For a machine to have knowledge, it looks like it has to be able to have beliefs, since when you know something you also believe it (though not conversely). And for a machine to have beliefs, it has to be able to form representations of how the world might be. So the answer to your question will depend in part on whether machines can form representations. This is a hotly debated question in the philosophy of mind, for the case where the machines in question are computers. The two most famous arguments are due to Alan Turing and to John Searle. Turing argued that there could be a computer that is able to engage in an extended intelligent conversation (by email perhaps) so good that it fools people into thinking it is a person, and that such a computer ought to be taken to have representational states. Searle argued that since we know how computers (traditional ones, anyway) actually create their end of the conversation, and that this involves only registering the electronic equivalent of the...

This is what David Hume's great skeptical argument seems to show. The claim that nature is (and will be) uniform, or such that our inductive practices will tend to take us to the truth, is itself something that it seems we could only know by using induction, but to use induction to justify induction seems worthless. For my money nobody has yet given a fully adequate reply to Hume's argument. And if his argument is sound, the our reliance on induction does seem to be a matter of faith: something we believe though we can have no good reason for it. As you probably know, there is a huge literature of attempts to solve the problem of induction. My own view is that the prospects for inductive justifications of induction are better than they first appear. For example, I think that the fact that a particular method of predictive the future has worked well so far can give some reason to trust it in future, even though that argument would of course have no force for someone who refused to use induction...

'All statements are false' is necessarily false, so there is at least one true statement.

A fair bit of philosophy consists in arguing that things most people think are obvious could in fact be wrong, and so are not really obvious at all. So I hesitate to offer an example of something that most philosophers would agree to be obvious. But here goes: simple logical truths, such as statements of the form 'P or not-P'. Actually, certain logicians have a problem with that one. So maybe the denial of a simple contradiction would be better, something like 'It is not the case that both P and not-P'. Even there you have a few philosophers who balk, but they are in small (though interesting) minority. Another sort of possible example of the obvious would include certain claims to do with observation. Not, of course, straightforward claims like 'There is a table in front of me'. Philosophers have a lot of trouble with those. But claims like 'It seems to me that there is a table in front of me' strike many people, even many philosophers, as pretty obvious.

You're right: the fact that you seem to remember something doesn't mean it really happened, even if what you seem to remember is your own past thought. And it is not as if you can go back to check. But you can still at least sometimes evaluate the reliability of a particular memory. How plausible is it that the sort of thing I seem to be remembering would happen? How does it fit with other things I believe (even if almost all of those other beliefs are also based on memory)? These are the sorts of checks we run regularly, to decide when to trust our memory and when not to trust it. But it is difficult to see how to block the extraordinary doubt that pretty much all our memories might be wrong. As Betrand Russell pointed out, there seems to be nothing impossible about the idea that we and the rest of the world only came into existence five minutes ago, with our minds pre-stocked with a full set of false memories. That's skepticism for you.

'Realism' is used in a number of senses. One of the most common is the idea that there is determinate world out there independent of us and that we can know something about it. This contrasts for example with idealism, according to which everything that exists is mental. 'Naive Realism' may be mean thinking that something is mind independent when one should know better. Thus a philosopher who thinks that colours are really just sensations (and perhaps even a philosopher who thinks that colours are powers to produce sensations) may call another philosopher who thinks that colours are as much 'out there' as shapes a naive realist. More generally, 'naive realism' is often used to refer to the view that we see things directly and that they have the properties they seem to have.

It does seem possible that nobody else exists: I just have a very lively imagination. An interesting line of thought to the contrary is that my very ability to think contentful thoughts depends on the existence of other people. In that case, if I can have the contentful doubt whether other people exist, then they do. But can I prove that I have contentful thoughts?

David has given you two arguments for extra universes based on scientific considerations. These sorts of case are particularly neat because, as I understand it, we are physically cut off from other universes: there is no causation between worlds. But your ant analogy suggests that you also wonder whether there might not be more than we can sense or know in our own universe. There is indeed much more in our world than we can sense, and our scientific theories describe a lot of it. But is there much more in our world than we can know, once we take account of how far beyond what we can sense science takes us? To be unknowable, it seems that features of the world would have not just to be unobservable but causally isolated from what we can detect. (That is why David's examples were neat.) But there are many events in our world with which we cannot interact causally, given how limited is our own existence in spacetime. And even where there is causal interaction, I suppose that, like the ants, we...

You can't think without thinking, but fortunately it doesn't follow that you can only think about thinking. There are wonderful philosophical questions about how we perform the feats of representing things in the wolrd and of distinguishing correct from incorrect representations; but the the undeniable fact that all our mental representations are indeed mental does not show these feats to be impossible.

Also because you want to know what the world is like (even when your life doesn't depend on it) and only true propositions tell you that. To have any beliefs at all is to manifest an interest in the truth and falsity of propositions.