THE FATE OF ANALYSIS, #36–Wittgenstein’s Rule-Following Paradox.
By Robert Hanna
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TABLE OF CONTENTS
II. Classical Analytic Philosophy
II.1 What Classical Analytic Philosophy Is: Two Basic Theses
II.2 What Classical Analytic Philosophy Officially Isn’t: Its Conflicted Anti-Kantianism
II.3 Classical Analytic Philosophy Characterized in Simple, Subtler, and Subtlest Ways
II.4 Three Kinds of Analysis: Decompositional, Transformative, and Conceptual
II.5 Frege, The First Founding Father of Classical Analytic Philosophy
II.6 Frege’s Project of (Transformative or Reductive) Analysis
II.8 Frege’s Semantics of Sense and Reference, aka Meaning
II.9 Some Biggish Problems For Frege’s Semantics
II.10 Husserl, Logic, and Logical Psychologism, aka LP
II.11 What LP is, and its Three Cardinal Sins
II.12 Husserl’s Three Basic Arguments Against LP
III. Moore, Brentano, Husserl, Judgment, Anti-Idealism, and Meinong’s World
III.1 G.E. Moore, the Second Founding Father of Classical Analytic Philosophy
III.2 Brentano on Phenomenology, Mental Phenomena, and Intentionality
III.3 Husserl on Phenomenology and Intentionality
III.4 Moore and the Nature of Judgment
III.5 Moore and the Refutation of Idealism
IV. Russell, Unlimited Logicism, Acquaintance, and Description
IV.1 Russell Beyond Brentano, Husserl, Moore, and Meinong
IV.2 Russell and Mathematical Logic versus Kant
IV.3 Russell’s Unlimited Logicist Project
IV.4 Pursued by Logical Furies: Russell’s Paradox Again
IV.5 Russell’s ‘Fido’-Fido Theory of Meaning
IV.6 Knowledge-by-Acquaintance and Knowledge-by-Description
IV.7 Russell’s Theory of Descriptions
IV.8 Russell’s Multiple-Relation Theory of Judgment
IV.9 Russellian Analysis, Early Wittgenstein, and Impredicativity Again
IV.10 Russell and The Philosophy of Logical Atomism
V. Wittgenstein and the Tractatus 1: The Title, and Propositions 1–2.063
V.1 A Brief Synopsis of the Tractatus
V.3 The Basic Structure of the Tractatus: A Simple Picture
V.5 Reconstructing Wittgenstein’s Reasoning
V.6 What Are the Objects or Things?
V.7 The Role of Logic in Tractarian Ontology
V.9 Tractarian Ontology, Necessity, and Contingency
V.10 Some Initial Worries, and Some Possible Wittgensteinian Counter-Moves
VI. Wittgenstein and the Tractatus 2: Propositions 2.013–5.55
VI.1 What is Logical Space? What is Real Space?
VI.3 Logical Space is Essentially More Comprehensive than Manifest or Phenomenal Space
VI.4 Why There Can’t/Kant Be a Non-Logical World
VI.5 A Worry About Wittgenstein’s Conception of Logic: Non-Classical Logics
VI.6 What is a Tractarian Proposition?
VI.7 Naming Objects or Things, and Picturing Atomic Facts
VI.8 Signs, Symbols, Sense, Truth, and Judgment
VII. Wittgenstein and the Tractatus 3: Propositions 4–5.61
VII.1 The Logocentric Predicament, Version 3.0: Justifying Deduction
VII.2 The Logical Form of Deduction
VII.3 Logic Must Take Care of Itself
VII.4 Tautologies and Contradictions
VII.6 Logic is the A Priori Essence of Language
VII.7 Logic is the A Priori Essence of Thought
VII.8 Logic is the A Priori Essence of the World
VIII. Wittgenstein and the Tractatus 4: Propositions 5.62–7
VIII.1 Tractarian Solipsism and Tractarian Realism
VIII.4 Is the Tractatus’s Point an Ethical One?
VIII.6 Three Basic Worries About the Tractatus
VIII.7 Natural Science and the Worry About the Simplicity of the Objects or Things
VIII.8 Natural Science and the Worry About the Logical Independence of Atomic Facts
VIII.9 Tractarian Mysticism and the Worry About Metaphilosophy
IX. Carnap, The Vienna Circle, Logical Empiricism, and The Great Divide
IX.1 Carnap Before and After the Tractatus
IX.2 Carnap, The Vienna Circle, and The Elimination of Metaphysics
IX.3 The Verifiability Principle and Its Fate
IX.4 The Davos Conference and The Great Divide
X. Gödel-Incompleteness and Formal Piety: The Death of Classical Logicism in Thirty-One Steps
X.1 Introduction
X.2 Twenty-Five of the Thirty-One Steps
X.3 Conclusion: The Last Six Steps
XI. Wittgenstein and the Investigations 1: Preface, and §§1–27
XI.1 From the Tractatus to the Investigations
XI.2 The Thesis That Meaning Is Use
XI.3 A Map of the Investigations
XI.4 The Critique of Pure Reference: What the Builders Did
XII. Wittgenstein and the Investigations 2: §§28–242
XII.1 The Picture Theory and the Vices of Simplicity
XII.2 Wittgenstein’s Argument Against The Picture Theory: A Rational Reconstruction
XII.3 Understanding and Rule-Following
XII.4 Wittgenstein’s Rule-Following Paradox: The Basic Rationale
XII.5 Wittgenstein’s Rule-Following Paradox: A Rational Reconstruction
XII.6 Kripkenstein’s Rule-Following Paradox: Why Read Kripke Too?
XII.7 Kripkenstein’s Rule-Following Paradox: A Rational Reconstruction
XII.8 How to Solve The Paradox: Wittgenstein’s Way and Kripkenstein’s Way
XII.8.1 Wittgenstein and The Rule-Following Paradox: A Rational Reconstruction
XII.8.2 Kripkenstein and The Rule-Following Paradox: A Rational Reconstruction
XIII. Wittgenstein and the Investigations 3: §§242–315
XIII.1 What is a Private Language?
XIII.2 The Private Language Argument: A Rational Reconstruction
XIII.3 Is Wittgenstein a Behaviorist? No.
XIII.4 Wittgenstein on Meanings, Sensations, and Human Mindedness: A Rational Reconstruction
XIV. Wittgenstein and the Investigations 4: §§316–693 and 174e-232e
XIV.1 Linguistic Phenomenology
XIV.2 Two Kinds of Seeing
XIV.3 Experiencing the Meaning of a Word
XIV.4 The Critique of Logical Analysis, and Logic-As-Grammar
XV. Coda: Wittgenstein and Kantianism
XV.1 World-Conformity 1: Kant, Transcendental Idealism, and Empirical Realism
XV.2 World-Conformity 2: Wittgenstein, Transcendental Solipsism, and Pure Realism
XV.3 World-Conformity 3: To Forms of Life
XV.4 The Critique of Self-Alienated Philosophy 1: Kant’s Critical Metaphilosophy
XV.5 The Critique of Self-Alienated Philosophy 2: Wittgensteinian Analysis as Critique
XVI. From Quine to Kripke and Analytic Metaphysics: The Adventures of the Analytic-Synthetic Distinction
XVI.1 Two Urban Legends of Post-Empiricism
XVI.2 A Very Brief History of The Analytic-Synthetic Distinction
XVI.3 Why the Analytic-Synthetic Distinction Really Matters
XVI.4 Quine’s Critique of the Analytic-Synthetic Distinction, and a Meta-Critique
XVI.5 Three Dogmas of Post-Quineanism
Chapter XVII. Crisis Management: Husserl’s Crisis, Post-Classical Analytic Philosophy, and The Ash-Heap of History
XVII.1 Husserl’s Crisis and Our Crisis
XVII.1.1 Introduction
XVII.1.2 The Thematic Structure of the Crisis
XVII.1.3 Theme 1: A Husserlian Critique of Science
XVII.1.4 Theme 2: A Teleological Interpretation of European Culture Since the 17th Century, Focused on the History of Modern Philosophy
XVII.1.5 Theme 3: The Core Notion of the Life-World
XVII.1.6 Theme 4: Transcendental Phenomenology
XVII.1.7 Crisis? What Crisis?
XVII.2 Formal and Natural Science After 1945, and the Rise of Natural Mechanism
XVII.3 The Emergence of Post-Classical Analytic Philosophy
XVII.4 The Two Images Problem and its Consequences
XVII.5 The Rise, Fall, and Normalization of Post-Modern Philosophy
XVII.6 Why Hasn’t Post-Classical Analytic Philosophy Produced Any Important Ideas in the Last Thirty-Five Years?
XVII.7 The Ballad of Donald Kalish and Angela Davis: A Micro-Study
XVII.7.1 Introduction
XVII.7.2 Stage-Setting
XVII.7.3 The Ballad
XVII.7.4 The Double Life Problem, and Your Options
XVII.8 On Irad Kimhi’s Thinking and Being, Or, It’s The End Of Analytic Philosophy As We Know It (And I Feel Fine)
XVII.8.1 Introduction
XVII.8.2 The Classical Analytic Package, and Kimhi
XVII.8.3 Kimhi’s Five Main Claims, and What’s Wrong With Them
XVII.8.4 Can Logic Absolve Us of Our Sins and Redeem the World?
XVIII. Epilogue: The New Poverty of Philosophy and Its Second Copernican Revolution
XVIII.1 Introduction
XVIII.2 Wittgenstein’s Philosophy of Philosophy Revisited
XVIII.3 The New Poverty of Philosophy
XVIII.4 How is Philosophy Really Possible Inside the Professional Academy? A Global Metaphilosophical Problem
XVIII.5 Philosophy’s Second Copernican Revolution, Part 1: The Metaphilosophical Paradigm Shift to Anarcho- or Borderless Philosophy
XVIII.6 Philosophy’s Second Copernican Revolution, Part 2: The Metaphysical Paradigm Shift to Humanistic Neo-Organicism
XVIII.7 Conclusion: Let’s Go There
BIBLIOGRAPHY
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The first 35 installments in this online series followed the 2020 working draft version of THE FATE OF ANALYSIS.
Starting with this installment, #36, all subsequent installments follow the 2021 final draft version of the book.
This installment contains sections XII.4 and XII.5.
Chapter X is new in the 2021 final draft version.
But you can also read or download a .pdf version of the complete 2021 final draft version of the book, which contains all eighteen chapters, including the new chapter X, and a full bibliography, HERE.
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XII.4 Wittgenstein’s Rule-Following Paradox: The Basic Rationale
In the fairly massive Wittgenstein-literature in mainstream post-classical Analytic philosophy from the 1950s through the 1980s and even into the 90s, the central parts of Investigations are generally known as the rule following considerations, because they’re mainly given over to, first, developing, and then, second, resolving, a deep skeptical worry about the notion of following a rule: The Rule-Following Paradox.
The basic rationale behind The Rule-Following Paradox has three elements.
First, The Rule Following Paradox exposes a fatal flaw in Rule-Based Semantics, according to which the meaning of a linguistic sign is nothing but a rule for manipulating or operating with that sign in some logical or mathematical calculus, or other non-formal language-system. This in turn exposes a fatal flaw in any function-based, compositional theory of meaning, according to which the meaning of a complex expression is nothing but a function of the meanings of its simple parts, since such functions are taken to provide rules for computing the meaning of any expression in the language-system, no matter how long and complex, thus explaining how infinitely large languages (whether natural or artificial, e.g., arithmetic) are learnable by finite cognizers like us from finite informational and behavioral inputs.
Second, the notion of following a rule is essential to Wittgenstein‘s own positive conception of linguistic understanding as manifest, public mastery of linguistic techniques in context. But, in view of later Wittgenstein‘s conception of philosophy as the active achievement of clarity by stating descriptive truisms in the right way, the correct characterization of rule-following can emerge and be philosophically illuminating only indirectly, by revealing the inadequacy and incoherence of various characterizations of rule-following that are overdetermined by bad philosophical pictures.
Third, the leading inadequate characterization of rule-following is also a version of Solipsistic Semantics — according to which the meaning of a name, sentence, or other linguistic sign is nothing but conscious mental representation or idea in the mind of some individual speaker. Hence the rejection of that particular inadequate characterization is also a crucial part of Wittgenstein‘s critique of Solipsistic Semantics.
That is, the rejection of that particular inadequate conception of rule-following is also a crucial part of The Private Language Argument.
XII.5 Wittgenstein’s Rule-Following Paradox: A Rational Reconstruction
1. The Rule Following Paradox begins with an implicit premise: We assume that the meaning of any linguistic sign is nothing but a rule for operating with that sign in some logical or mathematical calculus, or other non-formal language-system (i.e., Rule-Based Semantics).
2. Therefore, understanding the meaning of any linguistic sign S is being able to follow the rule for operating with S, i.e., being “guided” by the rule for S (PI §§ 172–184).
3. Every rule is expressible as a function-sign which determines a systematic mapping from inputs, or arguments of the function, to outputs, or values of the function (PI §§143- 146, 151, 185).
4. Moreover, the meaning of that function-sign — hence the complete set of its systematic mappings — is understood by grasping the rule in a flash (PI §§186–197).
5. But every function-sign can be multiply differently interpreted, such that although the interpretations yield the same mappings to outputs/values for all existing inputs/arguments, they diverge on some future inputs (PI §185).
6. And since every interpretation is in turn expressible as a higher-order function sign, then each interpretation itself stands in need of further interpretation, which itself in turn can be multiply differently interpreted, ad infinitum (PI §198).
7. So anything the speaker does with S can, on some interpretation or another, be in accordance with the rule (PI §201).
8. Correspondingly, anything the speaker does with S can, on some interpretation or another, be also in conflict with the rule (PI § 201).
9. So the speaker‘s actions, no matter what they are, neither accord with the rule nor conflict with the rule (PI § 201).
10. Therefore, it’s impossible for a speaker to follow a rule.
11. Therefore, it’s impossible for a speaker to understand the meaning of an expression.
12. So Rule-Based Semantics is false, by reductio.
So much for Rule-Based Semantics.
But here’s an important complication for Wittgenstein’s Rule Following Paradox. Even if Rule-Based Semantics is outright rejected by the argument I just spelled out, there’s still a serious leftover problem, precisely because Wittgenstein himself is committed to a version of step 2. in the argument:
understanding the meaning of any linguistic sign S is being able to follow the rule for operating with S, i.e., being “guided” by the rule for S.
This commitment is determined by Wittgenstein‘s antecedent commitment to Thesis 1 and Thesis 2, which, as we saw in section XI.3, followed respectively from the prolegomena on understanding and reading that prefaced “the rule-following considerations.” So The Rule-Following Paradox requires a more adequate and deeper solution.
AGAINST PROFESSIONAL PHILOSOPHY REDUX 516
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