formally declared.
    It is considered "good form" to see how far you can get this way,
    but everybody knows that you just can't have it all this way.

JA: In computational work, which is what I am almost always working toward these days,
    one is primarily concerned with public signs, and so it is convenient to let the
    domain of signs and the domain of interpretant signs be the same domain, S = I.
    In such a setting, I will typically refer to this as the "syntactic domain",
    in part because it will always be formalized as a formal language, with
    a formal grammar that defines its membership, and maybe a parser, too.

JA: Now, at this point it may sound almost as if all we need to worry about is the
    two sets O and S = I, plus the 2-adic relation of denotation that connects them.
    But that would be ignoring the realities of computation, which can be described
    as the job of taking obscure signs (like "5+7") for a formal object (a number)
    and transforming it somehow into a clear sign (like "12") for the same object.
    This process of passing from an initial sign s to an interpretant sign s' to
    another interpretant sign s", ..., and eventually to a canonical or a normal
    sign for the same object is a special case of a "sign process" or "semiosis".

JA: The full pragmatic sign relation is L c OxSxI.
    Syntax is the business of defining S as a set.
    Semantics is the 2-dim projection of L on OxS.
    Semiotic transitions are certain pairs in SxI.

JA: When the setting is very rich, with many types of objects,
    typically organized into an "ontological hierarchy" (OH),
    along with all of their corresponding sign classes, then
    I will try to organize the whole panoply of objects and
    signs into an "objective framework" (OF), on one side,
    and an "interpretive framework", on the other side.
    Now this works well enough as long as these sides
    do not overlap too much, but when you begin to
    need to start talking and thinking about your
    own syntax, that is, to make pieces of the
    IF into objects of discussion and thought,
    and thus to push them into the OF, then
    you have to become more sophisticated,
    and to need a structure that I call a
    "reflective interpretive framework",
    or a RIF.

In my own working languages I attempt or purport to distinguish
the object side of things as the "objective framework" (OF) and
the signy side of things as the "interpretive framework" (IF),
and each of these aspects of the developing sign relation is
relevant to the evolving discussion in its own special way.

Within the context of this particular discussion, the propositions
are the "logical" (abstract, hypostatic, ideal, platonic) objects,
perhaps the chief objects of the whole discussion, whereas the
corresponding sets and maps, regarded as mathematical objects,
are two different kinds of "models" (concretions, construals,
fleshings out, also known as "interpretations" in yet another
sense of that protean word) of these abstract propositions.
That is, sets and maps are the sorts of things that I can
personally imagine being able to grasp in somewhat more
"intuitive" (anschaulich, visual, visceral, vital) forms,
in what I think of as "geometric" and "functional" terms.

Jon Awbrey

06 Aug 2001 • 15:02 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Mon, 06 Aug 2001 15:02:11 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard Pattee wrote (HP):

HP: I have read the passages from Peirce you quote over and over,
    but I doubt if I could elaborate sensibly on what it means.
    I think a few specific examples might help me interpret
    how Peirce's definition of a sign and use of logic might,
    or might not, be related to any of the wide variety of
    inquiry that produced great discoveries in physics.

Yes, it is a little bit like reading Galois on Group Theory.
If you have a hundred years or so to get a grasp on what
a group is, then you can read his work and realize that
everything he says is perfectly apt.  Sadly, we are
not to that point yet, where the Theory of Signs
is a standard part of the undergrad curriculum.

My own advice would be to try and flesh out Peirce's intensional description
of a typical sign relation in the materials of concrete extensional examples.
Think of the theory of sign relations as a subject like algebra, or geometry,
or more concretely, group theory, or graph theory.  Most concretely, perhaps,
you might think of it in terms of relational databases, where sign relations
would be represented as a particular variety of three-column relation tables.

| No. 12.  'On the Definition of Logic'.
|
| Logic is 'formal semiotic'.  A sign is something, 'A', which brings
| something, 'B', its 'interpretant' sign, determined or created by it,
| into the same sort of correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in which itself stands to 'C'.
| This definition no more involves any reference to human thought than
| does the definition of a line as the place within which a particle lies
| during a lapse of time.  It is from this definition that I deduce the
| principles of logic by mathematical reasoning, and by mathematical
| reasoning that, I aver, will support criticism of Weierstrassian
| severity, and that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics',
| Four Volumes In Five Books,
| Edited by Carolyn Eisele,
| Mouton, The Hague, 1976.

HP: Simplifying:
    A brings B to correspond with C as A corresponds to C.
    So we can diagram it as a triangle:

|                               A (sign)
|                              / \
|                             /   \
|                            /     \
|                           /       \
|                         C - - - - - B 
|                  (object)           (interpretant sign)

HP: So, A creates B and also brings B into the relation BC which is
    the same (or lower?) relation as AC.  (Have I got that right?

No, the "correspondence" that is indicated here is a "triple correspondence",
what might be called a "3-place transaction" in database terms.  Let us name
this 3-place relation L.  Accordingly, to say that "A brings B to correspond
with C as A corresponds to C" is simply to say that A brings B into the same
3-place relation L with something else B' and C as A occupies in the 3-place
relation L with B and C.  Posed as an analogy with related terms in the form
<Object, Sign, Interpretant>, one has the proportion <C, A, B> as <C, B, B'>.
This is just a terse way of specifying that L is preserved in the transition
from the triple <C, A, B> to the triple <C, B, B'>.  People will often think
that this makes semiosis (the sign process) necessarily an infinite progress,
but this is a mistake, as nothing in this definition of a sign relation says
that an interpretant sign must be distinct from the initial sign of a triple.

|                               A (sign)
|                              / \
|                             /   \
|                            /  1  \
|                           /       \
|                (object) C - - - - - B (sign')
|                           \       /
|                            \  2  /
|                             \   /
|                              \ /
|                               B' (sign")

Because of the circumstance that rendering a 3-tuple <x, y, z> of any 3-adic relation
in the figure of a plane triangle will frequently mislead the viewer to imagine that
all 3-adic relations can be decomposed into 2-adic relations, in the way that the
triangle decomposes into its component line segments, I suppose, I will take the
liberty of redrawing your figure in the following fashion -- though it does not
prevent a really dedicated misreader of maps from rushing heedlessly on in this
form of misadventure, it at least e-quips the coarse of my account with e-nuff
of a caltrope to slow the worsted of the unthinking reeders down, just a bit.

|                                  A (sign)
|                                 /
|                                /
|                (object) C ----@
|                                \
|                                 \
|                                  B (interpretant sign)

HP: To me, so far, this is all uninterpreted formalism.

This is a formalism that is intended to help us talk about, think about,
analyze, design, realize, and amend the very activity of interpretation.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

HP: It's hard for me to imagine an interpretation that relates
    to a physical situation.  What does "create" mean?  By what
    process or action does a sign create an interpretant sign
    and a relation?  Why is the interpretant called a sign? 

HP: The next statement is a real puzzle, especially to a physicist: 

| This definition [of sign] no more involves any reference
| to human thought than does the definition of a line as the
| place within which a particle lies during a lapse of time.

HP: Does "line" refer to the trajectory of particle?  In which case the line
    may be defined by the particle but it is created by forces (other particles)
    and therefore line, particle, and forces are inextricably related. 

HP: In this comparison, he appears to mean that the sign corresponds to the line
    and human thought to the particle.  If so, then could he mean that human thought
    and external forces (experience, environment) create or define the sign?  That is
    the only sense I could make of this metaphor, but why would he leave out external
    forces and environments?  These are the ultimate sources of both particles and
    human thought.

HP: Finally, if he means by "deduce" what is normally meant,
    and his definition is considered axiomatic, then he is
    arriving at his logic by formal means. 

| It is from this definition [axiom] that I deduce the
| principles of logic by mathematical reasoning . . .

HP: So I would agree it is a "formal semiotics".
    What is lacking for me is an interpretation.

05 Aug 2001 • 18:00 • Logic Of Vague Expressions

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Logic Of Vague Expressions (What's LOVE Got To Do With It?)
Date: Sun, 05 Aug 2001 18:00:08 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

JA: By "autonomous external system", I mean an object system that is being regarded,
    and to a pertinent approximation usefully so, as a system in which we ourselves,
    as "agents of construal" (interpreters & observers) are negligible participants.
    Is that what you mean by "system modeled externally"?

SS: Yes.

SS: I would say that you are taking an internalist perspective, trying to get at
    generativity, which is in general not accessible to typical externalist (global,
    fully explicit, totalizing, atemporal) discourse.

JA: Not sure. I always tend to become a bit suspicious of any discourse, whether my own
    or others, that becomes too littered with these insuperable suffixes "-ism" and "-ist",
    and I do not think that any tried and true pragmatician such as I keep trying to be would
    rush to accept any such label as either "externalist" or "internalist".

SS: Well, I am just (as one interested in probing the internalist predicament) roughly
    classifying what you are saying into the exo/endo dichotomy.  Internalism is very
    broad, with many previous threads leading into it, so there can be more than one
    position concerning it.  Basically, it is the attempt to model systems as if the
    modeler were inside them, and so is prohibited many of the usual scientific tricks,
    like measuements from several instances or locales, or global models (as in classical
    thermodynamics).

I guess that I just don't get it.  We commonly assume a cosmos that all of us are "inside",
but in practice we very often have to work with isolated systems that are "outside" of us,
but inside the universe, the same universe that we are inside.  The "in"teresting question
for me is how do we come to construe these "ex"ternal systems from out of our "ex"perience.

JA: Side question: Are you using "generativity" in the sense of Chomsky?

SS: You decide -- I mean by a generative system or situation
    one from which new, unpredictable situations may arise.

I call this "reality".

SS: So, I think it is likely more general than Chomsky
    because, I suppose, he thinks he knows all the rules.

No, I cannot imagine that he would aver this,
even about the rules of any natural language.
Humorous hyperbole?

SS: A truly generative system generates new rules
    along with new permutations on the old ones.

Well, there is always this distinction to be made between
the rules that reality really follows, that may have been
fixed from the beginning, for all we know, and the rules
that we know that explain some portion of our ration of
reality, that are generally forever de-&-re-generating.

SS: It is not, I think, clear that in this discourse the kind of choice you refer to can be
    represented.  Different choices would not, I think, be available to the system AS choices.
    "Hints of forms", OK, "confusion", OK, "conception" and "birth", yes, "hints" perhaps.  So,
    "distinction" -- definitely not.  No distinctions would be available internally in my view.

Perhaps I just do not understand this way of talking.
We are born into experience and borne into experience.
There are so many distinctions that arise in experience,
pain and pleasure, and so on, and so on, ..., and sooner
or later some of us will construe or derive these other
distinctions, like external and internal, and who knows
what all, for who knows what purpose within experience.

SS: Distinctions are pre-eminently externalist things.  They are too crisp for vague internality.
    Vague groping guided by tendencies,  OK. Fuzzy distinctions might be more believable.

JA: Again, I am not sure what all is being suggested here -- I was hoping
    to give up the discussion of fuzzy concepts to a more disentangled thread,
    as I threaded to do with that old post on "Fuzzy Stuff" -- but I think that
    these issues are what drives me to use various families and sundry samples
    of triadic sign relations as my conceptual framework of choice.  Here, the
    "object domain" contains any old thing that we purport to make an object of
    "discussion and thought" (DAT), the domains of signs and interpretant signs
    contain the signs and mental ideas that we use to talk about and to think
    about the objects of the object domain.

SS: Well, I am suggesting that we do not yet have a vague logic
    with which to deal with generative situations.

I am supposed to ask "who's we?"

JA: What is NPI?

SS: The negentropy theory of information. That is, information is a reduction
    in possibilities ontologically, or of uncertainty epistemologically.

JA: Gosh, I feel so dense! "What the heck is the 'P' for?", asked Princess Principia.
    Negative Probability Integral?

SS: Oh! Sorry again! -- negentropy Principle of information.

SS: I note further that 'general' can only extend its hegemony IF
    'vagueness' differentiated more plentifully into a bigger tree.
    So it is not so dichotomous with 'vagueness' as one might think.
    It is its backward projection.

JA: I am not sure if we are talking about the same things by means of these words.
    Is backward projection the same thing as inverse projection, id est, a fiber?

SS: What I mean is that generality is constructed from particular instances,
    gradually uniting fewer and fewer properties of more and more instances.
    But instances themselves were developed out of a vague precursor, by
    differentiation among them during their development.  Thus, as Peirce
    suggests (somewhere) generality is a kind of explicit model of vagueness.
    So, what I was saying is that if a given vagueness developed into a greater
    tree of definite descendents, then the generality that can be constructed
    with respect to these will have greater hegemony.

JA: Give me some more clues and I will try to find this. I do not have the CD of CP yet --
    maybe some party on the Arisbe list will perk up and help us find it?

SS: I was afraid you wuld ask for chapter and verse.  Peirce was discussing different ways
    things can be indeterminate (this is the keyword, I suppose).  The discussion was cited
    in one or more of six different books -- Almeder, 1980; Buchler, 1951; Esposito, 1980;
    Merrell, 1991; Wiener, 1958; and/or Raposa, 1989.  I am sure you know most of these (any
    you don't I will cite in more detail).  I should say also, that the developmental twist is my
    own contribution (Development and Evolution: Complexity and Change in Biology, 1993, MIT Press.)

Did you look at the quotes I posted on the "Determination" thread about "general" and "vague"?

Jon Awbrey

06 Aug 2001 • 21:42 • Logic Of Vague Expressions

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Logic Of Vague Expressions
Date: Mon, 06 Aug 2001 21:42:00 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan,

One of the pursuits on which I wasted a good deal of my all too wasted youth
was a desperate search for almost any alternative to "establishment" versions
of logic and set theory, and so I "experimented" with just about every brand
of what was in those lazy hazy days called "deviant logic" that came off the
wagon from our Ol' Academus's Farm to hit the dim streets of our Alley Agora,
from the milder mixes of quantum logic to the uncrispy fritters of fuzzy sets.
But that was yesterday, and yesterday's gone, and now I have settled back to
classical logic and classical music, and cannot remember what all the fuzz
was about.  So I have not thought about these fuzzy general quantum vague
issues for quite some time, and mostly I am left with the impression that
if I had understood information and uncertainty better then I never would
have felt the need to wander down these interminable and meandering roads.

But if Peirce really thought that generality and vaguity were worth spending
a spell of his thinking time on, then I guess that I would be duty bound to
expend a second or a third thought on them.  So here are a couple of pieces
that he wrote on these subjects, which I thought that I might pass your way,
to see what you think.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Accurate writers have apparently made a distinction
| between the 'definite' and the 'determinate'.  A subject
| is 'determinate' in respect to any character which inheres
| in it or is (universally and affirmatively) predicated of
| it, as well as in respect to the negative of such character,
| these being the very same respect.  In all other respects it
| is 'indeterminate'.  The 'definite' shall be defined presently.
|
| A sign (under which designation I place every kind of thought,
| and not alone external signs), that is in any respect objectively
| indeterminate (i.e., whose object is undetermined by the sign itself)
| is objectively 'general' in so far as it extends to the interpreter
| the privilege of carrying its determination further.  'Example':
| "Man is mortal."  To the question, What man? the reply is that the
| proposition explicitly leaves it to you to apply its assertion to
| what man or men you will.
|
| A sign that is objectively indeterminate in any respect
| is objectively 'vague' in so far as it reserves further
| determination to be made in some other conceivable sign,
| or at least does not appoint the interpreter as its deputy
| in this office.  'Example':  "A man whom I could mention seems
| to be a little conceited."  The 'suggestion' here is that the
| man in view is the person addressed;  but the utterer does not
| authorize such an interpretation or 'any' other application of
| what she says.  She can still say, if she likes, that she does
| 'not' mean the person addressed.  Every utterance naturally
| leaves the right of further exposition in the utterer;  and
| therefore, in so far as a sign is indeterminate, it is vague,
| unless it is expressly or by a well-understood convention
| rendered general.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.447

http://suo.ieee.org/ontology/msg02384.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Perhaps a more scientific pair of definitions would be
| that anything is 'general' in so far as the principle of
| the excluded middle does not apply to it and is 'vague'
| in so far as the principle of contradiction does not
| apply to it.
|
| Thus, although it is true that "Any proposition
| you please, 'once you have determined its identity',
| is either true or false";  yet 'so long as it remains
| indeterminate and so without identity', it need neither
| be true that any proposition you please is true, nor that
| any proposition you please is false.
|
| So likewise, while it is false that "A proposition 'whose
| identity I have determined' is both true and false", yet
| until it is determinate, it may be true that a proposition
| is true and that a proposition is false.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448

http://suo.ieee.org/ontology/msg02387.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

SS: Well, I am just (as one interested in probing the internalist predicament) roughly
    classifying what you are saying into the exo/endo dichotomy.  Internalism is very
    broad, with many previous threads leading into it, so there can be more than one
    position concerning it.  Basically, it is the attempt to model systems as if the
    modeler were inside them, and so is prohibited many of the usual scientific tricks,
    like measuements from several instances or locales, or global models (as in classical    
    thermodynamics).

JA: I guess that I just don't get it.  We commonly assume a cosmos that all of us are "inside",
    but in practice we very often have to work with isolated systems that are "outside" of us,
    but inside the universe, the same universe that we are inside.  The in-teresting question
    for me is how do we come to construe these ex-ternal systems from out of our ex-perience.

SS: Yes, that is the standard logical and scientific standpoint.
    Internalism has a different aim.  So, I was wrong then that
    you seemed to be interested in internalist constructions.

I remember reading some stuff on "internal realism" in Hilary Putnam's papers,
but it was not one the things that stuck in my mind.  Is that what you mean?
I am sure that I still have those books somewhere.  But I am afraid that
I tend to go by that old adage that:  "An ism never did much for science,
except for prism".  It may be that I spent too much time in a couple
of settings where folks did almost nothing but sit around and gossip
about what ism had been "discredited" that week.  You may have noted
that I avoid even the terms "pragmatism" and "pragmatist" in favor
of "pragmatic thinking" and "pragmatician".  It may seem like such
a trivial punctilio but I am convinced that keeping "pragmatic" in
its place as an adjective will prevent it from getting the big head
of most other substantive doctrines, and "pragmatician", analogous
to "mathematician" and "mortician", is calculated to remind us that
our salvation depends on good works and not faith alone --- plus it
serves as a beneficial memento mori to remind us of our fallibility.

JA: Side question:  Are you using "generativity" in the sense of Chomsky?

SS: You decide -- I mean by a generative system or situation
    one from which new, unpredictable situations may arise.

JA: I call this "reality".

SS: Well, if you stick with externalist constructions, then internalism
    sounds just like (I would say) actuality -- the territory instead
    of a map.  But internalism is trying to construct new kinds of maps.

SS: A truly generative system generates new rules along with
    new permutations on the old ones.

JA: Well, there is always this distinction to be made between
    the rules that reality really follows, that may have been
    fixed from the beginning, for all we know, and the rules
    that we know that explain some portion of our ration of
    reality, that are generally forever de-&-re-generating.

SS: Well, it seems to some of us possibly worth while to think about
    making a model that could itself be truly generative.  Of course,
    it could not be based upon the usual scientific (two-valued) logic.
             ^^^
-------------|||-------------------------------------------------------

So then it's the same as what it's not?
Then how will I ever choose between it?
The two-valor bit comes not from logic
but from a need to make dicisive picks,
unless you really believe that you can
jump on your horse and ride off in all
directions at once.  I'm afraid that's
a horse of a whole utter wave-function.

SS: It is not, I think, clear that in [internalist] discourse the kind of
    choice you refer to can be represented.  Different choices would not,
    I think, be available to the system AS choices.  "Hints of forms", OK,
    "confusion", OK, "conception" and "birth", yes, "hints" perhaps.  So,
    "distinction" -- definitely not.  No distinctions would be available
    internally in my view.

JA: Perhaps I just do not understand this way of talking.
    We are born into experience and borne into experience.
    There are so many distinctions that arise in experience,
    pain and pleasure, and so on, and so on, ..., and sooner
    or later some of us will construe or derive these other
    distinctions, like external and internal, and who knows
    what all, for who knows what purpose within experience.

SS: We can make these distinctions because we are entrained by languages
    and (two-valued) logic.   We are looking for a more general logic,
    from which two-valued could be derived for/by mechanistic systems.

No, I have to go with Herr Doctor Sigismund Freud on this:
We are capable of being entranced by our mutter tongue and
our vatter brine because we enjoy and unjoy so intimately.

SS: Distinctions are pre-eminently externalist things.  They are too crisp
    for vague internality.  Vague groping guided by tendencies, OK.  Fuzzy
    distinctions might be more believable.

JA: Again, I am not sure what all is being suggested here -- I was hoping to give up
    the discussion of fuzzy concepts to a more disentangled thread, as I threaded to
    do with that old post on "Fuzzy Stuff" -- but I think that these issues are what
    drives me to use various families and sundry samples of triadic sign relations
    as my conceptual framework of choice.  Here, the "object domain" contains any
    old thing that we purport to make an object of "discussion and thought" (DAT),
    the domains of signs and interpretant signs contain the signs and mental ideas
    that we use to talk about and to think about the objects of the object domain.

It's buried a bit, I know, but this note still
contains the gist of my best thinking on fuzzy:

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Strangely enough, there is a funny sort of relationship between
ontological relativity (multi-perspectives?  poly-ontologies?),
fuzzy sets, and triadic relations, perhaps (I am still guessing)
of the sort that John Sowa had in mind.

Consider a fuzzy set as a triadic relation of the form x €^r S
among an element x, a degree of membership r, and a set S.
You may, of course, substitute "concept" for "set" if you
prefer that way of thinking about things.

Ask yourself:  Where do these assigned degrees of membership come from?
Imagine that they come from averaging the results of many judges binary
{0, 1} = {out, in} decisions.

Now consider the more fundamental triadic relation from which this
data is derived, the relation of the form x €_j S that exists among
an element x, an interpreter (judge, observer, user) j, and a set S.

If we use these sorts of relations as the basic formal structures of
our representation, then there is enough elbow room, I am guessing,
to have all of our cakes and to eat them too.  In other words, if
we consider JS's questions ("World's Largest Individual Organism",
17 Aug 2000 08:56 EDT):

| Do you represent a chair as a construction of wood and metal?
| Do you represent it as an enormous buzz of interacting atoms?
| Do you represent it as an object for human beings to sit on
| without considering the details of its construction?
|
| John Sowa (JS): http://suo.ieee.org/email/msg00608.html

Then it becomes possible to give them the Joycean answer:

Yes. Yes. Yes.

The not so Joyce-ful task is to keep each view parameterized by the
community of interpretation that finds it compelling, interesting,
practical, useful, or "to their purpose" at a given moment, and
to figure out how to maintain a not-too-chaotic form and medium
of communication among these diverse communities.

Yes? No? Indifferent?

http://suo.ieee.org/ontology/msg02990.html

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

SS: The triadic formulation could be used with less specified or more specified objects,
    I agree.  It is general enough for that.  The interpretants generated by the system
    of interpretance could get increasingly more specified as they lead from one to the
    next as the system constructs its view of the object.

Maybe that is one way to go about it, but the way that I am thinking about at present
is to make the interpretant the arbiter of the moment's classifications and decisions.

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Determination

http://suo.ieee.org/ontology/msg02377.html
http://suo.ieee.org/ontology/msg02378.html
http://suo.ieee.org/ontology/msg02379.html
http://suo.ieee.org/ontology/msg02380.html
http://suo.ieee.org/ontology/msg02384.html
http://suo.ieee.org/ontology/msg02387.html
http://suo.ieee.org/ontology/msg02388.html
http://suo.ieee.org/ontology/msg02389.html
http://suo.ieee.org/ontology/msg02390.html
http://suo.ieee.org/ontology/msg02391.html
http://suo.ieee.org/ontology/msg02395.html
http://suo.ieee.org/ontology/msg02407.html
http://suo.ieee.org/ontology/msg02550.html
http://suo.ieee.org/ontology/msg02552.html
http://suo.ieee.org/ontology/msg02556.html
http://suo.ieee.org/ontology/msg02594.html
http://suo.ieee.org/ontology/msg02651.html
http://suo.ieee.org/ontology/msg02673.html
http://suo.ieee.org/ontology/msg02706.html

07 Aug 2001 • 09:09 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Tue, 07 Aug 2001 09:09:55 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Mishtu Banerjee wrote (MB):
Howard Pattee wrote (HP):

HP: Jon, I have read the passages from Peirce you quote over and over, but I doubt
    if I could elaborate sensibly on what it means.  I think a few specific examples
    might help me interpret how Peirce's definition of a sign and use of logic might,
    or might not, be related to any of the wide variety of inquiry that produced great
    discoveries in physics.
 
MB: May I suggest a data set, from the world of physics.  The data set below is
    cited in B. Cohen's 'The Birth of a New Physics', in the chapter on Kepler.
    It's relevant to Peirce because he was deeply interested in the history of
    science, and spent a lot of time repeating the analyses of great scientists,
    attempting by re-doing the work as it were, to better apprehend their thought
    processes.  It was this approach and perspective that caused Peirce to re-analyze
    Kepler's original data for himself, to try and understand Kepler's point of view.
    He began quite critical of Kepler, and by the time he had worked his way through
    the data, and Kepler's reasoning, considered it a triumph of the power of induction.
    The data set was the basis for Kepler's third law:  "in equal time intervals, a line
    from the planet to the sun will sweep out equal areas".  Kepler tried to explain the
    third law's relevance in terms of celestial harmonies, derived analogies to musical
    scales, and the 5 regular polyhedra which he was obsessed with.  Most scientists
    did not know what to make of Kepler's "explanations" and ignored them. 
 
MB: The third law, was then put on deductive terms by Newton, where he showed
    that such motion would follow, assuming the following proposition to be true:
    Proposition 1.  Theorem 1.  "The area by which revolving bodies describe radii
    drawn to an immovable centre of force do lie in the same immovable planes, and
    are proportional to the times in which they are described".

MB: Now, to get at this proposition, Newton appeared to have had to "guess" at a
    different principle of inertia than his immediate predecessors.  They assumed
    that pure circular motion could be inertial (Galilean inertia).  Newton realized
    that even circular (or elliptical motion) required acceleration, thus a force for
    its continuance.  This force was universal gravity.  Newton's guess was that it
    applied not only to the force between the sun and a planet, but everywhere,
    to everything.  Cohen notes, "There is no mathematics -- whether algebra,
    geometry, or the calculus, to justify this bold step.  One can say of it
    only that it is one of those triumphs that humble ordinary men in the
    presence of genius". 
 
MB: Now Cohen, goes on to make a very interesting statement:
 
BC: | While it is true that the Newtonian mechanics is still applicable in the
    | range of phenomena for which it was intended, the student should not make
    | the mistake of thinking that the framework in which the system originally
    | was set was equally valid.  Newton believed there was a sense in which
    | space and time were 'absolute' physical entities.  Any deep analysis
    | of his writings shows how in his mind his discoveries depended on
    | these "absolutes".  To be sure, Newton was aware that clocks do
    | not measure absolute time, but only local time and that we deal
    | in our experiments with local space rather than absolute space.
 
MB: So: The induction was Keplers. ... gained via a labrous process
    of trial and error curve fitting (a formula to fit the data).
 
MB: The abduction, was Newton's guess at universal gravitation.
 
MB: The deduction followed, in terms of a series of propositions,
    the consequences of which could be worked out and tested, and
    which predicted the original data.  They explained Keler's data,
    but also explained a good deal more than just that data, including
    several open questions of the day, such as the phenomena of precession,
    where the axis of a spinning body (a spinning top, the earth) undergoes
    a conical motion:  an ancient observation, that was left unexplained
    until Newton explained it.
 
MB: More simply:  A localized pattern was apprehended (Kepler),
    a guess was made at a generality that might explain the observed pattern (Newton).
    Assuming the guess, deductions followed (More Newton with help from Galileo and
    the various others whose shoulders he was collectively standing upon), that led
    to corrolaries above and beyond the original pattern apprehened, that could
    further be empirically tested (the theory had excess empirical content, and
    explained much more than the data that led to it), and was ultimately found
    to hold within a range of observation (most things we see at the meso scale),
    even after the initial "perspective" that led to the ideas was found to be
    innacurate (absolute space).  The deductive system that resulted could be
    formalized.  Neither the basis for the original guess, nor the point of
    view that led to the guess could be formalized.  The guess, however
    informal, was about form:  it stated that two apparently different
    seeming phenomena -- motion of planets around the sun, falling of
    an apple to earth, may share the same form or relation:  that
    relation was gravitational attraction.  Peirce, poetically
    referred to the attractive force as love, and called it
    a firstness.  The relation had a specific indexical form,
    which could be stated as a formula, this was a Peircian
    2ndness.  The form of the relation, could be seen to
    mediate the motion of all material bodies in the
    universe, providing an interdependance of all
    things at some level, and in this mediative
    role, may be seen as a thirdness. 
 
MB: Peirce went one step further, in positing that laws were not "absolute", good
    for all places at all times, but rather evolutionary, a form of habit-taking.
    The "more general" laws that appeared universal, were merely older.  Laws were
    coming into being all the time, usually at some level of contingency.  Popper,
    reached similar conclusions, much much later, and apparently either independantly
    of Peirce, or without citing him.  What Popper calls "propensities" were Peirce's,
    "habit taking", and Peirce's explanation of the origins of propensities is given in
    his essay "The Doctrine of Necessity Examined" (reprinted in 'Chance, Love, and Logic',
    edited by Morris R. Cohen).  Popper relates propensity to the concept of conditional
    probabilities, whereas Peirce develops a notion of pure chance, which is not the same
    as probability, which he also sometimes refers to as vagueness.  Recall, that any
    probability requires one to be able to "count" in a very well defined combinatorial
    space.  Peirce posits, that vague (or underdefined) relations do not allow such
    counting initially -- as the relations develop, such counting becomes possible,
    and as the relations --- become fixed, or necessary, the relations appear to
    take on universality
 
MB: What I have tried to demonstrate is that Peirce's ideas of firstness, secondness, thirdness
    from which his diagramettic method followed, can be seen to naturally flow from a study of
    the history of physical science, by abstracting the method of scientists from the particular
    facts or even the hypotheses and theorems they posit.  But I am no expert on Peirce, and may
    be putting words in his mouth. 
 
MB: Here is an updated version of the data (from Cohen's book again).
    I leave it to Jon and Howard to place their cuts where they will:
    What is the sign, what is the interpretant, what is the object
    in the context of observations of planetary motion. 
 
    | Planet    Period(years)   Distance from Sun
    o---------------------------------------------
    | Mercury    0.24           0.387
    | Venus      0.615          0 .723
    | Earth      1.00           1.00
    | Mars       1.88           1.524
    | Jupiter   11.86           5.203
    | Saturn    29.457          9.539   
 
MB: I hope this example provides the kind of conrete example that Howard seemed to be seeking
    to ground the discussion, while also providing a very good starting point for discussing
    the scientific problems that provided impetus for Peirce's development of his ideas, and
    therefore a good jumping off (or jumping on) point for Jon also. 
 
MB: It may be that as someone trained as a scientist, I suffer from being overly pragmatic.
    But I often feel that discussions of Peirce's logic, separate from Peirce's science is
    like trying to discuss the dynamics of a forest, without discussing the roots of the
    trees.  Most of the "matter" of the forest, is actually underground, in those roots. 
 
MB: At the same time, the artist in me, often makes analogies to understand semiotic, in terms
    of a blank piece of paper, the appearance of a sign upon it at an artist's hand, the placing
    of the first mark, defining other marks, the creation of positive and negative space, and the
    final drawing as the mediation between negative and positive space. 
 
MB: The logic follows, once the cuts are made.
    Where the cuts are made ...... that is art
    (whether committed by scientific artists,
    or artistic scientists).

Yes, that sounds about right to me,
subject, off course, to the usual
uncertainties of a retrospective
analysis (Monday Morning QB'ing).
Which, per via, is just one of
the reasons why I would never
dare to start out -- and I am,
after all, still starting out,
after all these many years --
on such a full-blown, complex,
and rich example, but have to
try, and try, and try again to
get at, to grasp, or at least
to reach for the still and yet
still deeper roots, the finest
root-hairs of these ur-pflanzen
cacti, dandelions, grass-blades,
in hopes of oneday, if only maybe,
coming to see the forest, the tree.

Oh, by the way, here is an excellent book
on Peirce's pragmatic account of inquiry
that I have been meaning to recommend:

| Cheryl (C.J.) Misak,
|'Truth and the End of Inquiry : A Peircean Account of Truth',
| Oxford University Press, Oxford, UK, 1991.

Jon Awbrey

07 Aug 2001 • 17:26 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Tue, 07 Aug 2001 17:26:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard, I continue from where I left off last time.

Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: I have read the passages from Peirce you quote over and over,
    but I doubt if I could elaborate sensibly on what it means.
    I think a few specific examples might help me interpret
    how Peirce's definition of a sign and use of logic might,
    or might not, be related to any of the wide variety of
    inquiry that produced great discoveries in physics.

JA: Yes, it is a little bit like reading Galois on Group Theory.
    If you have a hundred years or so to get a grasp on what
    a group is, then you can read his work and realize that
    everything he says is perfectly apt.  Sadly, we are
    not to that point yet, where the Theory of Signs
    is a standard part of the undergrad curriculum.

JA: My own advice would be to try and flesh out Peirce's intensional description
    of a typical sign relation in the materials of concrete extensional examples.
    Think of the theory of sign relations as a subject like algebra, or geometry,
    or more concretely, group theory, or graph theory.  Most concretely, perhaps,
    you might think of it in terms of relational databases, where sign relations
    would be represented as a particular variety of three-column relation tables.

| No. 12.  'On the Definition of Logic'.
|
| Logic is 'formal semiotic'.  A sign is something, 'A', which brings
| something, 'B', its 'interpretant' sign, determined or created by it,
| into the same sort of correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in which itself stands to 'C'.
| This definition no more involves any reference to human thought than
| does the definition of a line as the place within which a particle lies
| during a lapse of time.  It is from this definition that I deduce the
| principles of logic by mathematical reasoning, and by mathematical
| reasoning that, I aver, will support criticism of Weierstrassian
| severity, and that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics',
| Four Volumes In Five Books,
| Edited by Carolyn Eisele,
| Mouton, The Hague, 1976.

HP: Simplifying:
    A brings B to correspond with C as A corresponds to C.
    So we can diagram it as a triangle:

|                               A (sign)
|                              / \
|                             /   \
|                            /     \
|                           /       \
|                         C - - - - - B 
|                  (object)           (interpretant sign)

HP: So, A creates B and also brings B into the relation BC which is
    the same (or lower?) relation as AC.  (Have I got that right?

JA: No, the "correspondence" that is indicated here is a "triple correspondence",
    what might be called a "3-place transaction" in database terms.  Let us name
    this 3-place relation L.  Accordingly, to say that "A brings B to correspond
    with C as A corresponds to C" is simply to say that A brings B into the same
    3-place relation L with something else B' and C as A occupies in the 3-place
    relation L with B and C.  Posed as an analogy with related terms in the form
    <Object, Sign, Interpretant>, one has the proportion <C, A, B> as <C, B, B'>.
    This is just a terse way of specifying that L is preserved in the transition
    from the triple <C, A, B> to the triple <C, B, B'>.  People will often think
    that this makes semiosis (the sign process) necessarily an infinite progress,
    but this is a mistake, as nothing in this definition of a sign relation says
    that an interpretant sign must be distinct from the initial sign of a triple.

    |                               A (sign)
    |                              / \
    |                             /   \
    |                            /  1  \
    |                           /       \
    |                (object) C - - - - - B (sign')
    |                           \       /
    |                            \  2  /
    |                             \   /
    |                              \ /
    |                               B' (sign")

JA: Because of the circumstance that rendering a 3-tuple <x, y, z> of any 3-adic relation
    in the figure of a plane triangle will frequently mislead the viewer to imagine that
    all 3-adic relations can be decomposed into 2-adic relations, in the way that the
    triangle decomposes into its component line segments, I suppose, I will take the
    liberty of redrawing your figure in the following fashion -- though it does not
    prevent a really dedicated misreader of maps from rushing heedlessly on in this
    form of misadventure, it at least e-quips the coarse of my account with e-nuff
    of a caltrope to slow the worsted of the unthinking reeders down, just a bit.

    |                                  A (sign)
    |                                 /
    |                                /
    |                (object) C ----@
    |                                \
    |                                 \
    |                                  B (interpretant sign)

HP: To me, so far, this is all uninterpreted formalism.

JA: This is a formalism that is intended to help us talk about, think about,
    analyze, design, realize, and amend the very activity of interpretation.

HP: It's hard for me to imagine an interpretation that relates
    to a physical situation.  What does "create" mean?  By what
    process or action does a sign create an interpretant sign
    and a relation?  Why is the interpretant called a sign? 

HP: The next statement is a real puzzle, especially to a physicist: 

CSP: | This definition [of sign] no more involves any reference
     | to human thought than does the definition of a line as the
     | place within which a particle lies during a lapse of time.

HP: Does "line" refer to the trajectory of particle?  In which case the line may
    be defined by the particle but it is created by forces (other particles) and
    therefore line, particle, and forces are inextricably related. 

HP: In this comparison, he appears to mean that the sign corresponds to the line
    and human thought to the particle.  If so, then could he mean that human thought
    and external forces (experience, environment) create or define the sign?  That is
    the only sense I could make of this metaphor, but why would he leave out external
    forces and environments?  These are the ultimate sources of both particles and
    human thought.

Peirce is expressing what he calls his "non-psychological conception of logic".
Notice that he says "non", not "anti".  The "non" in "non-psychological logic"
is like the "non" in "non-associative algebra" -- it generalizes the attached
subject by removing certain axioms, constraints, limitations, or restrictions.

Because psychology is a descriptive science and logic is a normative science,
they have different aims and ends, even on those domains where their surveys
of the phenomena of thinking overlap.  That makes them independent sciences.

My guess is that Peirce's allusion to lines and particle motions is intended
to call to the minds of his readers the typical sort of definition of a line,
a geometric object, that readers of the time would have known from treatises
of "analytical mechanics", construed in terms of a relation between geometry
and physics.  So I have two guesses about the purpose of the implied analogy:

Sign : Psyche :: Line : Physis.

Either he is saying that logic is independent of psychology
in the way that geometry is independent of dynamics, or he is
saying that logic is independent of psychology in the way that
both geometry and physics are independent of psychology.

HP: Finally, if he means by "deduce" what is normally meant,
    and his definition is considered axiomatic, then he is
    arriving at his logic by formal means.

There is still this distinction between "being formal" and "being formalized".
The first is a question of "what it is", which we may never know for certain.
The second is a question of what particular agents have actually achieved.

You have to keep on trying to remember that Peirce was an admirer
of a blossoming sense of "form" that was still connected to its
living roots in the "philosophical history of science" (PHOS),
before the so-called "formalists" yanked it out of the ground
of its former meaningfulness, clipped it off, chopped it up,
and grafted it onto all the oddly-shaped, strangely-twisted,
and unnaturally-formed hedges of their own "formal gardens".

CSP: | It is from this definition [axiom] that I deduce the
     | principles of logic by mathematical reasoning . . .

HP: So I would agree it is a "formal semiotics".
    What is lacking for me is an interpretation.

I think that this definition is axiomatic in the way that
we say "a group is defined by the following three axioms".

Logic, as a formal and normative branch of the theory of signs,
can be studied, must be studied within the setting of semiotic.
This means that we have all of the resources of sign theory to
use in examining logic, having cast it as circumscribed domain,
and this resource may call on forms of organized phenomenology
that are generally known as "mathematical reasoning", and that
reach beyond normative science, involving as they do empirical
components.  In order to see this clearly, it may be necessary
to drop a bit of our Western cultural mythology that says that
"Logic Or Rational Effability" (LORE) is identical with humane
consciousness itself.  The apotropaic rationale of this belief
is manifestly obvious when one comes to think about it.  Those
folks who still believe it have just not been paying attention.

Jon Awbrey

08 Aug 2001 • 03:21 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Wed, 08 Aug 2001 03:21:01 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Our Text For Today:

| No. 12.  'On the Definition of Logic'.
|
| Logic is 'formal semiotic'.  A sign is something, 'A', which brings
| something, 'B', its 'interpretant' sign, determined or created by it,
| into the same sort of correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in which itself stands to 'C'.
| This definition no more involves any reference to human thought than
| does the definition of a line as the place within which a particle lies
| during a lapse of time.  It is from this definition that I deduce the
| principles of logic by mathematical reasoning, and by mathematical
| reasoning that, I aver, will support criticism of Weierstrassian
| severity, and that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics',
| Four Volumes In Five Books,
| Edited by Carolyn Eisele,
| Mouton, The Hague, 1976.

HP: Howard wrote [trying to understand Peirce's language]:
    |
    | A brings B to correspond with C as A corresponds to C.
    | So we can diagram it as a triangle:
    |
    |                               A (sign)
    |                              / \
    |                             /   \
    |                            /     \
    |                           /       \
    |                         C - - - - - B
    |                  (object)           (interpretant sign)

HP: So, A creates B and also brings B into the relation BC which is
    the same (or lower?) relation as AC.  (Have I got that right?

JA: No, the "correspondence" that is indicated here is a "triple correspondence",
    what might be called a "3-place transaction" in database terms.  Let us name
    this 3-place relation L.  Accordingly, to say that "A brings B to correspond
    with C as A corresponds to C" is simply to say that A brings B into the same
    3-place relation L with something else B' and C as A occupies in the 3-place
    relation L with B and C.

HP: I don't see how Peirce's words say what you say they say.

Howard, my first time around in Peirce studies
was off and on all throughout my undergrad years,
a desulkory decade of dropping in and dropping out,
during which time I stayed mostly within the bounds
of CP 3&4, due to my interest in logic and math and
all things graphical.  I spent the last couple of
years of this period writing my Senior Thesis on
the puzzles arising out of one little paragraph,
CP 4.306.  The pursuit of enlightenment on this
problem, as it turned on Peirce's use of matrix
representations over B = {off, on} for logical
operators, led me back into mathematics proper,
from which I had been vacationing for a while
in philosophy.  I believe that it was toward
the end of this phase that I figured out what
Peirce was talking about when he wrote about
sign relations, but it was a cumulative grasp,
no sudden epiphany, no definitive succincture,
nor had I seen anything called a "definition"
that I would have regarded, nor imagined that
Peirce intended, as anything but a partially
illustrative gloss on the notion.  The best
clue that I had was the "Sunflower" example,
the text of which I cannot find at the moment,
but I can remember drawing pictures like this
to represent 3-tuples of the form <s, i, o>:

|            s     i
|             \  //
|              \//
|              |||
|              |||
|               o

What struck me as Peirce's most striking illustration
was a story about a sunflower, that in turning toward
the sun, and by virtue of that very act alone, brings
another sunflower to turn toward the sun.  The object
is the sun, the sign is the orienting of that initial
sunflower, and the interpretant sign is the orienting
of that next instructed sunflower, turning to the sun.
To illustrate this example of semiosis or sign-action
I vividly remember drawing a picture of the following
form, the best that I can render it in ASCII, anyway:

|          s        i
|         " \      //"
|        "   \    //  "
|       "     \  //    "
|      i\      \//      s
|       \\     |||     /
|        \\____|||____/
|         \==== o ====\
|         /    |||    \\
|        /     |||     \\
|       s      //\      \i
|        "    //  \     "
|         "  //    \   "
|          "//      \ "
|           i        s

Here, I was able to manage drawing only four 3-tuples,
and I had to use a line of ditto marks (") to indicate
that their termini are to be treated as identical nodes,
whereas as I was accustomed to draw it I would have had
eight or more 3-tuples, arranged in the form of a flower,
and I would have then been able simply to fuse the nodes
that were to be identified.  The point of the picture is,
of course, that s_1 -> i_1 = s_2 -> i_2 = s_3 -> i_3, ...,
and so on.

CSP: | A sign is something, 'A', which brings something, 'B',
     | its 'interpretant' sign, determined or created by it,
     | into the same sort of correspondence (or a lower implied
     | sort) with something, 'C', its 'object', as that in which
     | itself stands to 'C'.

HP, interpreting CSP:

    | A creates B and also brings B into the relation BC
    | which is the same (or lower?) relation as AC.

HP: What, exactly, did my shorter version leave out that essentially alters Peirce's meaning?

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Using the acronym "SOC" for "sort of correspondence",
let us try the following paraphrase of the criterion:

| A brings something into the same SOC with C
| as the SOC in which A stands to C.

In order to expand the expression correctly, one has to ask:

0.  What is the SOC in which A stands to C?

The SOC in which A stands to C is given by Formula 1.

1.  A brings something into some SOC with C,
    to wit, the SOC in which A stands to C.

If B enters into the same SOC with C as A stands in, that is to say,
if B takes up the same role that A had in Formula 1, then we obtain:

2.  B brings something into some SOC with C,
    to wit, the SOC in which A stands to C.

Let us give the name B' to the something in Formula 2.
Now, B' can either be something old or something new.
If old, it's in A, B, C.  If new, let's leave it B'.

In any case, we have:

3.  B brings B'into some SOC with C,
    the SOC in which A stands to C.

In sum, the bringing of a new, possibly old, thing
into the relation is part of being in the relation.

And so it goes ...

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

There are three important ideas that are involved in Peirce's definition
of a sign that are not themselves defined local to its immediate context:
"Correspondence", "Determination", "Formal".  It is common for thoroughly
modern readers to simply supply their own meanings without pausing to ask
if there could be other senses, in which case they read mush -- typically
hashing together a mess'o'misapprehensions about the 2-adic mirror images
of a 2-adic correspondence theory of truth, some enchanted doctrine about
a semiotic causal determinism imputed to Peirce, plus who knows what when
it comes to their pro forma reading of "formal".  But should anybody want
to know what the guy was really saying, all a body has to do is look into
the many other places where he says exactly what he means by these words.

HP: In other words, I fail to see how, from Peirce's definition alone, I would
    be justified in interpreting it as the "3-place transaction, L" you describe
    (whatever L is).  Is this called an elliptical definition?

Yes, in the sense that every word in the dictionary is defined elliptically,
if not in the orbits of another conic section, in terms of other words that
one must trace elsewhere, in their own proper spheres.

Jon Awbrey

08 Aug 2001 • 09:16 • Logic As Semiotic

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Logic As Semiotic
Date: Wed, 08 Aug 2001 09:16:39 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Logic, in its general sense, is, as I believe I have shown, only another name for
|'semiotic' ([Greek: semeiotike]), the quasi-necessary, or formal, doctrine of signs.
| By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the
| characters of such signs as we know, and from such an observation, by a process which
| I will not object to naming Abstraction, we are led to statements, eminently fallible,
| and therefore in one sense by no means necessary, as to what 'must be' the characters
| of all signs used by a "scientific" intelligence, that is to say, by an intelligence
| capable of learning by experience.  As to that process of abstraction, it is itself
| a sort of observation.  The faculty which I call abstractive observation is one which
| ordinary people perfectly recognize, but for which the theories of philosophers sometimes
| hardly leave room.  It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question, "Should I wish for
| that thing just the same, if I had ample means to gratify it?"  To answer that question, he
| searches his heart, and in doing so makes what I term an abstractive observation.  He makes
| in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what
| modifications the hypothetical state of things would require to be made in that picture, and
| then examines it, that is, 'observes' what he has imagined, to see whether the same ardent
| desire is there to be discerned.  By such a process, which is at bottom very much like
| mathematical reasoning, we can reach conclusions as to what 'would be' true of signs
| in all cases, so long as the intelligence using them was scientific.  (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editor's Note: "From an unidentified fragment, c. 1897."

08 Aug 2001 • 22:48 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Wed, 08 Aug 2001 22:48:32 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: So, to restate my main question:
    Does Peircean inquiry strictly separate the
    logical syntax of signs from the semantics
    of observation?

SS: Perhaps I could clarify things a bit by noting that o-s-i
    involves an elision concerning i.

JA: I did not understand that last sentence.

SS: I mean that in much semiotic literature 'interpretant' is used as
    though it just pops up as a mate for the object by way of the sign.
    Or, indeed, that a sign (as if it were "out there" prior to some
    semiosis) links an object with an interpretant.  That is, the
    system by which object and interpretant are linked via some
    (actually co-constructed) sign is left completely implicit.
    I have found this unworkable for myself because, for me,
    a SI (your SOI) can be of many kinds, not just some
    human system.

I am not sure if I read the literature that you are talking about.
Off the cuff, I would say that I do not believe that the sorts of
features you mention are obligatory attributes of sign relations,
but more like optional accessories that can happen in some cases.

SS: Therefore the SI needs to be stated up front.

If you are saying that the whole sign relation L c OxSxI is the thing,
in other words, the sine qua non of sensible discourse about signs,
then I think that I would agree.

SS: One SI may interact with an object quite differently than another does,
    and the signs used in mediating these interactions will be different.
    Put (more importantly) another way, the mediation is not done by the
    sign, but by the SI, which helped to create the sign.

I guess I could say that the sign relation L c OxSxI
is the "medium" of whatever "mediation" is going on.

SS: So, the SI is responsible for both the formalisms and the measurements.

JA: I believe that Nature, the ever pressent object reality,
    has its share of responsibility for our impressions and
    perforce must be assigned a part in the cosmic dialogue.

SS: Yes, but, because each SI will individuate during its development
    from vague beginnings, each one will have modified Nature's mode of
    impressions in its own way, and its signs will have its signature.

In those varieties of sign relation where Nature is the object,
a modified impression is but another form of interpretant sign.

SS: I Note that this also relates to Howard's
    "Are Peircean rules of inquiry formal?"
    They appear to be formal and therefore
    to apply universally for all inquiry
    conditions, like "laws of inquiry".

It seems that we have yet to converge on a sufficiently congruous collection
of connotations for the term "formal".  I am hopeful that the fragment from
Peirce that I posted under the heading of "Logic As Semiosis" will go toward
explaining his sense of "formal" as "quasi-necessary", and also clarify the
distinction that he observes between "logical" and "mathematical" reasoning.

SS: How, then, do the unique conditions of a specific observer or system under study
    enter the formal inquiry?  How is this different from normal physicist's inquiry?

Again, this question strikes me as a strangely familiar inquiry,
being one of the main tasks of my inquiry into inquiry to tackle.
I will let you know what I come up with.  But I have already come
to the conclusion that we cannot approach such complex and subtle
questions without much more adequate conceptual and computational
frameworks to support our effort.  So I have been working on that.

Another thought.  I just recognized that the type of question being asked here
is closely related to a standard question in pragmatic hermeneutics, as to the
status of the interpreter vis a vis the interpretant, in deed, as it stands in
regard to the entire sign relation in question.  Peirce's answer, which I take
to be a critical insight, is that the full sign relation is the primary entity
of our study, its bearing on interpretants being the next in importance, while
the agent of the interpretive activity is what such agents proto-typically are,
a hypostatic abstraction hypothesized to explain the phenomena of experience.

SS: I would say most obviously in the interpretants it constructs, or,
    in more standard science talk, in the interpretations.  However, it
    also comes in (as Uexküll urged), in the construction of the signs
    themselves (example: as organisms we would ignore ultraviolet
    sensations, while bees would be most impressed by them).

HP: When we want to use a formal symbol system to model a physical system we have
    to assign observable qualities to some of the otherwise meaningless symbols
    and then provide initial conditions for them by measurement.

SS: Here is where ultraviolet or some other medium would be chosen.

HP: If you do not make a strict distinction between the formal rule-system that
    represent universal, inexorable laws and the initial conditions which may be
    different for every observer, the model no longer makes sense.  To survive,
    inquiring physicists (bacteria and all living systems) want to know what
    they cannot influence and what they can change.

SS: But what would be fixed and unchangeable can differ between kinds of observers
    as well as the initial conditions -- these latter of which, however, will also
    differ between instances.

I tried to explain my take on the cut between "boundary" and "interior"
once before on the Complexity List -- maybe it is time to revisit the
runes of that debacle and to see if I can find some way to revise it.

o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o

Subj: Hit And Run Question On Functional Boundaries
Date: Wed, 14 Mar 2001 14:46:16 -0500
From: Jon Awbrey
  To: VCU Complexity Research Group

David Keirsey wrote (DK):
Jon Awbrey wrote (JA):

DK: I was looking for the parallel concept of the material reduction of "boundary",
    since the concept "part" has traction both in functional and structural reasoning.
    (The reason this struck me, my father of course *refuses* to acknowledge the lexical
    word "part" as applicable to "function" -- Rosen and we are of course using the
    reductionistic nonsense phrase of "functional part" -- bad, bad!)

DK: But the reason I was asking, I haven't seen anything pushing (abusing?!) this metaphor.
    You guys obviously haven't either, and find no use for the metaphor.  My initial guess
    would be a "functor" would be an example of a "functional boundary", but thanks anyway.

JA: I sense that I may be wandering into a discussion
    that started long before I was paying attention,
    but some of the terms that you are using here
    stir up some old thoughts of mine, so here:

JA: Let's say that I'm pursuing a "functional style" of programming,
    and so I am interested in "abstract objects" called "functions",
    but a specialized mutation called "recursive partial functions",
    and being a practical sort of person, I want more than anything
    to be able to "implement" them in the form of computer programs
    that really, really run.  And so now I am forced to think about
    two distinct domains, one "objective", in the sense of being my
    object or objective that is there independently of what I think
    to do about it, the other "syntactic", in the sense that I have
    to stick signs together in just the right ways to make anything
    of interest to me or anybody happen at all.  That is the set-up.
    Now, on the syntactic side of things, I can speak of a function
    as having components, specifically, the components that I break
    it into, and build it back out of, to dangle a few prepositions,
    and I can speak of the function as having a boundary, in regard
    to the circumstance that, being recursive, since computable, it
    has "arbitred", "boundary", "exceptional", "initial" conditions,
    on those "parts" of the domain of definition where the function
    values demand to be set by separate fiat, over and above accord
    with the generic part of the functional domain, regime, or rule.
    Now, all of this may just be me, having no justification in the
    nature of the abstract object itself, that is, in that function
    that I am trying to compute, but may just be the artifact of my
    particular way of going about it.  So that is what came to mind
    as I read what you wrote.  Is there a bearing on what you think?

09 Aug 2001 • 10:40 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Thu, 09 Aug 2001 10:40:37 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Our Text For Today:

| No. 12.  'On the Definition of Logic'.
|
| Logic is 'formal semiotic'.  A sign is something, 'A', which brings
| something, 'B', its 'interpretant' sign, determined or created by it,
| into the same sort of correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in which itself stands to 'C'.
| This definition no more involves any reference to human thought than
| does the definition of a line as the place within which a particle lies
| during a lapse of time.  It is from this definition that I deduce the
| principles of logic by mathematical reasoning, and by mathematical
| reasoning that, I aver, will support criticism of Weierstrassian
| severity, and that is perfectly evident.  The word "formal" in
| the definition is also defined.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics',
| Four Volumes In Five Books,
| Edited by Carolyn Eisele,
| Mouton, The Hague, 1976.

HP: Howard wrote [trying to understand Peirce's language]:

    | A brings B to correspond with C as A corresponds to C.
    | So we can diagram it as a triangle:
    |
    |                     A (sign)
    |                    / \
    |                   /   \
    |                  /     \
    |                 /       \
    |               C - - - - - B
    |        (object)           (interpretant sign)

HP: So, A creates B and also brings B into the relation BC which is
    the same (or lower?) relation as AC.  (Have I got that right?)

JA: No, the "correspondence" that is indicated here is a "triple correspondence",
    what might be called a "3-place transaction" in database terms.  Let us name
    this 3-place relation L.  Accordingly, to say that "A brings B to correspond
    with C as A corresponds to C" is simply to say that A brings B into the same
    3-place relation L with something else B' and C as A occupies in the 3-place
    relation L with B and C.

HP: I don't see how Peirce's words say what you say they say.

JA: Howard, my first time around in Peirce studies
    was off and on all throughout my undergrad years,
    a desulkory decade of dropping in and dropping out,
    during which time I stayed mostly within the bounds
    of CP 3&4, due to my interest in logic and math and
    all things graphical.  I spent the last couple of
    years of this period writing my Senior Thesis on
    the puzzles arising out of one little paragraph,
    CP 4.306.  The pursuit of enlightenment on this
    problem, as it turned on Peirce's use of matrix
    representations over B = {off, on} for logical
    operators, led me back into mathematics proper,
    from which I had been vacationing for a while
    in philosophy.  I believe that it was toward
    the end of this phase that I figured out what
    Peirce was talking about when he wrote about
    sign relations, but it was a cumulative grasp,
    no sudden epiphany, no definitive succincture,
    nor had I seen anything called a "definition"
    that I would have regarded, nor imagined that
    Peirce intended, as anything but a partially
    illustrative gloss on the notion.  The best
    clue that I had was the "Sunflower" example,
    the text of which I cannot find at the moment,
    but I can remember drawing pictures like this
    to represent 3-tuples of the form <s, i, o>:

JA: |            s     i
    |             \  //
    |              \//
    |              |||
    |              |||
    |               o

JA: What struck me as Peirce's most striking illustration
    was a story about a sunflower, that in turning toward
    the sun, and by virtue of that very act alone, brings
    another sunflower to turn toward the sun.  The object
    is the sun, the sign is the orienting of that initial
    sunflower, and the interpretant sign is the orienting
    of that next instructed sunflower, turning to the sun.
    To illustrate this example of semiosis or sign-action
    I vividly remember drawing a picture of the following
    form, the best that I can render it in ASCII, anyway:

JA: |          s        i
    |         " \      //"
    |        "   \    //  "
    |       "     \  //    "
    |      i\      \//      s
    |       \\     |||     /
    |        \\____|||____/
    |         \==== o ====\
    |         /    |||    \\
    |        /     |||     \\
    |       s      //\      \i
    |        "    //  \     "
    |         "  //    \   "
    |          "//      \ "
    |           i        s

JA: Here, I was able to manage drawing only four 3-tuples,
    and I had to use a line of ditto marks (") to indicate
    that their termini are to be treated as identical nodes,
    whereas as I was accustomed to draw it I would have had
    eight or more 3-tuples, arranged in the form of a flower,
    and I would have then been able simply to fuse the nodes
    that were to be identified.  The point of the picture is,
    of course, that s_1 -> i_1 = s_2 -> i_2 = s_3 -> i_3, ...,
    and so on.

An essential feature of this example, as Peirce described it,
was that Sunflower 1 transmits to Sunflower 2, not just the
transient impulse to turn toward the sun, but also the law,
or the continuity of this particular form of transition,
by which it conveys all of the above to future others.

CSP: | A sign is something, 'A', which brings something, 'B',
     | its 'interpretant' sign, determined or created by it,
     | into the same sort of correspondence (or a lower implied
     | sort) with something, 'C', its 'object', as that in which
     | itself stands to 'C'.

HP, interpreting CSP:

    | A creates B and also brings B into the relation BC
    | which is the same (or lower?) relation as AC.

HP: What, exactly, did my shorter version leave out
    that essentially alters Peirce's meaning?

o~~~~~~~~~o~~~~~~~~~o~INTERLUDE~o~~~~~~~~~o~~~~~~~~~o

Using the acronym "SOC" for "sort of correspondence",
let us try the following paraphrase of the criterion:

| A brings something into the same SOC with C
| as the SOC in which A stands to C.

In order to expand the expression correctly, one has to ask:

0.  What is the SOC in which A stands to C?

The SOC in which A stands to C is given by Formula 1.

1.  A brings something into some SOC with C,
    to wit, the SOC in which A stands to C.

If B enters into the same SOC with C as A stands in, that is to say,
if B takes up the same role that A had in Formula 1, then we obtain:

2.  B brings something into some SOC with C,
    to wit, the SOC in which A stands to C.

Let us give the name B' to the something in Formula 2.
Now, B' can either be something old or something new.
If old, it's in A, B, C.  If new, let's leave it B'.

In any case, we have:

3.  B brings B'into some SOC with C,
    the SOC in which A stands to C.

In sum, the bringing of a new, possibly old, thing
into the relation is part of being in the relation.

And so it goes ...

o~~~~~~~~~o~~~~~~~~~o~EDULRETNI~o~~~~~~~~~o~~~~~~~~~o

JA: There are three important ideas that are involved in Peirce's definition
    of a sign that are not themselves defined local to its immediate context:
    "Correspondence", "Determination", "Formal".  It is common for thoroughly
    modern readers to simply supply their own meanings without pausing to ask
    if there could be other senses, in which case they read mush -- typically
    hashing together a mess'o'misapprehensions about the 2-adic mirror images
    of a 2-adic correspondence theory of truth, some enchanted doctrine about
    a semiotic causal determinism imputed to Peirce, plus who knows what when
    it comes to their pro forma reading of "formal".  But should anybody want
    to know what the guy was really saying, all a body has to do is look into
    the many other places where he says exactly what he means by these words.

HP: In other words, I fail to see how, from Peirce's definition alone, I would
    be justified in interpreting it as the "3-place transaction, L" you describe
    (whatever L is).  Is this called an elliptical definition?

JA: Yes, in the sense that every word in the dictionary is defined elliptically,
    if not in the orbits of another conic section, in terms of other words that
    one must trace elsewhere, in their own proper spheres.

HP: Your elaborate exegesis of Peirce is interesting.
    My problem is that if Peirce's meaning was as subtle
    as you say, then would he not have realized how inadequate,
    if not misleading, was his 40-word definition if sign. Why, 
    then would he repeat what was for him a crucial definition,
    and claim derivations from it with Weierstrassian rigor?

HP, quoting JA:
    | ... But should anybody want to know what the guy was really saying,
    | all a body has to do is look into the many other places where he
    | says exactly what he means by these words.

JA: Since I know you have a good imagination,
    Peirce's own words would be more convincing.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Howard,

I was on point of thanking you for your persistence
in pressing for clarity on this issue, as I believe
that it has forced me to write a couple of the most
clear and most detailed expositions of this example
of definition that I have ever written, and yet now
my gratitude is sicklied o'er with the pale cast of
gratification delayed by the circumstance that your
appreciation of my interpretation underwhelms mine.

The NEM volumes did not come out until 1976, and though it is
just possible that I might have run across them in my favorite
hide-out corner of the math library while I was starting on my
3rd cycle through math and my 2nd cycle through Peirce studies,
I am pretty sure that I did not encounter this particular text
until a good deal later, when I was already approaching my 3rd
encounter with Our Maestro.  In 1989 I finished up my work on
my "Theme One" program, that integrated a few of the simpler
aspects of inductive learning and deductive reasoning over
a shared resource base of graph-theoretic data structures
and functionally-implemented algorithms.  Then it struck
me that abductive reasoning was the missing piece, and
that is what brought me back to a more dedicated and
more deliberate reading of what Peirce, along with
all of the current literature, had to say on the
subject.  But none of these ductions makes any
sense in isolation from the cycle of inquiry,
and so here we are ...

Anyway, I can tell you that I clearly remember that I did not
find this definition, and recognize it for what it was, until
it occured to me one day that Peirce, as a real mathematician,
just must have taken the time sometime to write out a genuine,
properly mathematical defintion of this most important notion,
and so I went out looking for it, and as I sought, I found it.

Do I need to tell you that I do not find this definition
of signs to be in the least bit inadequate or misleading?

I do find that I often have to explain to a certain class of people,
who have been trained to follow in certain lines of trickety tracks,
that our theories, however approximal to our own severe limitations,
must still be designed so as to respect the complexity and subtlety
of their intended subjects, and that the conduct of inquiring minds,
and how their inquiring minds conceivably might be embodied, is one
of the complexer and the subtler bodies of phenomena that we'll see,
but, of course, I scarcely have any cause to amuse our present fine
body of complices with that particular lecture.

The sum of it is that Peirce was the sort of person who was able to derive,
out of sheer mathematical insight, and through a remarkable logical power,
all sans hint of a clue from his contemporaries, a "theory of information"
and a version of what we today call "non-standard analysis", both of which,
as initial as he left them, have features in advance of our current renditions.

The analysis of the sign definition that I teased out here in my last couple of tries --
and I deliberately avoided bringing in the machineries of quantificational calculus --
are just the barest echoes of a form of analysis that Peirce repeated on a routine
basis, and that he developed into an exact art by means of his Existential Graphs.

I will, of course, supply examples.

The reference to Weierstrass is an allusion in part to the theory of limits,
which Peirce thought was critical to analyzing semiosis in continuous media.

What Peirce means by "formal", along with his sense of the relation
between logical and mathematical reasoning, is covered by the quote
that I posted under "Logic As Semiotics".  I recur to it again here:

o~~~~~~~~~o~~~~~~~~~o~CITATION~o~~~~~~~~~o~~~~~~~~~o

| Logic, in its general sense, is, as I believe I have shown, only another name for
|'semiotic' ([Greek: semeiotike]), the quasi-necessary, or formal, doctrine of signs.
| By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the
| characters of such signs as we know, and from such an observation, by a process which
| I will not object to naming Abstraction, we are led to statements, eminently fallible,
| and therefore in one sense by no means necessary, as to what 'must be' the characters
| of all signs used by a "scientific" intelligence, that is to say, by an intelligence
| capable of learning by experience.  As to that process of abstraction, it is itself
| a sort of observation.  The faculty which I call abstractive observation is one which
| ordinary people perfectly recognize, but for which the theories of philosophers sometimes
| hardly leave room.  It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question, "Should I wish for
| that thing just the same, if I had ample means to gratify it?"  To answer that question, he
| searches his heart, and in doing so makes what I term an abstractive observation.  He makes
| in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what
| modifications the hypothetical state of things would require to be made in that picture, and
| then examines it, that is, 'observes' what he has imagined, to see whether the same ardent
| desire is there to be discerned.  By such a process, which is at bottom very much like
| mathematical reasoning, we can reach conclusions as to what 'would be' true of signs
| in all cases, so long as the intelligence using them was scientific.  (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editors' Note: From an unidentified fragment, c. 1897.

o~~~~~~~~~o~~~~~~~~~o~NOITATIC~o~~~~~~~~~o~~~~~~~~~o

What Peirce means by "determination" is key to his theory of information.
I began a special study of the topic a while back and have been posting
the running accumulation of source materials and other highlights here:

http://suo.ieee.org/ontology/msg02377.html
http://suo.ieee.org/ontology/msg02378.html
http://suo.ieee.org/ontology/msg02379.html
http://suo.ieee.org/ontology/msg02380.html
http://suo.ieee.org/ontology/msg02384.html
http://suo.ieee.org/ontology/msg02387.html
http://suo.ieee.org/ontology/msg02388.html
http://suo.ieee.org/ontology/msg02389.html
http://suo.ieee.org/ontology/msg02390.html
http://suo.ieee.org/ontology/msg02391.html
http://suo.ieee.org/ontology/msg02395.html
http://suo.ieee.org/ontology/msg02407.html
http://suo.ieee.org/ontology/msg02550.html
http://suo.ieee.org/ontology/msg02552.html
http://suo.ieee.org/ontology/msg02556.html
http://suo.ieee.org/ontology/msg02594.html
http://suo.ieee.org/ontology/msg02651.html
http://suo.ieee.org/ontology/msg02673.html
http://suo.ieee.org/ontology/msg02706.html

For my own part, I find that I often like
Peirce's more folksy and poetical glosses.
Here's my favorite one on "Determination":

| To determine means to make a circumstance different
| from what it might have been otherwise.  For example,
| a drop of rain falling on a stone determines it to be
| wet, provided the stone may have been dry before.  But
| if the fact of a whole shower half an hour previous is
| given, then one drop does not determine the stone to be
| wet;  for it would be wet, at any rate.  (CE 1, 245-246).
|
| Charles Sanders Peirce,
|"Harvard Lecture on Kant, 1865",
|'Writings of Charles S. Peirce:
| A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press,
| Bloomington, IN, 1982.
|
| http://suo.ieee.org/ontology/msg02550.html

In general, it is best to interpret Peirce's notion of determination
in an "informational" or an "instructural" sense, rather than in the
causal sense, though of course the two are occasionally linked.  One
may also find it instructive to think of how the word is employed in
mathematics, as in "two points determine a line", and "a determinant
is an invariant of a linear transformation".  My guess is that these
senses would not have been too far from Peirce's thought as he wrote.

I do not know what to tell you about about Peirce's use
of "correspondence" in the definition of sign relations.
I do recall seeing one or two places where he actually
uses the phrase "triple correspondence", and I could
go chasing after that, but I am getting the feeling
that it might be for nought.  The fact that Peirce
is talking about genuine and irreducible 3-adic
relations as the subject matter of his theory
of signs is rife throughout everything that
he says about them, and if you find that
a matter for controversy then I just
do not see how I might address it.

But I glad to see that you do, after all,
appreciate the skills of scholasticism
beyond the arts of imagination.

Jon Awbrey

10 Aug 2001 • 11:48 • Inquiry Into Inquiry

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Subj: OCA: Re: Inquiry Into Inquiry
Date: Fri, 10 Aug 2001 11:48:04 -0400
From: Jon Awbrey
  To: Organization Complexity Autonomy
  CC: Arisbe, Ontology

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):

SS: I mean that in much semiotic literature 'interpretant' is used as
    though it just pops up as a mate for the object by way of the sign.
    Or, indeed, that a sign (as if it were "out there" prior to some semiosis)
    links an object with an interpretant.  That is, the system by which object
    and interpretant are linked via some (actually co-constructed) sign is left
    completely implicit.  I have found this unworkable for myself because, for
    me, a SI (your SOI) can be of many kinds, not just some human system.

JA: I am not sure if I read the literature that you are talking about.
    Off the cuff, I would say that I do not believe that the sorts of
    features you mention are obligatory attributes of sign relations,
    but more like optional accessories that can happen in some cases.

SS: Therefore the SI needs to be stated up front.

I do not understand.  We are talking about empirical phenomena.
At best we have our mits on a mere paltry sample of what may be.
There is a thing that we may call a "universal sign relation" (USR),
consisting of all the actual, or maybe posable, or maybe just possible
moments in the Conscious Cosmos when something (s) means something (i)
to someone (j) in 3-ads of the form of <s, i, j>, or posed another way,
when something (s) means something (i) about something (o) permused in
3-tuples of the form <o, s, i>, but the question is what it always is:
Does the spirit come when we call it?  Though we may spill out the ink
that it takes to form the letters of "Cosmos" or "Universe", in deed
we can scarcely do better than to focus on this or that drop of it.

JA: If you are saying that the whole sign relation L c OxSxI is the thing,
    in other words, the sine qua non of sensible discourse about signs,
    then I think that I would agree.

SS: No, I am saying that OxSxI are relations that,
    IF they are meant to be taking place in the
    material world, ...

I am purely a material thinker.
I can not imagine where else
they might be taking place.
But I know of no "anti"
to form for a' that.

SS: No, I am saying that OxSxI are relations that,
    IF they are meant to be taking place in the
    material world, require a locus to carry
    the viewpoint that will be reflected in
    the interpretants.  That locus or locale
    I call the system of interpretance (SI).

Now, it begins to sound like your SI is the interpreter?

SS: One SI may interact with an object quite differently than another does,
    and the signs used in mediating these interactions will be different.
    Put (more importantly) another way, the mediation is not done by the
    sign, but by the SI, which helped to create the sign.

JA: I guess I could say that the sign relation L c OxSxI
    is the "medium" of whatever "mediation" is going on.

SS: Well, that sounds like a kind of idealism to me.
    That is, not rooted in the frictive material world,
    but a free floating relation which might alight where
    it will.

By "medium" I mean the material whirl --
I was not calling on Madame Blavatsky.

SS: So, the SI is responsible for both the formalisms and the measurements.

JA: I believe that Nature, the ever pressent object reality,
    has its share of responsibility for our impressions and
    perforce must be assigned a part in the cosmic dialogue.

SS: Yes, but, because each SI will individuate during its development
    from vague beginnings, each one will have modified Nature's mode
    of impressions in its own way, and its signs will have its signature.

JA:  In those varieties of sign relation where Nature is the object,
     a modified impression is but another form of interpretant sign.

SS: Yes, development can be viewed as a concatenation of interpretants.

Okay.

SS: I note that this also relates to Howard's
    "Are Peircean rules of inquiry formal?"
    They appear to be formal and therefore
    to apply universally for all inquiry
    conditions, like "laws of inquiry".

JA: It seems that we have yet to converge on a sufficiently congruous collection
    of connotations for the term "formal".  I am hopeful that the fragment from
    Peirce that I posted under the heading of "Logic As Semiosis" will go toward
    explaining his sense of "formal" as "quasi-necessary", and also clarify the
    distinction that he observes between "logical" and "mathematical" reasoning.

SS: What I mean by formal is just that there is a form or framework that can be applied
    anywhere to analyze or understand situations.  That is, the Peircean triad, among
    other formalism, can be used as frame for understanding situations.  It is a tool
    for making models.

Well, it appears that everybody has his or her own definition of "form" these days,
which tells me that the Latin intuition is likely the most apt, "forma" = "beauty",
and thus in the eye of the beformer.  It is this very diversity that drove me back
to Homer and Plato and Aristotle, and to cling like a bat to the tree of etymology.

But I do like the bit about frameworks and instruments and mock-ups, whatever you call it.

SS: How, then, do the unique conditions of a specific observer or system under study
    enter the formal inquiry?  How is this different from normal physicist's inquiry?

JA: Again, this question strikes me as a strangely familiar inquiry,
    being one of the main tasks of my inquiry into inquiry to tackle.
    I will let you know what I come up with.  But I have already come
    to the conclusion that we cannot approach such complex and subtle
    questions without much more adequate conceptual and computational
    frameworks to support our effort.  So I have been working on that.

JA: Another thought. I just recognized that the type of question being asked here
    is closely related to a standard question in pragmatic hermeneutics, as to the
    status of the interpreter vis a vis the interpretant, in deed, as it stands in
    regard to the entire sign relation in question.  Peirce's answer, which I take
    to be a critical insight, is that the full sign relation is the primary entity
    of our study, its bearing on interpretants being the next in importance, while
    the agent of the interpretive activity is what such agents proto-typically are,
    a hypostatic abstraction hypothesized to explain the phenomena of experience.

SS: Well, I think this places your understanding here well within idealism.

I wish I were an ideal thinker, but I am far too fallible for that.
I mean, I think in ideas about Ideas, but my ideas fall miserably
short of the Ideal.  But maybe I should ask what you mean by your
idealism?

SS: But I may be making an oversimple reaction to this statement.  In science we are
    used to looking at systems.  We habitually imagine them to be composed of, AND
    to be precipitated BY entities.  Here you seem to opt for relations as being
    primary.  I think scientists tend to see relations as relating pre-existing
    entities.  Here instead you seem to see entities fitting into, or even
    coming into existence under the guidance of, pre-existing relations.
    If semioticians wish to talk to scientists, these issues will have
    to be cleared up.  (I am not saying either way is incorrect,
    of course.)

And where do you think that I learned this stuff, this POV, and how to think this way?
I did not begin as a student of antique philosophies and only lately catch up in my
reading to the 1800's.  It was in my "relativity and quantum mechanic" (RAQM) days
that I was re-trained to think in terms of relations and reciprocant observations,
and to see these bits of stuff flitting about the cosmos as congellid invariants
from the sol of a crypto-pythagorean geometry: "All Is Numb, And Getting Number".

But that was yesterday ...

Jon Awbrey