The case of the brains in a vat
Here is a science fiction possibility discussed by philosophers: imagine that a human being (you can imagine this to be yourself) has been subjected to an operation by an evil scientist. The person's brain (your brain) has been removed from the body and placed in a vat of nutrients which keeps the brain alive. The nerve endings have been connected to a super-scientific computer which causes the person whose brain it is to have the illusion that everything is perfectly normal. There seem to be people, objects, the sky, etc.; but really, all the person (you) is experiencing is the result of electronic impulses travelling from the computer to the nerve endings. The computer is so clever that if the person tries to raise his hand, the feedback from the computer will cause him to 'see' and 'feel' the hand being raised. Moreover, by varying the program, the evil scientist can cause the victim to 'experience' (or hallucinate) any situation or environment the evil scientist wishes. He can also obliterate the memory of the brain operation, so that the victim will seem to himself to have always been in this environment. It can even seem to the victim that he is sitting and reading these very words about the amusing but quite absurd supposition that there is an evil scientist who removes people's brains from their bodies and places them in a vat of nutrients which keep the brains alive. The nerve endings are supposed to be connected to a super-scientific computer which causes the person whose brain it is to have the illusion that...
When this sort of possibility is mentioned in a lecture on the Theory of Knowledge, the purpose, of course, is to raise the classical problem of scepticism with respect to the external world in a modern way. (How do you know you aren't in this predicament?) But this predicament is also a useful device for raising issues about the mind/world relationship.
Instead of having just one brain in a vat, we could imagine that all human beings (perhaps all sentient beings) are brains in a vat (or nervous systems in a vat in case some beings with just a minimal nervous system already count as 'sentient'). Of course, the evil scientist would have to be outside — or would he? Perhaps there is no evil scientist, perhaps (though this is absurd) the universe just happens to consist of automatic machinery tending a vat full of brains and nervous systems.
This time let us suppose that the automatic machinery is programmed to give us all a collective hallucination, rather than a number of separate unrelated hallucinations. Thus, when I seem to myself to be talking to you, you seem to yourself to be hearing my words. Of course, it is not the case that my words actually reach your ears — for you don't have (real) ears, nor do I have a real mouth and tongue. Rather, when I produce my words, what happens is that the efferent impulses travel from my brain to the computer, which both causes me to 'hear' my own voice uttering those words and 'feel' my tongue moving, etc., and causes you to 'hear' my words, 'see' me speaking, etc. In this case, we are, in a sense, actually in communication. I am not mistaken about your real existence (only about the existence of your body and the 'external world', apart from brains). From a certain point of view, it doesn't even matter that 'the whole world' is a collective hallucination; for you do, after all, really hear my words when I speak to you, even if the mechanism isn't what we suppose it to be. (Of course, if we were two lovers making love, rather than just two people carrying on a conversation, then the suggestion that it was just two brains in a vat might be disturbing.)
I want now to ask a question which will seem very silly and obvious (at least to some people, including some very sophisticated philosophers), but which will take us to real philosophical depths rather quickly. Suppose this whole story were actually true. Could we, if we were brains in a vat in this way, say or think that we were?
I am going to argue that the answer is 'No, we couldn't.' In fact, I am going to argue that the supposition that we are actually brains in a vat, although it violates no physical law, and is perfectly consistent with everything we have experienced, can not possibly be true. It cannot possibly be true, because it is, in a certain way, self-refuting.
The argument I am going to present is an unusual one, and it took me several years to convince myself that it is really right. But it is a correct argument. What makes it seem so strange is that it is connected with some of the very deepest issues in philosophy. (It first occurred to me when I was thinking about a theorem in modern logic, the 'Skolem-Löwenheim Theorem', and I suddenly saw a connection between this theorem and some arguments in Wittgenstein's Philosophical Investigations.)
A 'self-refuting supposition' is one whose truth implies its own falsity. For example, consider the thesis that all general statements are false. This is a general statement. So if it is true, then it must be false. Hence, it is false. Sometimes a thesis is called 'self-refuting' if it is the supposition that the thesis is entertained or enunciated that implies its falsity. For example, 'I do not exist' is self-refuting if thought by me (for any 'me'). So one can be certain that one oneself exists, if one thinks about it (as Descartes argued).
What I shall show is that the supposition that we are brains in a vat has just this property. If we can consider whether it is true or false, then it is not true (I shall show). Hence it is not true.
Before I give the argument, let us consider why it seems so strange that such an argument can be given (at least to philosophers who subscribe to a 'copy' conception of truth). We conceded that it is compatible with physical law that there should be a world in which all sentient beings are brains in a vat. As philosophers say, there is a 'possible world' in which all sentient beings are brains in a vat. (This 'possible world' talk makes it sound as if there is a place where any absurd supposition is true, which is why it can be very misleading in philosophy.) The humans in that possible world have exactly the same experiences that we do. They think the same thoughts we do (at least, the same words, images, thought-forms, etc., go through their minds). Yet, I am claiming that there is an argument we can give that shows we are not brains in a vat. How can there be? And why couldn't the people in the possible world who really are brains in a vat give it too?
The answer is going to be (basically) this: although the people in that possible world can think and 'say' any words we can think and say, they cannot (I claim) refer to what we can refer to. In particular, they cannot think or say that they are brains in a vat (even by thinking 'we are brains in a vat').