THE FATE OF ANALYSIS, #13–The Tractatus, Logical Space, & Real Space.

By Robert Hanna



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

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

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. 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


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


VI. Wittgenstein and the Tractatus 2: Propositions 2.013–5.55

VI.1 What is Logical Space? What is Real Space?

This space is “logical” precisely because it’s the way that logic manifests itself in the world, namely, as the immanent logical structure of all actual or possible facts.

What supplies the other condition, which, together with logical space, is strictly sufficient for the facts, is the domain of objects.

This other condition is relatively independent of logic, and in that sense it’s simply “given” to the representing subject.

Hence logic is before the “How” (i.e., the actual or possible facts), but not before the “What” (i.e., the substance of the world, the objects or things) (5.552).

Furthermore, one of the three basic logical forms of objects is what, in order to distinguish it from logical space, I’ll call real space (2.0233).

Since one of the other basic forms is color, this implies that real space is manifest or phenomenal space.

This in turn guarantees that all atomic facts are facts about spatiotemporal manifest or phenomenal objects.

Do these two points together imply

either (i) that the objects or things themselves are spatiotemporal manifest or phenomenal objects?,

or (ii) that logical space is identical to real manifest or phenomenal space?

The answer is no in both cases.

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

Empirical reality is limited by the totality of objects (5.5561), but empirical reality is not merely a collection of objects.

In other words, the objects or things necessarily determine all the facts and occur in all the facts, but also, necessarily, subsist at an ontological level that’s below the facts.

It’s crucial to note that this point strongly militates against the Russellian logical atomist and Vienna Circle-style logical empiricist/positivist reading of the Tractatus, according to which the objects or things are sense data or sensory experiences of some sort.

The Tractarian Wittgenstein is a logicistic neo-Kantian, and not a logical atomist or logical empiricist/positivist.

Closely connected with this point is Wittgenstein‘s striking idea that the mere occurrence of a set of objects in a fact, even the mere occurrence of the objects in a certain order, does not in and of itself determine precisely which fact it is: the very same set of objects in the very same order might in fact give rise to two distinct facts, as in the case of The Necker Cube (5.5423).

What’s going on in the case of The Necker Cube is that two distinct orientations of the same perceiving subject are possible, relative to the same spatial figure: the two aspects of The Necker Cube are in fact enantiomorphic or right-handed/left-handed mirror images of one another: so they’re what Kant calls incongruent counterparts.

This is possible only in an orientable space with intrinsic right-hand and left-hand directions.

So the occurrence of the two facts requires not merely the objects or things, and not merely their occurrence in a certain order, but also the non-trivial, fundamental a priori presupposition of a spatial framework of representation that’s contributed by the representing subject or ego.

Kant, of course, made this very point in the Transcendental Aesthetic section of the Critique of Pure Reason.

And in the Tractarian framework, this crucial Kantian point generalizes.

Every actual or possible fact expresses not only the objects or things and relations between them but also the a priori formal representational contributions of a representing subject or ego: therefore, all facts are partially determined by our forms of representation.

The crucial difference is that whereas Kant takes this representational contribution to be purely intuitional, hence non-conceptual, non-logical, and non-propositional in character, Wittgenstein takes it to be purely logical and propositional in character.

So pure logic for Wittgenstein plays essentially the same representational role that Kant’s pure forms of spatial and temporal intuition play in the Transcendental Aesthetic.

Substituting Fregean/Russellian pure logic for pure intuition, in turn, is a classical neo-Kantian move, especially characteristic of early 20th century members of the Marburg School, e.g., Ernst Cassirer.[i]

In this way, for Wittgenstein, whereas the objects or things and their internal qualities are the ontological inputs to the constitution of facts, the facts themselves are the ontological outputs of the objects or things together with the a priori structure of logical space and the logical activities of the representing subject or ego.

Objects or things are “nothing for us,” no matter they might be in themselves, until and just insofar as they occur in such facts.

In this connection, however, it would be a big mistake to think of the contribution of the representing subject or ego to facts as a passive template that could somehow be detached from the representing subject or ego and then separately isolated and analyzed, like “spatial spectacles” (4.0412).

The problem here is one of vicious infinite regress: isolating a spatial template would involve placing it in a still more comprehensive, or larger, space and then spatially comparing it to what was seen through the spectacles.

So the active contribution of the representing subject or ego to the facts cannot itself be represented as a fact: it is a non-trivial, fundamental non-empirical presupposition and therefore immanent in the act of linguistic and propositional factual representation itself.

VI.3 Logical Space is Essentially More Comprehensive than Manifest or Phenomenal Space

Over and above the simple or atomic facts, each of which is modally independent of all the others, are the complex or molecular facts, which are connected by various logical relations, including negation, conjunction, disjunction, conditionalization, etc.

Wittgenstein‘s view is that all of these relations are truth-functional in Frege‘s sense: that is, they express systematic mappings from truth-values to truth-values.

E.g., the conjunction sign ‘and’ (or ‘&’, or whatever) expresses the 2-place truth-function which maps from T and T to T, but otherwise maps to F for all other combinations of T and F.

Some of these mappings always yield truth and thus correspond to logical tautologies (e.g., any proposition of the form “[(P & Q)–>P]”).

Some of these mappings always yield falsity (e.g., any proposition of the form “[P & not-P”]) and thus correspond to logical impossibilities or contradictions.

And some of these mappings are sometimes true and sometimes false (e.g., “[P & Q]”) and thus correspond to contingent propositions (4.46).

Now the scope of logic is essentially more comprehensive than the scope of geometry; correspondingly, logical space is essentially more comprehensive than manifest or phenomenal space.

In manifest or phenomenal space, which is a three-dimensional, egocentrically-centered, orientable space, it’s geometrically or spatially impossible for the right and left hands to coincide, i.e., to be congruent, even despite the fact that they’re one-to-one mirror-reflected counterparts (enantiomorphism).

But Wittgenstein also holds that it’s logically possible for there to be perfect congruence of the right and left hands in a four-dimensional egocentrically-centered space (6.36111).

So what’s geometrically or spatially impossible can still be logically possible.

On this Tractarian picture, physical possibility is even narrower than geometric or spatial possibility, since some possible atomic facts violate the laws of physics.

Only the actual world necessarily obeys the laws of logic, geometry, and physics.



Mr Nemo, W, X, Y, & Z, Saturday 30 May 2020

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