Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. Originally published in German in 1921 as Logisch-Philosophische Abhandlung, when its author was just 32, it is now widely considered one of the most important philosophical works of the twentieth century. The Latin title was originally suggested by G. E. Moore, and is a homage to Tractatus Theologico-Politicus by Benedictus Spinoza. There are seven "main" propositions.
The slim volume (less than eighty pages) sets forth a complete philosophical system that may be construed as the completion of Bertrand Russell's early philosophy of "logical atomism." The book comprises a system of short, vatic utterances, numbered 1, 1.1, 1.11, 1.12, etc., so that 1.1 is a comment on or elaboration of 1, 1.11 and 1.12 comment on 1.1, and so forth, to demonstrate their nested interrelations.
There are seven main propositions:
- The world is everything that is the case.
- What is the case (a fact) is the existence of atomic states of affairs.
- A logical picture of facts is a thought.
- A thought is a proposition with sense.
- A proposition is a truth-function of elementary propositions.
- The general form of a proposition is the general form of a truth function, which is [p, ξ, N(ξ)]. This is the general form of a proposition.
- What we cannot speak of we must pass over in silence.
The world, as Wittgenstein uses it, is not a group of things, but of facts about those things(1.1). The world is explained as the totality of existing states of affairs (2.04). These states of affairs are like linked chains of objects, objects being the substance of the world.
Propositions are explained as being a picture of reality; that shares the same logical structure as reality. This is his picture theory of language. A state of affairs is thinkable, and so these pictures are thinkable. A proposition is an expression of such a thought. The proposition is congruent with the thought, which is congruent with the state of affairs. Language is the expression of these thoughts. Propositions have meaning only in so far as they agree or disagree with states of affairs. In effect language must therefore be congruent with those states of affairs. Complex propositions can be understood only by analysing them into elementary propositions.
The appropriate way to analyse complex propositions is to treat them as the logical functions of elementary propositions. So one can analyse any proposition into the concatenation of elementary propositions and logical operators. This approach links the work to Russell’s "Logical Atomism". Furthermore, logic in effect delineates the extent of language, and hence of thought and of understanding.
Under 4. and 5. and their subsidiaries, Wittgenstein uses "truth tables," which are now the standard method of explaining semantics for sentential logic (such as proposition 5.101), and gives a rigorous if rather opaque account of formal logic generally, covering notation, Russell's paradox, and the notions of tautology and contradiction, and truth-functions. He moves increasingly into questions of language, connections with science, belief, and induction, giving a rather austere view of all these things. ("Superstition is just belief in the causal nexus.")
In 6. he moves on to more philosophical reflections on logic, which connect to ideas of knowledge, thought, and the "a priori" and "transcendental." The final pages suggest logic and language can supply no meaning, and that since they perfectly reflect the world, neither can it. Ethics and aesthetics can say nothing. He begins talking of the will, life and death, and veers rather deliberately into strangely mystical remarks ("If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present," "The riddle does not exist") all the while increasingly hinting that his own project of trying to explain language is impossible for exactly these reasons. He compares the book to a ladder that must be thrown away after one has climbed it, then the book ends with 7: "What we cannot speak of we must pass over in silence."
Logical propositions are tautologies, and tell us nothing. Scientific principles, such as causality and conservation laws, are not really propositions but forms which propositions might take. As such, they do not take part in scientific explanation, but provide a way in which to group similar scientific propositions.
Since all propositions share a similar form, they are of equal value. Hence there can be no ethical propositions, and the study of ethics is void.
Metaphysical propositions are similarly senseless. Wittgenstein finishes with the famous aphorism What we cannot speak of we must pass over in silence. As the last line in the book, proposition 7 has no supplementary propositions.
Reception and Influence of the Work
Wittgenstein himself concluded that with the Tractatus he had resolved all philosophical problems, and upon its publication he retired to become a schoolteacher in Austria.
Meanwhile the book was translated into English by C. K. Ogden with help from the Cambridge mathematician and philosopher Frank Ramsey, then still in his teens. Ramsey later visited Wittgenstein in Austria. The Tractatus also caught the attention of the philosophers of the Vienna Circle, especially Rudolf Carnap and Moritz Schlick. The group spent many months working through the text out loud, line-by line. Schlick eventually convinced Wittgenstein to meet with members of the circle to discuss the Tractatus when he returned to Vienna (he was then working as an architect).
Wittgenstein would not meet the circle proper, but only a few of its members, including Schlick, Carnap, and Waissman. Often, though, he refused to discuss philosophy, and would insist on giving the meetings over to reciting poetry with his chair turned to the wall. He largely broke off formal relations even with these members of the circle after coming to believe Carnap had used some of his ideas without permission.
Nonetheless, it was conversations with Schlick during this period that were largely responsible for drawing Wittgenstein back to philosophy. He began to doubt both the ideas and methods of the Tractatus, and in 1929 returned to Cambridge. He worked extensively but published nothing for the next twenty years. Shortly after his death in 1951 his second magnum opus, Philosophical Investigations was edited and published by his executors. Much of it is given over to critiquing the ideas of the Tractatus.
English online versions: