Mill says "We have no conception of Mind itself, as distinguished from its conscious manifestations". In other words, although we understand the mind to be present, we don't have direct experience of it; rather we have experience of the different types of mental processes such as thought, belief, desire, pain, etc. which we assume to be consequences of having a mind. An analogy to this might be the diaphragm of a loudspeaker: we infer its existence because when it vibrates we can hear various sounds, although we never hear the diaphragm per se. Similarly, we have the idea of the diaphragm continuing to exist when it's not vibrating, just as we have the idea that our minds continue to exist even at times when we are not conscious of anything.

While Mill seems to take as beyond debate the notion that our own minds exist, it can be argued that it is impossible to know that other minds do. It is certainly true that since I am me, I cannot be someone else; therefore I can't ever have first-hand evidence that someone else has a mind. However, as Mill says: "..there is nothing in this doctrine to prevent me from conceiving, and believing, that there are other successions of feelings besides those of which I am conscious.." In other words, the fact that I can't be 100% certain that other minds exist doesn't prove that they don't. As Ayer says, "Let us allow it to be necessarily true that I cannot know the experiences of others in the way I know my own. It by no means follows that I cannot have good reasons to believe in their existence..."

Mill says that when he examines his own behaviour, he can see that "antecedent" events cause feelings (i.e. aspects of mind) and that those feelings go on to have consequences. "I am conscious in myself of a series of facts connected by a uniform sequence, of which the beginning is modifications of my body, the middle is feelings, the end is outward demeanour." Looking at other people, he can see the antecedents and consequences, but obviously not what's going on in between. But he believes it is reasonable, based on personal experience, to infer that since other people behave as if they had minds like his, they actually do.

This "proof" that other minds exist is an inductive one - moving "from premisses about objects we have examined to conclusions about objects we haven't examined" (Okasha). Mill defends this approach by referring to the example of Newton, who used the same approach to "prove" that planets orbit the sun based on the example of an apple falling to the ground, and points out that all of the available evidence he has supports his contention: "having made this generalization, I find that all other facts within my reach accord with it".

It can be argued that the experience I have of my own mind provides a very small, subjective and specific set of data from which to form an argument to explain all the other minds that I believe to exist. However, this is the only empirical data we have, and so may be the best proof we can hope for.