In §256, Wittgenstein characterizes a private language as that language which describes my inner experiences and which only I myself can understand. Words of this language cannot be connected with my natural expressions of sensation – if they were, the language could not be private, but is rather public, for anyone might understand my natural expressions and so come to understand my purportedly private language. That is, if a private language is connected with natural expressions, then the expressions of the language are public/observable – its expressions cannot be understood uniquely by me. So if we are to have a private language, it cannot be connected with natural expression – rather, it must work the following way: we have sensations (which are in some sense private) and come to associate names with the sensations and use these names in descriptions (which, presumably, cannot violate the privacy).
In §258, Wittgenstein asks us to consider the following case. I want to keep a diary about the recurrence of a certain sensation or I have. I associate the sign “S” with the sensation, and write this sign in the diary every day on which I have the sensation. This is the only means by which I “express” my experience of the sensation – there are no natural expressions of the sensation, all the outside observer can see is the “S”-writing behavior. I cannot formulate a definition for “S”. Why? Suppose I say, or think, that “`S’ is defined as such-and-such”. If the “such-and-such” is some combination of familiar, public words (in English, let’s say), then my sensation is publicly expressible and cannot be private, contrary to our hypothesis. Or else if the “such-and-such” is some other private sign like “S”, then those signs must also be given some definition, and so on.
Recall that to give an ostensive definition of a thing is to “attach a nametag” to it by gesturing toward the thing and producing an utterance. You might think that “S” could be defined ostensively. Not so. For in what sense can you gesture toward a sensation? It is not as though I could point to the S-sensation in my head (I’d just be pointing at my head!). But you might think that in some sense you can point to your sensation insofar as you “concentrate [your] attention on the sensation [so as to] `point inwardly’”. But this, too, would be a mistake. For we can ask “what is this `ceremony’ of concentrating your attention for?” What does it mean to “concentrate your attention” on this thing rather than that – and what does it actually accomplish? You might think it accomplishes this: by concentrating your attention on the sensation and committing to memory a connection between the sensation and “S”, you bring about the connection between the sensation and “S”.
Committing the connection to memory just means that this process [concentrating the attention] brings it about that I remember the connection correctly in the future. If concentrating your attention makes it the case that you remember the connection correctly in the future, then there must already be some fact of the matter regarding a correct connection between the sensation and “S”. But in the case we are asked to consider, there is no criterion of correctness. I can’t bring it about that I remember the connection correctly in the future unless I have the resources to say that it was correct to apply “S” to the sensation in the first case. There’s a temptation to say that because this is my private sensation and my private language whatever seems correct to me is correct. And so because applying “S” to the sensation seems correct to me, it in fact is. This, however, is not right. To say “whatever seems correct to me is correct” is just to say that “we cannot talk about `correct’”.
A brief elaboration. My “concentration of attention” doesn’t seem like it should change anything about how “S” may be used, nor does it affect the sensation; there is no tangible connection brought about. It cannot be the case that whatever seems right and wrong is in fact what is right and wrong. For if it were, then understanding how to “go on” would just be a matter of conforming to the thought or formula which seems right in your head. But we saw in §154 that understanding how to go on or continue a series is not a matter of having a formula occur in your head and conforming to that. Likewise, what is right or wrong is not so because of some occurrence in your head – like “seeming right”. Suppose I wake up one morning and what seemed right to me yesterday now suddenly seems wrong – has the status of what is right or wrong suddenly changed? Intuitively, we want to say “no”. Because I cannot mentally set my own standard of correctness, then in this situation there can be no “right” or correct use (of “S”).
We can strengthen this point with considerations from §257. If I invent a name for my sensation in my private language, I cannot make myself understood when I use the word. That is, I could never use “S” in a sentence and have someone understand what I mean by it. If I cannot make myself understood to others when I use the sign, then in what sense do I understand “S” when I use it? It seems like I can just stick “S” to whatever sensation I feel like, whenever I feel like—so in what sense could this sign have any meaning to me? Insofar as it a name? Not so, for there is still no criterion of correct usage. A name is used to refer to an object, and I cannot use this name for anything (as no one understands it) – it has no purpose and cannot be used to refer. Should I use “S” to refer to some other thing, no one can tell me I’ve used the sign wrong – if “S” can refer to whatever I like, then there cannot be a fact of the matter as to the correct use of “S”.
In order to give something a name, there must a role existing in the language for that word to occupy. There must be a post at which the word is stationed – a role the world plays. But there is nothing in the grammar of any public language – no station – which fixes the use of the term “S”. So we cannot under the notion of a private language.