It seems that we all have privileged access to our own inner sensations. I am directly aware of my pain, but everyone else can only surmise it or be told about it. However, it is difficult to talk coherently about the nature of this privileged access. "I know I am in pain," says no more than, "I am in pain." Saying that sensations are private is not a statement of fact so much as a grammatical statement about how we are to use the word, "sensation."
Wittgenstein confronts the difficulties of talking about inner sensations with the idea of a private language: if it is possible to talk meaningfully about my own sensations as something that only I have access to, then I should be able to formulate a private language that refers to these sensations so that no one but myself will understand it. Suppose I take note of a certain sensation, and write "S" in my diary on every day that I experience that sensation.
The practices that surround our ordinary language-games and give them meaning are absent with private language. There are no criteria for saying whether I have understood or am using "S" correctly, and so "S" has no clear function. There is no distinction between what is a correct use of "S" and what seems correct to me. Without an external means of justification, there is no concept of justifying the proper use of that sign.
One of the peculiarities about privacy is that we have no access to other people's private experience: your sensation of red may be totally different from mine. When we talk about "red," we are not talking about our own private sensations, but a common experience of what we call "red." Though we can talk about sensations such as color-impressions or pain, we only talk about them insofar as they are common experiences.
This is not to say that there is no such thing as pain, but only pain-behavior, or that sensations only exist insofar as other people can share them. Rather, it is meant to highlight what "pain" means by observing how we use the word. "Pain" does not simply refer to an inner thing in the same way as "chair" refers to an outer thing: it is accompanied by a whole set of notions about what it means to be a person who feels, senses, lives, and so on. We do not learn how to use "pain" from our own experience of it, but from our shared experience, from observing other people having similar experiences and talking about them in similar ways.
Suppose everyone has a box with something in it, but people can only see the contents of their own box and nobody else's: different people may or may not have different things in their boxes. We could call this something a "beetle," but the word "beetle" does not play the role of a name in this language-game: what is actually in the box is irrelevant to how "beetle" is used. Private sensations are not objects that we refer to, because referring to them becomes irrelevant if only we experience them.
The initial mistake lies in the assumption that when we talk about sensations, we are talking about states or processes. Wittgenstein's denial of private language seems to be a denial that these states or processes exist. He is not denying that there is more to pain than just pain-behavior, but he is denying that we can talk about what lies behind the behavior in any coherent way.
Wittgenstein's analysis of private language is one of the most discussed passages in the Philosophical Investigations largely because there is little agreement even as to what he is trying to say, let alone what conclusions he reaches.
One approach to this section is to read Wittgenstein as responding to skepticism about other minds. The skeptic believes that I can know my own pain in a way that I can never know other people's pain: I base my judgment that someone else is in pain on that person's outward behavior and not on the pain itself. I can never know with certainty that the other person is not pretending to be in pain; further, I can never know that what other people call "pain" feels like what I call "pain." Further, I can never know that other people even exist: perhaps everyone but me is just an automaton built to act human, and lacks all the inner experiences that I associate with words like "pain."
Wittgenstein suggests that these skeptical arguments, and the different responses and refutations to them, are not so much false as incoherent. They are parasitic on the way we normally talk about things like knowledge, doubt, and justification, but do not use these terms in their proper contexts. For instance, in section 246, Wittgenstein says, "It can't be said of me at all (except perhaps as a joke) that I know I am in pain." Ordinary talk about knowledge involves questions of investigation, verification, justification, and so on. I am at a loss how to answer someone who asks, "how do you know you are in pain?" because there is no evidence or justification I can appeal to beyond the simple fact that I am in pain. My own pain is not the kind of thing I can talk about in terms of knowing.
This line of reasoning goes directly against the skeptic, who wants to set up his knowledge of his own pain as a paradigmatic case of certainty, against which my knowledge of other people's pain seems sorely lacking. A skeptic would say that his experience of his own pain is not a clearer, more certain version of his experience of someone else's pain: it is a different sort of thing altogether.
Part of the problem with the idea of a private language is that it tries to set up a way of talking about inner sensations in the same ways that I talk about outer facts. But talk about outer facts is indeed tied up with questions of investigation, verification, justification, and so on: it is part of our ordinary language-games that we can ask questions like, "how do you know?" "on what grounds do you say this?" and so on. These questions do not make sense in reference to my own sensations, so a mark like "S" cannot be taken to state or claim anything in the way that we might want it to. Insofar as we can ask questions, justify, or provide evidence regarding pain, we can only talk about other people's pain and the behavior they exhibit.
Wittgenstein is aware that he might be mistaken for a behaviorist, as asserting that "pain" means "pain behavior," and that when we talk about our own pain we cannot be referring to private sensations. However, is arguing that it is not a question of whether we can or cannot refer to our private sensations. Instead, Wittgenstein says that this talk of referral to private sensations is itself misguided. Talk of words referring to things belongs with talk about justification and verification since it is coherent only when dealing with objects of public knowledge. Of course, the pain I feel is different from the pain behavior I exhibit, but I cannot then build any coherent statements about this pain as a private entity.
Part of the problem with understanding Wittgenstein is that he does not arrive at any definite position. Though this section is called the "private language argument," Wittgenstein is not establishing a particular philosophical position that we can then debate. Rather, he is leading us through the various ways we are inclined to talk about the nature of private sensations, and show us that we are not licensed to claim any discoveries about the nature of knowledge, the mind, or anything else. He does not leave us with definite conclusions, but rather with a more cautious outlook toward philosophical positions built upon talk about private sensations.