These sections begin what is often referred to as the “private language argument,” and it is not hard to cast the material in this section as an argument against the idea of a private language. But it would run counter to Wittgenstein’s view of philosophy to attempt to prove the impossibility of a private language since that would be a philosophical thesis that isn’t immediately obvious. It would be consistent with his view of philosophy for him to bring us to see that we can’t make sense of the idea, however much we feel inclined to, so you might try thinking of these sections in that light.

• §§243-245. The connection between words and sensations. Wittgenstein’s view of language seems to preclude a language that is private in the sense that, in principle, only one person could use it. As an example of such a language, think of Russell’s idea of names of sense data; Wittgenstein seems to have something like this in mind in §243. Thinking of Russell’s account of the results of analysis, we might be led to suppose such a language must lie behind our normal talk about sensations, and much that Wittgenstein does will be devoted to dispelling that picture. His basic approach is laid out quickly. In §244, he points to a different model of the connection of talk about sensations to those sensations; and, in §245, he hints at later points where he rejects the assumption that some sort of identification or description must lie behind expressions of pain and other sensations.

• §§246-255. Privacy as grammatical. The privacy of sensation is a grammatical feature of our talk of sensations: it doesn’t make sense to say that one is in doubt about one’s own sensations, but it can make sense to say that others are in doubt (§246-248). Notice Wittgenstein’s insistence that doubt does not always make sense (§§249-250). And notice also that Wittgenstein is inclined to say that, where it doesn’t make sense to speak of doubt, it doesn’t make sense to speak of knowledge either. §§251-252 provide further examples of the same attitude. In §253, another expression of privacy is also presented as grammatical: in the sense in which sensations are private, it doesn’t make sense to say that two people have (or don’t have) the same one.

• §§256-269. Inward understanding. These sections are the heart of Wittgenstein’s consideration of the idea of private language. First of all, the words of such a language could not be tied up with the natural expression of sensations (§256). And if we suppose that a tie between a word and a sensation is simply stipulated, this stipulation raises problems. First of all, it leaves no room for the sort of stage-setting that is needed to give naming its sense (§257—recall §§26-32). Also, it provides no way to give sense to talk of correctness (§258—recall §§202 and 240-242). Indeed, it is hard to see how public terms like “sensation,” “has,” and “something” could be applied (§261). Most of the rest of the sections through §268 develop one or another of these concerns. We are intended to be left feeling that we are walking on ice when we try to apply the concept of a private language. Finally §269 provides a kind of use where the concept does take bite (but is no longer the sort of philosophical “super-concept” we began with).

• §§270-280. The inner object drops out. If we imagine a genuine use for a sign that we might take to denote a private sensation, the correct identification of the sensation becomes irrelevant so long as our use of the sign is in accord with public criteria (§270). If we took the identity of the sensation to be significant, we would pretend to give meaning to a question that is in principle unanswerable (§272). The sections §§277-279 could be understood as an attempt to explain our readiness to speak of private languages; Wittgenstein traces a wish to distinguish between public and private senses of terms to the differences in our experiences when we attempt to contemplate such senses, a diagnosis that is analogous to those in §§38 and 173. In §280, he applies the considerations of the preceding sections to reject the idea of private information, an issue that will turn up again in §§288ff.