Let's define sensations as everything we experience through our senses, from the red color of an apple to the feeling of pain after stubbing one's toe. But how do I know about this we? I'm not really experiencing your sensations, am I? Of course not, for surely I only have access to my own experience, my own feelings of pleasure, color, texture, and so on. One may have empathy with another's pain, or look at the same object as someone else, but these 'shared' experiences are always mediated through my own personal experience, and I can only extrapolate from that as to what somebody else is feeling. Thus we can say that we all have our own 'private' experience, from which we name sensations that seem to be in common with those of others. We can verify that they are in common from the behavior of others, their way of using the same words.
From this picture of things, however, some troubling questions naturally emerge. If I only have access to my own private experience, how do I know that the words I use for certain sensations mean the same as the words you use? That is, how do I know what I call 'blue' refers to the same color-experience as what you call 'blue'? Someone could be color-blind their whole life and never know it, thinking their private experience was in line with that of others, able to use the same language consistently, and yet, never experience the same color. This problem extends all the way to skepticism of other minds: how do I know I'm not the only conscious being in the universe, and everyone else are just automata pretending to have the same inner experiences?
Before accepting this skepticism, we should ask how this confusion springs up from such a common-sense look at our own experience. Perhaps there is something wrong with the common-sense view that produces these questions, and I believe the locus of the problem is in the concept of 'private'. We like to imagine our consciousness as supremely mine, in which a constant stream of thoughts and feelings flow, like a private movie theater where I am the only one watching. But we should take note that this concept of a private space of consciousness is an interpretation, not a fact, of experience. So let's see how this interpretation holds up.
To get clear on our intuitions, imagine a lone meditator observing the cinema of his mind. Having been raised in normal society, one day this man decided to abandon it all in order to meditate alone in a cave, all day and every day. There he develops awareness of the many different sensations in his body. At first, he would experience feelings he and others have felt before, the feelings we have names for in common language: heat, cold, pain, pleasure, tingling, itching, and so on. But as he develops his awareness, he would also have some feelings we are not familiar with, sensations that perhaps require his unique experience and time dedicated to meditation in order to feel. Suppose he were to reach such a state of awareness as to observe a sensation that there is no name for in any language. How are we to imagine this situation? Would he feel the new sensation, and give it a new name? Suppose he calls it 'schmu'. Over time, perhaps he would develop a dictionary of names only he can understand, referring to these unique sensations.
If you are inclined to accept that the dictionary of the lone meditator would be meaningful, then you may have succumbed to a trick of language. Ludwig Wittgenstein in his Philosophical Investigations outlines some useful ways to think about such scenarios. The example I just outlined provides an instance of something Wittgenstein calls a 'private language', and it's a concept the possibility of which he argues strongly against. We are misled by our linguistic habits to think that names are meaningful because they 'point' to the things we mean; in this case, the meditator does a kind of inner pointing with his awareness to the sensation. But this inner pointing will necessarily lack meaning.
Suppose the meditator experiences schmu for the first time. We can imagine a kind of inner dialogue: "I'll call this feeling 'schmu', and so anytime it happens again, I'll recognize it by the same feeling and know it is schmu." That is to say, the definition of schmu consists of such-and-such feelings. But this is begging the question: the such-and-such feelings are the very thing that need clarifying when defining schmu. There is no real correlation being established here between feelings and a word. It seems like there is a correlation, but really the word 'schmu' has no sense; it is referring to itself. As Wittgenstein aptly puts it: "Imagine someone saying: 'But I know how tall I am!' and laying his hand on top of his head to prove it" (§279).
The problem is also one of verification. If a word had no rules by which to verify its use, there would be no difference between thinking you were obeying a rule, and actually obeying one. That is, there would be no difference between thinking you felt schmu, and actually feeling it. The meditator could have used it to label any private feeling whatsoever that he believed was like his first one, and there would be no way for him or anyone else to know if it was being used correctly. Therefore there would be no way to ascertain the meaning of the word 'schmu', even for the meditator himself experiencing his own feeling. To quote another helpful analogy from Wittgenstein, it would be "as if someone were to buy several copies of the morning paper to assure himself that what it said was true" (§265).
The issue with the ordinary view of our minds with which we begun is that we actually think of all private sensations as the meditator thinks of 'schmu'. For instance, we think the word 'pain' is a uniquely private sensation, felt inwardly and brought into a correlation with some word so as to communicate it, to others or ourselves. Wittgenstein tells us this account of meaning is nonsense, for the use of the word 'pain' functions independently of any private movie screen experience. We know this because we cannot analyze our sensation of pain any further than "I am in pain", and any attempt to say that pain actually refers to a mental state or inner process is simply rewording, without adding anything of substance, the phrase "I am in pain". The meaning of 'pain' could not be a description of a private inner process, for then it would fall into the same trap as 'schmu', and no one else could understand it.
The skepticism of other minds discussed earlier can now be dismissed as nonsensical (although not necessarily untrue). For the meaning of something like 'blue' is not dependent on the private impression I have of it, but rather its expression in accordance with rules for use which others clearly understand. We simply cannot speak of the private color-experience as if it is what our words refer to; this is not their meaning. The misplaced attention on privateness is really the effect of an underlying metaphysics produced by misuse of language, one which separates what's private from what's public.
Wittgenstein himself stops his analysis at the level of language. He does not have a definite position on the existence of private sensations, or what their relationship to public things is. All he has done is shown that we cannot talk about it. When pressed to say what he thinks a sensation is by an imaginary interlocutor, he responds: "It is not a something, but not a nothing either! The conclusion was only that a nothing would serve just as well as a something about which nothing could be said. We have only rejected the grammar which tries to force itself on us here" (§304). Of course, the temptation now is to wonder how something can be neither something nor nothing. But Wittgenstein would rather we dissolve the question entirely.
Let's consider the lone meditator one more time. It is worth noting that I have constructed somewhat of a strawman meditator, as any good practitioner knows you should never verbalize or give names to the sensations you experience when meditating. This would not be accepting reality as it is, but an attempt to shape reality yourself. In fact, Buddhist metaphysics often holds that language is built upon illusions, and is at best limited, at worst deceptive. The subject-object distinction inherent in our grammar goes against the view of no-self, the division of the world into things goes against the emptiness of all so-called essences. Now, I think Wittgenstein would be just as skeptical of this picture as its opposite, but I can't help but think it is more compatible with his critique of private language. Maybe the reason why we cannot meaningfully have a private language is that the dichotomy of private vs public things is simply wrong, not just meaningless. It may be impossible to mean a purely private sensation, not just because of the limits of language, but because of the non-dualistic nature of reality.
If the meditator keeps his practice to just observing sensations without attempting to refer them to words, this might be something like what he realizes. A sensation is really the same as any other content of consciousness, private or public. Of course, what this collapsed distinction really entails is still vague and highly speculative, and many possible pictures could follow from it. Either the dichotomy is reduced to just one of its elements (so that everything is private, or everything public), or neither is a satisfactory description.
It is worth remembering too, ironically, that other more famous lone meditator who came to almost the exact opposite conclusions. According to the thought of Wittgenstein and many Buddhists, it was language that led him astray; although perhaps the only way to be sure is to observe your own sensations, and see for yourself.