Tractatus Logico-Philosophicus by Ludwig Wittgenstein

Context

The Tractatus Logico-Philosophicus is the only book Ludwig Wittgenstein published in his lifetime. Written during the First World War, in which he served on the Austrian front, and published in 1921 in German (the English translation of 1922 included an introduction by Bertrand Russell), it is a short, numbered sequence of aphorisms that attempts nothing less than the final solution of the problems of philosophy. Its title echoes Spinoza's Tractatus Theologico-Politicus, and its style — seven principal propositions, each with a decimal numbering tree — mirrors the logical structure it propounds. Wittgenstein had studied with Russell at Cambridge, where he absorbed the new logic of Gottlob Frege and Russell himself, and the book is the culmination of that program: logic as the skeleton of language and of the world. Its famous closing line — "whereof one cannot speak, thereof one must be silent" — is the summary of its ethics as much as its logic.

Core Arguments

The Tractatus builds a single vision in seven propositions. The world is everything that is the case (1): the world is the totality of facts, not of things. What is the case is the existence of states of affairs (2): facts are combinations of objects. The logical picture of the facts is the thought (3): we think by picturing facts. A thought is a proposition with a sense (4): language pictures reality; the proposition is a logical picture of what it represents. A proposition is a truth-function of elementary propositions (5): all complex propositions are built by logical operations from elementary ones — the heart of the picture theory of language. The general form of the truth-function is [p, xi, N(xi)] (6): there is one general form of proposition, and hence of the world. Whereof one cannot speak, thereof one must be silent (7): the limits of language are the limits of the world. The argument is that language, at its deepest level, shares a logical form with reality, and that this form — which logic displays and philosophy tries to state — cannot itself be said in language. What can be shown (logical form, the existence of the world, ethics, aesthetics, religion) cannot be said: propositions about the most important things are senseless, and the correct method of philosophy is to show that such pseudo-propositions are senseless.

Key Concepts

• The picture theory: a proposition is a picture of reality; its elements stand for objects, and its structure mirrors the structure of what it represents.
• Saying and showing: what can be said (facts) versus what can only be shown (logical form, the limits of the world) — the doctrine that makes the book's ethics possible.
• Tautology and contradiction: the limits of sense; logic's propositions are not factual but tautologous, showing nothing about the world.
• The ladder: the book's own propositions are nonsense to be climbed and thrown away — "he who understands me finally recognizes them as senseless."
• Logical atomism: the world as composed of simple objects and elementary facts; the view that Russell and the early Wittgenstein shared.
• The limits of language: what lies beyond the sayable — the ethical and the mystical — which the book gestures at by being silent.

Legacy & Influence

The Tractatus reshaped philosophy. The logical positivists of the Vienna Circle read it as the charter of verificationism: A. J. Ayer's Language, Truth, and Logic translated its picture theory into the claim that meaningful statements must be verifiable — an interpretation Wittgenstein rejected, since he held that the book's own sentences were nonsense, not a theory of meaning. It set the agenda for analytic philosophy for a generation, until Wittgenstein himself dismantled its central assumptions in the Philosophical Investigations, replacing the picture of language as representation with language as a family of practices or "language games." The later Wittgenstein did not so much refute the Tractatus as expose what it had hidden: meaning as use. Yet the book's influence on logic, the philosophy of language, and the very idea of philosophy as therapy persists, and its lapidary style has made it one of the few genuinely literary works of philosophy. Its treatment of the limits of language continues to frame debates about science, religion, and ethics: questions of truth and knowledge within the world remain answerable; questions beyond the world remain, in the book's phrase, for silence.

Reading Guide

The Tractatus rewards slow, careful reading despite its brevity — it runs to roughly eighty pages. Read the seven main propositions first (they are numbered 1-7) to grasp the architecture, then work through the tree of numbered sub-propositions, which elaborate each main claim in order. Propositions 1-4 present the picture theory; 5 covers truth-functions and the general form of the proposition; 6 covers logic, science, ethics, and the mystical; 7 is the conclusion. Because the book deliberately says the unsayable, readers should not expect each proposition to yield to paraphrase; the standard companion is G. E. M. Anscombe's An Introduction to Wittgenstein's Tractatus, and the best translation is the bilingual edition by C. K. Ogden or the later one by D. F. Pears and B. F. McGuinness. Read it once for the vision, and again for the details.

Related Works

• Organon by Aristotle — the founding of the logic the Tractatus brings to its culmination
• The Logic of Scientific Discovery by Popper — the contemporaneous attempt to fix the boundary of science, against the positivist reading of the Tractatus
• Against Method by Feyerabend — the later rejection of the picture of science the Tractatus supported
• Enquiry Concerning Human Understanding by Hume — the earlier skeptical account of the limits of knowledge the Tractatus radicalizes
• See what is logic and what is truth for the concepts the book transforms