Tractatus Logico-Philosophicus

The Tractatus Logico-Philosophicus is the only philosophical book Ludwig Wittgenstein published in his lifetime, and one of the most influential and enigmatic works of twentieth-century philosophy. Written largely during the First World War, while Wittgenstein served as a soldier in the Austro-Hungarian army, and completed in an Italian prisoner-of-war camp, it was published in German in 1921 and in English, with the Latin title suggested by G. E. Moore in homage to Spinoza‘s Tractatus Theologico-Politicus, in 1922. In fewer than eighty pages of numbered remarks it offers a theory of the world, of language and of logic, and claims to show the limits of what can be said — beyond which lie ethics, aesthetics, God, the meaning of life and philosophy itself. Its preface announces that “the truth of the thoughts communicated here is unassailable and definitive”, and that the problems of philosophy have “in essentials” been solved — adding: “it shows how little has been achieved when these problems have been solved”.

At a glance

The argument

The book’s seven main propositions are:

1. The world is all that is the case.
2. What is the case — a fact — is the existence of states of affairs.
3. A logical picture of facts is a thought.
4. A thought is a proposition with a sense.
5. A proposition is a truth-function of elementary propositions.
6. The general form of a truth-function is [p̄, ξ̄, N(ξ̄)]. This is the general form of a proposition.
7. Whereof one cannot speak, thereof one must be silent.

The world. The book begins with ontology. “The world is the totality of facts, not of things” (1.1): not a collection of objects, but of objects standing in configurations. The simplest facts — atomic states of affairs — consist of simple objects combined in determinate ways; objects are “the substance of the world”, unchanging, while their configurations change. Atomic facts are independent of one another: from the existence or non-existence of one, nothing follows about another.

The picture theory. Wittgenstein said the idea came to him on reading of a Paris court case in which a car accident was represented with model cars and dolls. “We picture facts to ourselves” (2.1). A picture is a model of reality: its elements stand for objects, and the way its elements are arranged represents the way the objects are arranged. A picture can represent any reality whose form it has; what it shares with reality — its logical form — it cannot itself depict, but only display. A thought is a logical picture of facts; a proposition is a thought made perceptible in signs. A proposition has sense because it pictures a possible state of affairs; it is true if the state of affairs exists, false if it does not. Ordinary language disguises thought — “it is not humanly possible to gather immediately from it what the logic of language is” (4.002) — and philosophy’s task is the logical clarification of thoughts: “philosophy is not a body of doctrine but an activity” (4.112).

Logic. All complex propositions are truth-functions of elementary propositions: their truth depends only on the truth or falsity of their parts, as set out in truth tables, which the Tractatus helped make famous. Some propositions are true however the facts are — tautologies, like “either it is raining or it is not raining” — and some are false whatever happens: contradictions. These “say nothing”; they are senseless (sinnlos), though not nonsense. The propositions of logic are tautologies; they show the logical structure of language and the world, but do not describe any fact. “My fundamental idea is that the ‘logical constants’ are not representatives” (4.0312): “and”, “not” and “or” name nothing. Mathematics, likewise, consists of equations, which are “pseudo-propositions”. The laws of science are not truths about necessity in the world but a network for describing it; “the belief in the causal nexus is superstition” (5.1361).

The self. “The limits of my language mean the limits of my world” (5.6). The subject that thinks is not a thing in the world; “the subject does not belong to the world: rather, it is a limit of the world” (5.632) — as the eye is not part of its own visual field. Solipsism, rightly understood, “coincides with pure realism”.

The mystical. In the final pages, the book turns to what cannot be said. “The sense of the world must lie outside the world. In the world everything is as it is, and everything happens as it does happen: in it no value exists” (6.41). Ethics cannot be put into words; “ethics and aesthetics are one” (6.421). Death is not an event in life: “we do not live to experience death… Our life has no end in just the way in which our visual field has no limits” (6.4311). “Not how the world is, is the mystical, but that it is” (6.44). “We feel that even when all possible scientific questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer” (6.52). “The solution of the problem of life is seen in the vanishing of the problem” — which is why those who have found the sense of life after long doubt have been unable to say what it consisted in (6.521). “There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical” (6.522).

The ladder. Then comes the book’s most startling move. The correct method in philosophy would be to say nothing except what can be said — the propositions of natural science — and to show anyone who wanted to say something metaphysical that he had failed to give a meaning to some of his signs. “My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright” (6.54). And then: “Whereof one cannot speak, thereof one must be silent” (7).

Interpretation

What the book means by its own nonsense has divided readers. The Vienna Circle took it as a positivist manifesto: only the propositions of science have sense; metaphysics is meaningless. But Wittgenstein wrote to the publisher Ludwig von Ficker that the book’s point was ethical, and that it consisted of two parts: the one written, and “all that I have not written. And it is precisely this second part that is the important one.” On the traditional, “ineffability” reading, the book gestures at truths that cannot be stated but can be shown. On the “resolute” reading of Cora Diamond and James Conant, the book’s propositions are plain nonsense, and its aim is to free us from the illusion that there is anything to be shown at all.

Reception

The book appeared thanks to Russell, whose introduction Wittgenstein disliked. Frank Ramsey, aged nineteen, helped translate it and travelled to Austria to discuss it with its author, then a village schoolteacher. The Vienna Circle studied it for two years; it became the founding text of logical positivism. In 1929 Wittgenstein submitted it at Cambridge as his doctoral thesis, examined by Russell and Moore. By then he had begun to criticise it, and his later work, the Philosophical Investigations, attacked its central ideas — the picture theory, logical atomism, the single essence of language.

In conversation

• “Whereof one cannot speak, thereof one must be silent” — the limit of sense.
• The ladder — propositions to be climbed and thrown away.
• “Not how the world is, but that it is” — the mystical.