The Tractatus consists of a series of terse propositions numbered in a decimal form from 1 to 7. It divides roughly into three parts: propositions 1 to 2.063 deal with the nature of the world; 2.1 to 4.128 deal with the nature of language; and 4.2 to 7 deal with the nature of logic and its implications for mathematics, science, philosophy, and the meaning of life.
Proposition 1.1 announces, “The world is the totality of facts and not things.” A complete description of the world is not a list of all the objects in the world but a list of all the facts that are true of the world. In other words, facts are metaphysically prior to objects: an object only has being insofar as it is a constituent of a fact. Facts can be logically analyzed into constituent parts. Fundamental, atomic facts that cannot be further analyzed are called states of affairs, and they are all logically independent of one another. Any given state of affairs can be true or false regardless of the truth or falsity of any other state of affairs. Objects link together to form facts by virtue of their logical form, much as pieces of a jigsaw puzzle link together by virtue of their shape.
Language depicts reality by virtue of sharing a logical form in common with reality. We know that a picture of a sunset represents a sunset because both the picture and the sunset share a similar “pictorial form.” Similarly, a proposition and what it represents share a similar “logical form”: a proposition depicts a fact, and just as a fact can be analyzed into independent states of affairs, a proposition can be analyzed into independent elementary propositions.
Wittgenstein draws an important distinction between saying and showing: while a proposition says that such-and-such fact is the case, it shows the logical form by virtue of which this fact is the case. The upshot of this distinction is that we can only say things about facts in the world; logical form cannot be spoken about, only shown. Because logical form shows itself and cannot be spoken about, there is no need for the so-called logical objects, the connecting glue between different propositions that plays a central role in the logic of Frege and Russell. Wittgenstein asserts that most philosophical confusion arises from trying to speak about things that can only be shown.
At proposition 4.31, Wittgenstein introduces his method of truth tables, which show how logical form makes itself apparent without the need for logical relations or objects. One consequence of this view is that all the propositions of logic are tautologies—they are the set of propositions that are true no matter what. As such, they tell us nothing about the world, and they are all equivalent.
The foregoing reflections on the nature of the world, language, and logic lead Wittgenstein to address a series of long-standing philosophical problems. He suggests that solipsism, the belief that we have no knowledge of a world outside of our own minds, is technically valid but that there is no distinction between solipsism and realism that can properly be expressed in language. He claims that mathematics can be derived from the successive application of logical operations and that the laws of science are neither logical laws nor empirical observations but rather an interpretive method. Because language can speak about only facts in the world, we can say nothing about the world as a whole (metaphysics) or about the value of things in the world (ethics and aesthetics).
Philosophy has no propositions. Properly speaking, philosophy is the activity of clarifying language, and the correct method in philosophy is to remain silent and only to speak up to correct people who misuse language. Since Wittgenstein has already asserted that only propositions that depict facts in the world have meaning, he concludes that all the propositions in the Tractatus are meaningless. They are like a ladder that one can cast away once one has climbed up it. He concludes with the mystical reflection, “What we cannot speak about we must pass over in silence.”
The Tractatus opposes Frege and Russell’s universalist conception of logic. In the universalist view, logic is the supremely general set of laws, the foundation on which the edifice of knowledge is built. Wittgenstein, by contrast, argues that logic is not a set of laws at all. Logic is not distinct from the sciences simply by virtue of being more general but by virtue of being something entirely different altogether from the sciences. According to Wittgenstein, logic has no laws, and there are no logical objects or relations. The assumption that there must be laws, objects, and relations is a holdover from the assumption that logic is like the sciences, only more general. Laws, objects, and relations are the content of a body of knowledge, and according to Wittgenstein, logic is all form and no content. If the universalist conception sees logic as the foundation on which the edifice of knowledge is built, Wittgenstein sees logic as the metallic framework around which the edifice is structured. Logic itself says nothing, but it determines the form and structure of everything that can be spoken about.
Relying on the say–show distinction, the Tractatus draws strict limits to what can be said intelligibly. Wittgenstein limits the sayable to empirical propositions: language is suited to describing facts in the world. By contrast, we cannot say anything that speaks about the world as a whole, that speaks about value, or that purports to speak from a perspective outside the world. Consequently, metaphysics, ethics, aesthetics, and most of philosophy goes out the window. Wittgenstein does not claim that these things are useless, simply that language is unsuited to dealing with them. For instance, the attitude we hold toward the world and the way we go about living expresses our ethical worldview. Wittgenstein criticizes the notion that this worldview can be put into words in the form of ethical maxims or laws and still remain meaningful. For him, our ethical worldview can only be shown and cannot be said. In asserting that most of what we consider philosophy lies beyond the limits of what can be said, Wittgenstein reconceives the role of philosophy. Philosophy should stand as a watchdog at the limits of what can be said and correct those who try to say the unsayable.
The final few self-refuting propositions of the Tractatus are the subject of great scholarly controversy. What should we make of Wittgenstein’s claim that all the propositions in the Tractatus are nonsense? One school of thought takes the Tractatus to be the last word in nonsense, so to speak. According to this interpretation, the propositions of the Tractatus are nonsense, strictly speaking, but it is only by understanding them that we can recognize that they are nonsense. Although they are nonsense, the propositions of the Tractatus point to deeper truths, and once we have recognized these deeper truths we can reject the Tractatus along with all the other nonsense that makes up philosophy. An alternative school of thought rejects this previous interpretation as being too soft. If the propositions of the Tractatus are nonsense, then they are nonsense, and that is all there is to it. The important thing, according to this second interpretation, is to grasp the frame of mind that would think that these propositions make sense and, by grasping it, to recognize the inconsistency of this frame of mind. According to this view, the propositions of the Tractatus do not point to deeper truths. There are no deeper truths, and we can only appreciate this once we have grasped that the propositions of the Tractatus are nonsense.