Logical Atomism
This is the view that the world can be analyzed into fundamentally simple, unanalyzable, indivisible, and mutually independent objects or facts. Wittgenstein inherited this position from Russell, and it is a feature of logical analysis. If we can analyze a proposition into simpler parts, and analyze those parts into even simpler parts, where does this analysis end? Either it would have to go on forever, which is problematic for a number of reasons, or it would have to reach a definite terminus. Wittgenstein draws this terminus at objects, which are logical form without content, and states of affairs, which are simple, mutually independent facts that constitute all of reality.
The logical atomism of the Tractatus is one of its shakiest elements: Wittgenstein provides very little argument in its favor, but simply assumes the world must consist of such atomic elements. This was one of the first aspects of the Tractatus that Wittgenstein abandoned upon his return to philosophy in 1929, and it was by pulling on this thread that he gradually dismantled the entire work.
Logical Form
According to Wittgenstein, logic is not a body of propositions, nor is it an axiomatic system. Logic represents the architectural structure of reality. Logic in itself does not say anything, nor does it tell us anything about the world. Rather, it determines the form taken by things in this world. Propositions can represent facts, and thoughts can represent propositions, because they all share a common logical form. The salient point of Wittgenstein's conception of logic as consisting of form rather than content is that logic itself cannot be explained. We do not need laws or propositions to tell us how logic works because the workings of logic make themselves manifest in everything we say and experience.
Say/show Distinction
Throughout the Tractatus, Wittgenstein draws a sharp line between things that can be said and things that can be shown. Anything that can be said can be expressed as a proposition with a sense, and propositions with sense concern only facts about things in the world. Anything that does not concern facts about the world cannot be said, but can at best be shown. Among the many things that we cannot say are propositions concerning ethics, aesthetics, the meaning of life, the immortality of the soul, the nature of language, the nature of logic, the nature of mathematics, and the fundamental structure of the world. Many of these things show themselves in the ways we can and cannot talk about the world, and the ways in which our discourse is structured. The distinction between saying and showing effectively sweeps away what had hitherto been thought of as philosophy. What philosophers try to say, Wittgenstein argues, cannot be said, and is therefore nonsense.
Criticism of Frege and Russell
The Tractatus is largely a response to the logical philosophy of Frege and Russell. While Wittgenstein attacks these philosophers on a number of points, we can draw out several major themes. Foremost is their assumption that logic consists of propositions that are deduced from fundamental, self-evident axioms. Wittgenstein objects, first, to the idea that logic should be hierarchical, and some truths be more fundamental than others; and second, to the idea that the certainty of logic should ultimately rest on nothing more than self-evidence. He also criticizes their failure to distinguish between what he calls formal concepts, and concepts proper. That is, they treat "x is a horse" and "x is a number" as being concepts of the same form. His "fundamental idea" (4.0312) also contains a criticism of Frege and Russell: logical objects that are used to define the logical structure of a proposition cannot themselves be representative of any kind of object. The elements of a proposition should hold together on their own strength, and not on the strength of these so-called logical "objects."
Wittgenstein's difference from Frege and Russell is well expressed in a letter he wrote to Russell in 1912, asserting: "Logic must turn out to be a totally different kind than any other science." While Frege and Russell had tried to develop logic as a supremely general body of propositions, Wittgenstein insisted that logic cannot be considered a body of propositions, or of knowledge at all.
The Role of Philosophy
The Tractatus can be read as fundamentally concerned with the question of what philosophy is and what it is meant to do. Wittgenstein criticizes attempts to voice metaphysical and ethical ideas as being misguided attempts to say the unsayable. Philosophy is not a body of knowledge analogous to other sciences. We cannot talk about metaphysics and ethics as being "branches of philosophy" in the same way that we can talk about dynamics and electro-magnetism as being "branches of physics." While dynamics and electro-magnetism deal only with a specific aspect of reality, the concerns of philosophy touch on all aspects of life. We cannot talk about life as a limited whole, so we cannot voice the concerns of philosophy. Rather, Wittgenstein argues, we should view philosophy as a kind of clarifying activity. Since philosophy cannot step outside the boundaries of language, it should act as a watchdog at those boundaries, clarifying vague propositions and showing those who try to make philosophical claims that they have in fact spoken nothing but nonsense.
The Tractatus as Nonsense
In the penultimate proposition of the Tractatus, Wittgenstein tells us that if we have understood him, we will understand that the propositions of the Tractatus are nonsense. We will view them as a ladder that, having climbed, we can now safely throw away. These remarks have generated a great deal of controversy as to how they are to be interpreted. Effectively, Wittgenstein is asking us to reconsider everything that we have just read. We can no longer straightforwardly accept take the world is all that is the case or that the world is the totality of facts, not of things. We now have to see these claims as subversive pieces of nonsense, leading us toward a proper understanding of logic, language, and the world.
Ethics
Wittgenstein scarcely mentions ethics in the Tractatus, and he does so only in telling us that ethics cannot be put into words. On the other hand, in a letter to his publisher, he wrote that "the book's point is ethical." It is important to understand that Wittgenstein remains silent about ethics, not because he sees ethics as unnecessary, but because he feels any talk about it can only cheapen it. Ethics, according to the Tractatus, is not a body of knowledge, nor is it a set of maxims that we can live by. Ethics represents a general outlook on life, and because we can make no general claims about the nature of the world, we can say nothing about ethics. Ethics, in effect, makes itself manifest in the way that we deal with the world. In this sense, we could say, our ethical outlook defines the world we inhabit. Thus, for Wittgenstein, ethics is of supreme importance, but for precisely this reason, it cannot be put into words.
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