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Denying the external world essentially denies the existence of everyone else. I become only sure of that which I am aware of myself. I thought perhaps Berkeley might have undergone a similar enterprise, but I'm not sure if he has a sufficient answer to the problem of other minds.

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The answer is sensitive to what is meant by "external" and "denial". For instance, one could say that the expression "external world" is incomprehensible (since we can not get out of ourselves to understand what it means), and that can be called "denying it". Kant's position can be read in this way, and also positions of many anti-realists (Husserl, Wittgenstein, Dummett, etc.). On such a position we do not get to construe other minds as some entities "like us", because externalizing our view of us is itself meaningless. All "experience" manifests as ours and ours alone, as Wittgenstein would put it, it can not be both ours and "the other". The words get their meanings from dealing with the world, and we get to deal with others long before we get to ask if they have minds, see What is Wittgenstein's "criterial solution" to the problem of other minds? So analogized "other minds like us" are empty words, and the "problem" comes from abuse of language. In other words, anti-realists dissolve the problem of other minds by denying that it can be intelligibly stated. This clever move does not stop their opponents from calling them "subjective idealists", who "slide into solipsism".

Despite his bad reputation Berkeley was not a solipsist, and not even an anti-realist, he admits that "external world" is intelligible in principle, just inaccessible. He even produced an argument for other minds by analogy and inference:

Philonous: That from a cause, effect, operation, sign, or other circumstance, there may reasonably be inferred the existence of a thing not immediately perceived, and that it were absurd for any man to argue against the existence of that thing, from his having no direct and positive notion of it, I freely own. (Dialogues II)

as we conceive the ideas that are in the minds of other spirits by means of our own, which we suppose to be resemblances of them: so we know other spirits by means of our own soul... it is plain that we cannot know the existence of other spirits, otherwise than by their operations, or the ideas by them excited in us... Hence the knowledge I have of other spirits is not immediate, as is the knowledge of my ideas; but depending on the intervention of ideas, by me referred to agents or spirits distinct from myself, as effects or concomitant signs. (Principles 140-145)

For more see Berkeley's Argument for Other Minds by Falkenstein.

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