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]


Outline of the Project : Inquiry Into Inquiry



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



Onus of the Project : No Way But Inquiry

A Modulating Prelude

A Fugitive Canon

Option of the Project : A Way Up To Inquiry

Initial Analysis of Inquiry : Allegro Aperto

Discussion of Discussion

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

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

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

Recursion in Perpetuity

Processus, Regressus, Progressus

Rondeau : Tempo di Menuetto

Part 2


The Informal Context

The Epitext

The Formative Tension

Recurring Themes

Preliminary Notions

Intermediary Notions

Propositions and Sentences

Empirical Types and Rational Types

Articulate Sentences

Stretching Principles

Stretching Operations

The Cactus Patch

The Cactus Language : Syntax

Grammar 1
Grammar 2
Grammar 3
Grammar 4
Grammar 5
Grammar 6

Generalities About Formal Grammars

The Cactus Language : Stylistics

The Cactus Language : Mechanics

The Cactus Language : Semantics

Stretching Exercises

Syntactic Transformations

Syntactic Transformation Rules

Derived Equivalence Relations

Digression on Derived Relations

Part 3

Outlook of the Project : All Ways Lead to Inquiry

The Matrix of Inquiry

Inquiry as Conduct
Types of Conduct
Perils of Inquiry
Forms of Relations
Models of Inquiry

The Moment of Inquiry

The Modes of Inquiry

Deductive Reasoning
Inductive Reasoning
Abductive Reasoning
Analogical Reasoning

Obstacles to the Project : In the Way of Inquiry

The Initial Unpleasantness

The Justification Trap

A Formal Apology

Category Double-Takes
Conceptual Extensions
Explosional Recombinations
Interpretive Frameworks

A Material Exigency

A Reconciliation of Accounts

Objections to Reflective Inquiry

Empirical Considerations

Computational Considerations

A Form of Recursion
A Power of Abstraction

Orientation of the Project : A Way Into Inquiry

Initial Description of Inquiry

Terms of Analysis

Digression on Signs
Empirical Status of ID

Expansion of Terms


Anchoring Terms in Phenomena

A Mistaken ID
Phenomenology of Doubt
Modalities of Knowledge

Sets, Systems, and Substantive Agents

Interpretive Systems

Syntactic Systems
Semantic Systems
Pragmatic Systems

Inquiry Driven Systems

A Definition of Inquiry
The Faculty of Inquiry
A Definition of Determination
A Definition of Definition

Organization of the Project : A Way Through Inquiry

The Problem : Inquiry Found as an Object of Study

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

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

Objectives of the Project : Inquiry All the Way

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

Instrumental Objective

Coordination of Objectives

Recapitulation — Da Capo, Al Segno

Discussion of Inquiry

Approaches to Inquiry

The Classical Framework : Syllogistic Approaches

The Pragmatic Framework : Sign-Theoretic Approaches

The Dynamical Framework : System-Theoretic Approaches

Inquiry and Computation
Inquiry Driven Systems

The Context of Inquiry

The Field of Observation

The Problem of Reflection

The Problem of Reconstruction

The Trivializing of Integration

Tensions in the Field of Observation

Problems of Representation and Communication

The Conduct of Inquiry


The Types of Reasoning


Hybrid Types of Inference


Details of Induction


The Stages of Inquiry

Interlude : The Medium and Its Message

Reflective Expression

Casual Reflection

Ostensibly Recursive Texts
Analogical Recursion

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
Recursions : Possible, Actual, Necessary
Ostensibly Recursive Texts
The Freedom of Interpretation
The Eternal Return
Information in Formation
Reflectively Indexical Texts
The Discursive Universe

Reflective Inquiry

Integrity and Unity of Inquiry

Apparitions and Allegations

A Reflective Heuristic

Either/Or : A Sense of Absence

Apparent, Occasional, and Practical Necessity

Approaches, Aspects, Exposures, Fronts

Synthetic A Priori Truths

Priorisms of Normative Sciences

Principle of Rational Action

The Pragmatic Cosmos

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

Reflection on Reflection

Looking Back

The Light in the Clearing

The Face in the Mirror

Points Forward

Reflective Interpretive Frameworks

The Phenomenology of Reflection

A Candid Point of View

A Projective Point of View

A Formal Point of View

Three Styles of Linguistic Usage

Basic Notions of Group Theory

Basic Notions of Formal Language Theory

A Perspective on Computation

Higher Order Sign Relations : Introduction

Higher Order Sign Relations : Examples

Higher Order Sign Relations : Application

Issue 1. The Status of Signs

Issue 2. The Status of Sets

Issue 3. The Status of Variables

Propositional Calculus

Recursive Aspects

Patterns of Self-Reference

Practical Intuitions

Examples of Self Reference

Three Views of Systems

Building Bridges Between Representations

Extensional Representations of Sign Relations

Intensional Representations of Sign Relations

Literal Intensional Representations

Analytic Intensional Representations

Differential Logic and Directed Graphs

Differential Logic and Group Operations

The Bridge : From Obstruction to Opportunity

Projects of Representation

Connected, Integrated, Reflective Symbols

Relations in General

Partiality : Selective Operations

Sign Relational Complexes

Set-Theoretic Constructions

Reducibility of Sign Relations

Irreducibly Triadic Relations

Propositional Types

Considering the Source

Prospective Indices : Pointers to Future Work

Dynamic and Evaluative Frameworks

Elective and Motive Forces

Sign Processes : A Start

Reflective Extensions

Reflections on Closure

Intelligence => Critical Reflection

Looking Ahead

Mutually Intelligible Codes

Discourse Analysis : Ways and Means

Combinations of Sign Relations

Revisiting the Source

Part 7

Divertimento : Eternity in Love with the Creatures of Time

Reflections on the Presentation of Examples

Searching for Parameters

Defect Analysis

The Pragmatic Critique

Pragmatic Operating Notions

Defects of Presentation

Dues to Process

Duties to Purpose

Computational Design Philosophy

Intentional Objects and Attitudes

Imperfect Design and Persistent Error

Propositional Reasoning About Relations

Dynamic and Evaluative Frameworks

Discussion of Examples

Information and Inquiry

Overview of the Domain : Interpretive Inquiry

Interpretive Bearings : Conceptual and Descriptive Frameworks

Catwalks : Flexible Frameworks and Peripatetic Categories

Eponymous Ancestors : The Precursors of Abstraction?
Reticles : Interpretive Flexibility as a Design Issue

Heuristic Inclinations and Regulative Principles

Features of Inquiry Driven Systems

The Pragmatic Theory of Signs

Sign Relations
Types of Signs

The Pragmatic Theory of Inquiry


Examples of Inquiry Driven Systems

“Index” : A Program for Learning Formal Languages

“Study” : A Program for Reasoning with Propositions

Discussion and Development of Objectives

Objective 1a : Propositions as Types

Objective 1b : Proof Styles and Developments

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