This is a problem that has been addressed by both Bertrand Russell and A J Ayer. Russell puts forward one solution: the argument from analogy. We see that other people's behavior resembles our own, and we know that our own behaviour arises from mental processes, so it follows that other people also have these processes, though, of course, this proceeds from intuition, it might be said, rather than proof. The example here is that if I experience pain on the basis of certain unpleasant experiences, then if someone else reports pain I assumer that they are having the same unpleasant experience.
It's not a particularly strong argument, as Ayer was quick to recognise. To assume that it is possible to generalise one's own thoughts to those of other people is not a justifiable inference. Ayer also rejects a behaviour-based version of the argument from analogy. We learn what words like 'pain' mean by observing the behaviour of others. This means that our justification for attributing pain to them simply comes from the fact that their behaviour exemplifies what pain means. Put this way pain doesn’t refer to a particular type of inner sensation at all. It is, rather, whatever causes a certain type of behaviour. In other words, if the behaviour is present so, too must pain, as pain is simply the cause of the behaviour. In such ways is the problem of mind dissolved.
But for Ayer this is quite wrong, because he sees no reason to suppose that the meaning of words should be strictly determined by the way in which they were learned. Just because we learn what mind-words mean by observing behaviour, this does not imply that the meanings of these words can be exhausted by what can be observed in behaviour. It is a mistake, as Ayer sees it, to confuse the method of learning a word with its actual meaning. You may learn what a tiger is from seeing a photo of a tiger, but it does not follow that 'tiger' means 'photo of a tiger’. So, on this basis, it does not follow from the fact that we learn about mental concepts from behaviour that the manifestation of certain kinds of behaviour ensure that which the mental concepts refers to are present.
The argument between Russell and Ayer gets ever more complex to the point where it seems impossible to discuss the problem of mind on any common philosophical grounds. But Ayer offers a solution in the work of Hilary Putnam, who argued that the belief that others have minds like mine is justified because it explains human behaviour. More than that, there is no other rival theory which explains human behaviour so well.
I suppose it's a solution, it might be said, of simple exhaustion; it is because it is! For, as with all other sceptical problems, we simply cannot prove beyond all doubt that other people have minds. In the end the words of Aristotle have abiding relevance-"It is a mark of the trained mind never to expect more precision in the treatment of any subject than the nature of that subject permits." Amen!
