Tractatus Logico-Philosophicus

The Tractatus Logico-Philosophicus is a work of analytic philosophy by Ludwig Wittgenstein, composed as a series of numbered propositions organized in a strict hierarchical system. The book attempts to identify the logical structure that language must share with reality in order to represent it and to draw a firm boundary between what can be said and what can only be shown or must be passed over in silence.

In his Preface, Wittgenstein states that the book addresses the problems of philosophy and contends that these problems arise from a misunderstanding of the logic of language. He summarizes the work's central thesis: "What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent" (27). The book aims to draw a limit not to thinking itself but to the expression of thoughts in language. Wittgenstein acknowledges debts to the logician Gottlob Frege and the philosopher and mathematician Bertrand Russell, and expresses confidence that the problems of philosophy have been finally solved in essentials, while noting how little this accomplishment amounts to.

Russell's Introduction provides context for the work's central concerns. He identifies Wittgenstein's core question as a logical one: What relation must one fact, such as a sentence, have to another in order to serve as a symbol for it? Russell highlights what he calls the work's most fundamental thesis: Something must be in common between the structure of a sentence and the structure of the fact it asserts, and this shared structure cannot be stated in language but can only be shown. Russell also notes, with some reservation, that Wittgenstein "manages to say a good deal about what cannot be said" (xxiv).

The work opens with the foundational claim that the world is everything that is the case: the totality of facts, not of things. Wittgenstein defines a fact as the existence of atomic facts, which are combinations of objects, or simple entities. Objects form the substance of the world and cannot be compound; their forms include space, time, and color. The structure of an atomic fact is the determinate way its objects are combined; the form is the possibility of that structure. Atomic facts are independent of one another: From the existence or non-existence of one, nothing can be inferred about another. The total reality, comprising the existence and non-existence of all atomic facts, constitutes the world.

Wittgenstein then introduces what is known as the picture theory of representation. Human beings make pictures of facts. A picture is a model of reality: its elements correspond to objects, and the way those elements are combined represents the way things are combined in reality. What the picture must share with reality in order to represent it is its form of representation. A picture cannot depict its own form of representation; it can only show it. What every picture must share with reality is the logical form, the form of reality itself. What the picture represents is its sense; the agreement or disagreement of that sense with reality constitutes its truth or falsity. No picture is true a priori, meaning independently of experience; truth requires comparison with reality.

The logical picture of the facts is a thought. In a proposition, a thought is expressed perceptibly through the senses. The propositional sign stands in a projective relation to the world, meaning its elements map onto possible arrangements in reality. Simple signs in propositions are called names. A name means its object; names can only name, not assert. A proposition can say how a thing is, but not what it is.

Wittgenstein observes that everyday language breeds philosophical confusion because the same word often signifies in different ways. To avoid such errors, one must use a symbolism that obeys the rules of logical grammar. He articulates the principle behind Occam's razor, the principle of parsimony: If a sign is not necessary, it is meaningless. He critiques Russell's Theory of Types, a system designed to avoid logical paradoxes, arguing that no proposition can say anything about itself because the propositional sign cannot contain itself.

The totality of propositions is language. Colloquial language disguises thought, and most propositions written about philosophical matters are not false but senseless, arising from a failure to understand the logic of language. Propositions are pictures of reality, as Wittgenstein illustrates through the analogy of the gramophone record, the musical score, and sound waves: all share a structural correspondence that allows each to represent the others. Philosophy is not a theory but an activity whose result is the logical clarification of thoughts. Philosophy limits the thinkable from within and means the unspeakable by clearly displaying the speakable.

Propositions can represent reality, but they cannot represent the logical form they share with reality. To represent logical form, one would have to stand outside logic, outside the world. What can be shown cannot be said. Wittgenstein distinguishes formal concepts such as "object," "number," and "fact" from ordinary concepts. Expressions like "there are objects" are senseless because they treat formal concepts as if they were proper concepts.

Elementary propositions, the simplest kind, assert the existence of atomic facts and consist of names in immediate combination. They are logically independent of one another. The truth-possibilities of elementary propositions are presented through truth-table schemata, or tables listing every combination of truth and falsehood and the resulting truth-values. Two extreme cases exist: tautology, which is true for all possibilities and says nothing, and contradiction, which is false for all. All propositions are truth-functions of elementary propositions, meaning their truth or falsehood depends solely on the truth or falsehood of their constituent elementary propositions. Wittgenstein introduces the operation N(ξ̄), the simultaneous negation of all propositions in a given set, as the single fundamental operation from which every truth-function can be constructed.

On inference and causality, Wittgenstein argues that all inference takes place a priori. There is no causal nexus justifying inference from one state of affairs to another. The events of the future cannot be inferred from those of the present.

The limits of one's language mean the limits of one's world. This provides a key to solipsism, the view that only one's own mind is certain to exist: What solipsism means is correct, but it cannot be said, only shown. The thinking subject does not exist as a thing in the world but is a limit of the world. Solipsism, strictly carried out, coincides with realism, since the self shrinks to an extensionless point and only the world remains.

The propositions of logic are tautologies and say nothing; logic is transcendental, meaning it concerns the conditions and limits of language rather than describable facts. Mathematics is a logical method; its propositions are equations and pseudo-propositions, apparent propositions that assert nothing. Scientific principles such as causation and continuity are not descriptions of facts but non-empirical constraints on the possible form of scientific propositions. At the basis of the modern worldview lies the illusion that laws of nature explain natural phenomena.

The world is independent of one's will. All propositions are of equal value. The sense of the world must lie outside the world; within it, everything simply is as it is. Ethics cannot be expressed in propositions; it is transcendental. Ethics and aesthetics are one. Death is not an event of life. Not how the world is, but that it is, is the mystical. The feeling of the world as a limited whole is the mystical feeling.

Even if all scientific questions were answered, the problems of life would remain untouched. The right method of philosophy is to say nothing except propositions of natural science and to demonstrate to anyone attempting metaphysical claims that certain signs in their propositions have no meaning. Wittgenstein acknowledges the self-undermining character of the work: His own propositions are elucidations that the reader must ultimately recognize as senseless. "He must so to speak throw away the ladder, after he has climbed up on it" (108). The work concludes with its final proposition: "Whereof one cannot speak, thereof one must be silent" (108).