# THE FATE OF ANALYSIS, #19–Justifying Deduction, & The Return of The Logocentic Predicament.

# By Robert Hanna

# ***

**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

**II. 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.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. Wittgenstein and the Investigations 1: Preface, and §§1–27**

X.1 From the *Tractatus* to the *Investigations*

X.2 The Thesis That Meaning Is Use

X.3 A Map of the *Investigations*

X.4 The Critique of Pure Reference: What the Builders Did

**XI. Wittgenstein and the Investigations 2: §§28–242**

XI.1 The Picture Theory and the Vices of Simplicity

XI.2 Wittgenstein’s Argument Against The Picture Theory: A Rational Reconstruction

XI.3 Understanding and Rule-Following

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

XI.5 Wittgenstein’s Rule-Following Paradox: A Rational Reconstruction

XI.6 Kripkenstein’s Rule-Following Paradox: Why Read Kripke Too?

XI.7 Kripkenstein’s Rule-Following Paradox: A Rational Reconstruction

XI.8 How to Solve The Paradox: Wittgenstein’s Way and Kripkenstein’s Way

XI.8.1 Wittgenstein and The Rule-Following Paradox: A Rational Reconstruction

XI.8.2 Kripkenstein and The Rule-Following Paradox: A Rational Reconstruction

**XII. Wittgenstein and the Investigations 3: §§242–315**

XII.1 What is a Private Language?

XII.2 The Private Language Argument: A Rational Reconstruction

XII.3 Is Wittgenstein a Behaviorist? No.

XII.4 Wittgenstein on Meanings, Sensations, and Human Mindedness: A Rational Reconstruction

**XIII. Wittgenstein and the Investigations 4: §§316–693 & 174e-232e**

XIII.1 Linguistic Phenomenology

XIII.2 Two Kinds of Seeing

XIII.3 Experiencing the Meaning of a Word

XIII.4 The Critique of Logical Analysis, and Logic-As-Grammar

**XIV. Coda: Wittgenstein and Kantianism**

XIV.1 World-Conformity 1: Kant, Transcendental Idealism, and Empirical Realism

XIV.2 World-Conformity 2: Wittgenstein, Transcendental Solipsism, and Pure Realism

XIV.3 World-Conformity 3: To Forms of Life

XIV.4 The Critique of Self-Alienated Philosophy 1: Kant’s Critical Metaphilosophy

XIV.5 The Critique of Self-Alienated Philosophy 2: Wittgensteinian Analysis as Critique

**XV. From Quine to Kripke and Analytic Metaphysics: The Adventures of the Analytic-Synthetic Distinction**

XV.1 Two Urban Legends of Post-Empiricism

XV.2 A Very Brief History of The Analytic-Synthetic Distinction

XV.3 Why the Analytic-Synthetic Distinction *Really *Matters

XV.4 Quine’s Critique of the Analytic-Synthetic Distinction, and a Meta-Critique

XV.5 Three Dogmas of Post-Quineanism

**XVI. Analytic Philosophy and The Ash-Heap of History**

XVI.1 Husserl’s *Crisis* and Our Crisis

XVI.2 Why Hasn’t Post-Classical Analytic Philosophy Produced Any Important Ideas in the Last Thirty-Five Years?

XVI.3 On Irad Kimhi’s *Thinking and Being*, Or, It’s The End Of Analytic Philosophy As We Know It (And I Feel Fine)

XVI.4 Thinking Inside and Outside the Fly-Bottle: The New Poverty of Philosophy and Its Second Copernican Revolution

# ***

**This installment contains sections VII.1 and VII.2.**

**But you can also read or download a .pdf version of the complete book ****HERE****.**

# ***

**VII. Wittgenstein and the ***Tractatus* 3: Propositions 4–5.61

*Tractatus*3: Propositions 4–5.61

**VII.1 The Logocentric Predicament, Version 3.0: Justifying Deduction**

As I mentioned in section II.1 above, one fundamental problem in the philosophy of logic is what Harry M. Sheffer (inventor of the Sheffer stroke function) aptly called “the logocentric predicament”: in order to explain or justify logic, logic must already be presupposed and used, hence logic is inexplicable, unjustifiable, and rationally groundless.[i]

In fact, the logocentric predicament has several interestingly different sub-specific versions, including Lewis Carroll‘s famous “What-the-Tortoise-Said-to-Achilles” syllogistic regress problem,[ii] and W.V.O. Quine‘s argument against the conventionalist theory of logical truth in “Truth by Convention.”[iii]

And there’s also a sub-specific version 3.0, as it were, *the problem of justifying deduction*:

1. Logical deduction can be justified either deductively or non-deductively.

2. A deductive justification of logical deduction is circular.

3. A non-deductive justification of logical deduction (e.g., inductive, intuitive, holistic, pragmatic, etc.) is insufficient.

4. Therefore, logical deduction is inexplicable and unjustifiable, i.e., deduction is rationally groundless.

In his pre-Tractarian 1913 “Notes on Logic,” Wittgenstein saw this problem clearly:

*Deductions only proceed according to the laws of deduction but these laws cannot justify deduction*.[iv]

Indeed, one illuminating way of construing Wittgenstein’s Tractarian theory of the nature of logic is that it’s essentially an extended attempt to solve the problem of justifying deduction, as a crucial sub-species of the fully *general* problem of the logocentric predicament.[v]

**VII.2 The Logical Form of Deduction**

I’ve already looked briefly at one part of Wittgenstein‘s theory of the logical form of propositions: the idea that there are as many ways of generalizing propositions as there are ways of abstracting out names as variables and holding the other propositional elements fixed (3.31–3.317).

The general form of a proposition is the limit case of abstraction in which all names are replaced by variables, and the proposition itself is considered as a single variable (4.5).

A deduction, by contrast to a single proposition in isolation, is a sequence of propositions that are related by “laws of inference,” such that the last proposition in the sequence (the conclusion) is a logical consequence of the other propositions in the sequence (the premises), according to those laws.

Wittgenstein‘s idea is that the conclusion of every such deduction is “internally related” to the complex proposition that’s the true conjunction of all its premises, and thereby “contained” in that complex proposition (5.131).

Another way of putting this, is to say that in deduction the conditions under which all the premises are true will suffice for the truth of the conclusion (5.11, 5.123–5.124).

But the most perspicuous way of putting this is to say that the logical *structure *of the complex proposition that’s the true conjunction of all the premises, guarantees the truth of the conclusion (5.13).

What’s going on here?

Figuring that out involves our getting a handle on Wittgenstein‘s general theory of the logical form of propositions.

This has four basic parts.

**First**, all propositions can be reduced to logical operations on atomic or elementary propositions (5.21–5.3).

**Second**, all logical operations on propositions and also all logical relations between propositions (represented by the logical constants) are exclusively *truth-functional operations* and *truth-functional relations* (4.3–4.45, 5).

**Third**, the truth definition of the universal quantifier is that it’s an extended conjunction of all the atomic propositions generated by replacing the individual variables by individual constants (= the logical product); and the truth definition of the existential quantifier is that it is an extended disjunction of all the atomic propositions generated by replacing the individual variables by individual constants (= the logical sum) (5.521–5.524).

**Fourth** and finally, all truth-functional relations between propositions can be reduced to the single Sheffer stroke function, aka continuous negation:

*(P|Q) ≡ (~P & ~Q) [or alternatively: (~P v ~Q)]*

Now using the classical De Morgan equivalences relating negation, conjunction, and disjunction:

*(P & Q) ≡ (~P v ~ Q)*

*(P v Q) ≡ (~P & ~Q)*

and also the equivalence between the conditional, and negation, disjunction, and conjunction, i.e.,

*(P–>Q) ≡ (~P v Q)*

*(P–>Q) ≡ ~ (P & ~Q)*

It’s easy enough to see informally how every truth-functional relation can be expressed as a function of the Sheffer stroke, e.g.,

*[P|(Q|Q)] ≡ (P–>Q)*

Now this four part theory of logical form entails that every valid deduction can be represented by a truth-table showing that for every assignment of truth-values to the atomic propositions of the premises, their true conjunction will suffice to guarantee the truth of the conclusion.

So Wittgenstein‘s over-arching thesis here is that because logical deductions are fully guaranteed by the internal truth- functional structure of complex propositions, then “laws of inference” are in fact unnecessary, and deduction is thereby *internally justified* *a priori* (5.132–5.133).

This in turn provides a uniquely Tractarian solution to sub-specific version 3.0 of the logocentric predicament, i.e., the problem of justifying deduction.

For Wittgenstein, the justification of deduction is *self- intimating *or *self-manifesting* — in effect, logically supervenient — on the truth-functional connections underlying the deductive structure of the valid argument.

The error in the original problem of justifying deduction was the implicit assumption that the justification had to be logically *said*: on the contrary, it’s logically *shown*.

**NOTES**

[i] H.M. Sheffer, “Review of Principia Mathematica, Volume I, second edition,” *Isis *8, (1926): 226–231, at p. 228.

[ii] L. Carroll, “What the Tortoise Said to Achilles,” *Mind* 4 (1895): 278–280.

[iii] W.V.O. Quine, “Truth by Convention,” in W.V.O. Quine, *The Ways of Paradox*, 2nd edn., Cambridge, MA: MIT Press, 1976), pp. 77–106

[iv] L. Wittgenstein, “Notes on Logic,” in L. Wittgenstein, *Notebooks 1914–1916*, trans. G.E.M. Anscombe (2nd edn., Chicago, IL: Univ. of Chicago Press, 1979), Appendix I, pp. 93–107, at p. 93.

[v] See also R. Hanna, *Rationality and Logic* (Cambridge, MA: MIT Press, 2006), ch. 3, also available online in preview, **HERE**.

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