The target is a philosopher's fantasy: a language in which the speaker writes "S" in a diary each time a certain sensation occurs, with the intention to use "S" in future to denote that same sensation. The sensation is private — no one else can experience it. The name's correctness can be checked only by consulting one's own memory of what "S" was meant to name. Wittgenstein's question: is there any genuine criterion of correctness here, or only the appearance of one?
If I decide that "S" names this sensation, and tomorrow I use "S" again, I verify my use by remembering: "Yes, that was the sensation I called S." But the memory itself cannot be verified against anything external. Whatever seems right will count as right. And that means that we cannot really speak of what is right — only of what seems right to me. The distinction between correct use and incorrect use, which any genuine language requires, has collapsed. I haven't defined a term; I've only performed a gesture in the dark.
A rule, for Wittgenstein, is not a mental object or a hidden fact. A rule is manifest in practice — in what we are trained to do, in how we correct one another, in the shared reactions that give "same" and "different" their meaning. Language is a social institution: the norms of correct use are grounded in shared practice, not in a private mental act of ostensive definition. The private linguist has no practice, no training, no correction — and therefore no language. What they have is the illusion of meaning, produced by the seductive grammar of our ordinary talk about sensations.
The private language argument is developed in §§243–315 of the Investigations. Its interpretation remains deeply contested: Kripke's reading (sceptical paradox + community) and the classical reading (grammar of sensation-language) are the two dominant lines. The beetle-in-a-box thought experiment appears at §293.
