Inquiry Driven Systems

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Author: Jon Awbrey

ContentsPart 1Part 2Part 3Part 4Part 5Part 6Part 7Part 8AppendicesReferencesDocument History


I put down the cup and turn to my mind. It is up to my mind to find the truth. But how? What grave uncertainty, whenever the mind feels overtaken by itself; when it, the seeker, is also the obscure country where it must seek and where all its baggage will be nothing to it. Seek? Not only that: create. It is face to face with something that does not yet exist and that only it can accomplish, and bring into its light.

  — Marcel Proust, In Search of Lost Time, [Pro, 1.48]


1. Introduction

1.1. Outline of the Project : Inquiry Into Inquiry

1.1.1. Problem

1.1.2. Method The Paradigmatic and Process-Analytic Phase The Paraphrastic and Faculty-Synthetic Phase Reprise of Methods

1.1.3. Criterion

1.1.4. Application

1.2. Onus of the Project : No Way But Inquiry

1.2.1. A Modulating Prelude

1.2.2. A Fugitive Canon

1.3. Option of the Project : A Way Up To Inquiry

1.3.1. Initial Analysis of Inquiry : Allegro Aperto

1.3.2. Discussion of Discussion

1.3.3. Discussion of Formalization : General Topics A Formal Charge A Formalization of Formalization? A Formalization of Discussion? A Concept of Formalization A Formal Approach A Formal Development A Formal Persuasion

1.3.4. Discussion of Formalization : Concrete Examples Formal Models : A Sketch Sign Relations : A Primer Semiotic Equivalence Relations Graphical Representations Taking Stock The “Meta” Question Iconic Signs The Conflict of Interpretations Indexical Signs Sundry Problems Review and Prospect Objective Plans and Levels Formalization of OF : Objective Levels Application of OF : Generic Level Application of OF : Motive Level The Integration of Frameworks Recapitulation : A Brush with Symbols C'est Moi Entr'acte

1.3.5. Discussion of Formalization : Specific Objects The Will to Form The Forms of Reasoning A Fork in the Road A Forged Bond A Formal Account Analogs, Icons, Models, Surrogates Steps and Tests of Formalization A Puckish Referee Partial Formalizations A Formal Utility A Formal Aesthetic A Formal Apology A Formal Suspicion The Double Aspect of Concepts A Formal Permission A Formal Invention

1.3.6. Recursion in Perpetuity

1.3.7. Processus, Regressus, Progressus

1.3.8. Rondeau : Tempo di Menuetto

2. Part 2

2.1. Reconnaissance

2.1.1. The Informal Context

2.1.2. The Epitext

2.1.3. The Formative Tension

2.2. Recurring Themes

2.2.1. Preliminary Notions

2.2.2. Intermediary Notions

2.2.3. Propositions and Sentences

2.2.4. Empirical Types and Rational Types

2.2.5. Articulate Sentences

2.2.6. Stretching Principles

2.2.7. Stretching Operations

2.3. The Cactus Patch

2.3.1. The Cactus Language : Syntax Grammar 1 Grammar 2 Grammar 3 Grammar 4 Grammar 5 Grammar 6

2.3.2. Generalities About Formal Grammars

2.3.3. The Cactus Language : Stylistics

2.3.4. The Cactus Language : Mechanics

2.3.5. The Cactus Language : Semantics

2.3.6. Stretching Exercises

2.4. Syntactic Transformations

2.4.1. Syntactic Transformation Rules

2.4.2. Derived Equivalence Relations

2.4.3. Digression on Derived Relations

3. Part 3

3.1. Outlook of the Project : All Ways Lead to Inquiry

3.1.1. The Matrix of Inquiry Inquiry as Conduct Types of Conduct Perils of Inquiry Forms of Relations Models of Inquiry

3.1.2. The Moment of Inquiry

3.1.3. The Modes of Inquiry Deductive Reasoning Inductive Reasoning Abductive Reasoning Analogical Reasoning

3.2. Obstacles to the Project : In the Way of Inquiry

3.2.1. The Initial Unpleasantness

3.2.2. The Justification Trap

3.2.3. A Formal Apology Category Double-Takes Conceptual Extensions Explosional Recombinations Interpretive Frameworks

3.2.4. A Material Exigency

3.2.5. A Reconciliation of Accounts

3.2.6. Objections to Reflective Inquiry

3.2.7. Empirical Considerations

3.2.8. Computational Considerations A Form of Recursion A Power of Abstraction

3.3. Orientation of the Project : A Way Into Inquiry

3.3.1. Initial Description of Inquiry

3.3.2. Terms of Analysis Digression on Signs Empirical Status of ID

3.3.3. Expansion of Terms Agency Abstraction Analogy Accuracy Authenticity

3.3.4. Anchoring Terms in Phenomena A Mistaken ID Phenomenology of Doubt Modalities of Knowledge

3.3.5. Sets, Systems, and Substantive Agents

3.3.6. Interpretive Systems Syntactic Systems Semantic Systems Pragmatic Systems

3.3.7. Inquiry Driven Systems A Definition of Inquiry The Faculty of Inquiry A Definition of Determination A Definition of Definition

3.4. Organization of the Project : A Way Through Inquiry

3.4.1. The Problem : Inquiry Found as an Object of Study

3.4.2. The Method : Inquiry Found as a Means of Study Conditions for the Possibility of Inquiry into Inquiry Conditions for the Success of Inquiry into Inquiry

3.4.3. The Criterion : Inquiry in Search of a Sensible End The Irritation of Doubt, and The Scratch Test Enabling Provision 1 : The Scenes and Context of Inquiry Enabling Provision 2 : The Stages and Content of Inquiry

3.5. Objectives of the Project : Inquiry All the Way

3.5.1. Substantial Objective Objective 1a : The Propositions as Types Analogy Objective 1b : The Styles of Proof Development Objective 1c : The Analysis of Interpreters, or A Problem with Authority

3.5.2. Instrumental Objective

3.5.3. Coordination of Objectives

3.5.4. Recapitulation — Da Capo, Al Segno

4. Discussion of Inquiry

4.1. Approaches to Inquiry

4.1.1. The Classical Framework : Syllogistic Approaches

4.1.2. The Pragmatic Framework : Sign-Theoretic Approaches

4.1.3. The Dynamical Framework : System-Theoretic Approaches Inquiry and Computation Inquiry Driven Systems

4.2. The Context of Inquiry

4.2.1. The Field of Observation

4.2.2. The Problem of Reflection

4.2.3. The Problem of Reconstruction

4.2.4. The Trivializing of Integration

4.2.5. Tensions in the Field of Observation

4.2.6. Problems of Representation and Communication

4.3. The Conduct of Inquiry

4.3.1. Introduction

4.3.2. The Types of Reasoning Deduction Induction Abduction

4.3.3. Hybrid Types of Inference Analogy Inquiry

4.3.4. Details of Induction Learning Transfer Testing

4.3.5. The Stages of Inquiry

5. Interlude : The Medium and Its Message

5.1. Reflective Expression

5.1.1. Casual Reflection Ostensibly Recursive Texts Analogical Recursion

5.1.2. Conscious Reflection The Signal Moment The Symbolic Object The Endeavor to Communicate The Medium of Communication The Ark of Types : The Order of Things to Come The Epitext The Context of Interpretation The Formative Tension The Vehicle of Communication : Reflection on the Scene, Reflection on the Self (7) (6) Recursions : Possible, Actual, Necessary Ostensibly Recursive Texts (3) The Freedom of Interpretation The Eternal Return (1) Information in Formation Reflectively Indexical Texts (4) (5) (6) (7) (8) The Discursive Universe (7) (6) (5) (4) (3) (2) (1)

5.2. Reflective Inquiry

5.2.1. Integrity and Unity of Inquiry

5.2.2. Apparitions and Allegations

5.2.3. A Reflective Heuristic

5.2.4. Either/Or : A Sense of Absence

5.2.5. Apparent, Occasional, and Practical Necessity

5.2.6. Approaches, Aspects, Exposures, Fronts

5.2.7. Synthetic A Priori Truths

5.2.8. Priorisms of Normative Sciences

5.2.9. Principle of Rational Action

5.2.10. The Pragmatic Cosmos

5.2.11. Reflective Interpretive Frameworks Principals vs. Principals The Initial Description of Inquiry An Early Description of Interpretation Descriptions of the Mind Of Signs and the Mind Questions of Justification The Experience of Satisfaction An Organizational Difficulty Pragmatic Certainties Problems and Methods

5.3. Reflection on Reflection

Looking Back

The Light in the Clearing

The Face in the Mirror

Points Forward

6. Reflective Interpretive Frameworks

6.1. The Phenomenology of Reflection

6.2. A Candid Point of View

6.3. A Projective Point of View

6.4. A Formal Point of View

6.5. Three Styles of Linguistic Usage

6.6. Basic Notions of Group Theory

6.7. Basic Notions of Formal Language Theory

6.8. A Perspective on Computation

6.9. Higher Order Sign Relations : Introduction

6.10. Higher Order Sign Relations : Examples

6.11. Higher Order Sign Relations : Application

6.12. Issue 1. The Status of Signs

6.13. Issue 2. The Status of Sets

6.14. Issue 3. The Status of Variables

6.15. Propositional Calculus

6.16. Recursive Aspects

6.17. Patterns of Self-Reference

6.18. Practical Intuitions

6.19. Examples of Self Reference

6.20. Three Views of Systems

6.21. Building Bridges Between Representations

6.22. Extensional Representations of Sign Relations

6.23. Intensional Representations of Sign Relations

6.24. Literal Intensional Representations

6.25. Analytic Intensional Representations

6.26. Differential Logic and Directed Graphs

6.27. Differential Logic and Group Operations

6.28. The Bridge : From Obstruction to Opportunity

6.29. Projects of Representation

6.30. Connected, Integrated, Reflective Symbols

6.31. Relations in General

6.32. Partiality : Selective Operations

6.33. Sign Relational Complexes

6.34. Set-Theoretic Constructions

6.35. Reducibility of Sign Relations

6.36. Irreducibly Triadic Relations

6.37. Propositional Types

6.38. Considering the Source

6.39. Prospective Indices : Pointers to Future Work

6.40. Dynamic and Evaluative Frameworks

6.41. Elective and Motive Forces

6.42. Sign Processes : A Start

6.43. Reflective Extensions

6.44. Reflections on Closure

6.45. Intelligence => Critical Reflection

6.46. Looking Ahead

6.47. Mutually Intelligible Codes

6.48. Discourse Analysis : Ways and Means

6.49. Combinations of Sign Relations

6.50. Revisiting the Source

7. Part 7

7.1. Divertimento : Eternity in Love with the Creatures of Time

7.1.1. Reflections on the Presentation of Examples

7.1.2. Searching for Parameters

7.1.3. Defect Analysis

7.1.4. The Pragmatic Critique

7.1.5. Pragmatic Operating Notions

7.1.6. Defects of Presentation

7.1.7. Dues to Process

7.1.8. Duties to Purpose

7.2. Computational Design Philosophy

7.2.1. Intentional Objects and Attitudes

7.2.2. Imperfect Design and Persistent Error

7.2.3. Propositional Reasoning About Relations

7.2.4. Dynamic and Evaluative Frameworks

7.2.5. Discussion of Examples

7.2.6. Information and Inquiry

8. Overview of the Domain : Interpretive Inquiry

8.1. Interpretive Bearings : Conceptual and Descriptive Frameworks

8.1.1. Catwalks : Flexible Frameworks and Peripatetic Categories Eponymous Ancestors : The Precursors of Abstraction? Reticles : Interpretive Flexibility as a Design Issue

8.1.2. Heuristic Inclinations and Regulative Principles

8.2. Features of Inquiry Driven Systems

8.2.1. The Pragmatic Theory of Signs Sign Relations Types of Signs

8.2.2. The Pragmatic Theory of Inquiry Abduction Deduction Induction

8.3. Examples of Inquiry Driven Systems

8.3.1. “Index” : A Program for Learning Formal Languages

8.3.2. “Study” : A Program for Reasoning with Propositions

8.4. Discussion and Development of Objectives

8.4.1. Objective 1a : Propositions as Types

8.4.2. Objective 1b : Proof Styles and Developments

8.4.3. Objective 1c : Interpretation and Authority


Logical Translation Rule 1

Geometric Translation Rule 1

Logical Translation Rule 2

Geometric Translation Rule 2


Document History

ContentsPart 1Part 2Part 3Part 4Part 5Part 6Part 7Part 8AppendicesReferencesDocument History