THE FATE OF ANALYSIS, #36–Wittgenstein’s Rule-Following Paradox.

By Robert Hanna

THE FATE OF ANALYSIS: Analytic Philosophy From Frege to The Ash-Heap of History, And Toward A Philosophy of the Future



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.7 Frege’s Dead End

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

II.13 Has Husserl Begged the Question Against LP? Enter The Logocentric Predicament, and a Husserlian Way Out

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

III.6 Meinong’s World

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.2 The Tractatus in Context

V.3 The Basic Structure of the Tractatus: A Simple Picture

V.4 Tractarian Ontology

V.5 Reconstructing Wittgenstein’s Reasoning

V.6 What Are the Objects or Things?

V.7 The Role of Logic in Tractarian Ontology

V.8 Colorless Objects/Things

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.2 Atomic Facts Necessarily Are in Manifest or Phenomenal Space, But Objects or Things Themselves Necessarily Aren’t in Manifest or Phenomenal 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

VI.9 Propositions Again

VI.10 Language and Thought

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.5 What is Logic?

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.2 Tractarian Solipsism

VIII.3 Tractarian Realism

VIII.4 Is the Tractatus’s Point an Ethical One?

VIII.5 The Meaning of Life

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



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.


XII.4 Wittgenstein’s Rule-Following Paradox: The Basic Rationale

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

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.


Mr Nemo, W, X, Y, & Z, Monday 25 January 2021

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