Wittgenstein’s Tractatus is made up of short sections that I will refer to as “remarks.” The key remarks for our purposes are numbered n, n.m, or n.0m. It has been suggested, for the remarks with such numbers, that n.1, n.2, etc. lead up to n+1 while n.01, n.02, etc. fall under n as further elaborations. Most, but not all, remarks with such numbers are included on the handout. A few other remarks are included when they provide especially good examples of some of the ideas in the work.
• For our purposes, the key idea in the remarks before 4.1 is what is known as the “picture theory of meaning” (see, for example, 2.1 and the remarks following it). It is an alternative to the account of meaning you’ve seen in Russell according to which the propositions we can understand must be analyzable into “constituents” with which we are acquainted. Wittgenstein’s “objects” play a role analogous to Russell’s “constituents” with the important difference that an “object” in this sense brings with it all the possibilities of combining it with other objects to form a state of affairs. (Russell said, on the contrary, that we can be acquainted with a constituent without knowing anything about its relations.) The range of possible combinations of objects is one of the things Wittgenstein has in mind when he speaks of “logical space.”
• From 4.1 on, Wittgenstein can be understood to develop an alternative to an account of a priori knowledge offered by Russell. According to Russell, a priori knowledge was substantive knowledge of facts about universals (i.e., properties and relations). Remarks 4.46, 6.1, and 6.3 present the basic statement of Wittgenstein’s view, but his characterization of Newtonian mechanics as a conventional framework for describing nature (6.341 and 6.35) provides a more concrete way into the idea. Another way Wittgenstein uses to make his point that a priori truths have no content is the idea that they say nothing although they may show the structure of a language (see, for example, 6.12 and 6.13). Finally, notice the conception of philosophy sketched in the last few remarks and think how it is related to this conception of the a priori.
Some of Wittgenstein’s symbolic notation appears on the handout. He uses the tilde (~) for the negation or denial, so if p is It’s raining then ‘~ p’ is It’s not raining. The letter ‘N’ indicates the denial of each of the collection of propositions to which it is applied. A bar is used for a collection of values of a variable, so ‘p’ in 6 stands for a collection of propositions; and N(ξ) is a proposition denying each of the propositions in ξ. Finally, the bracket notation ‘[-, -, -]’ indicates a result of beginning with the values indicated by the first item and repeatedly applying the operation indicated by transition from the second to the third, so ‘[0, ξ, ξ+1]’ indicates any result of beginning with 0 and repeatedly adding 1, and ‘[p, ξ, N(ξ)]’ stands for any proposition constructed from the propositions p using the operation N.