User:Jon Awbrey/In My Third Mind

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ISW -- In My Third Mind 2017

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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.

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

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.

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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

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| 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.

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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

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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

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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

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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

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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.

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Note 16

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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

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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

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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.

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