You are right. If you and I each assumes that our own thoughts are all the thoughts there are, then we are both wrong. Of course if I am really the only thinker, then my assumption would be correct, but it does not look like I could justify that assumption, since if you were out there too, you would be in just the same situation as I am. The way out of this, I think, is to see that the point is not that I have reason to believe that there are no thoughts other than my own, but that my own thoughts are the only ones I can be completely sure about. However much experience and however many thoughts I have, it is still possible that there is nobody else out there. Of course we all believe (rightly, in my view!) that there are other people and their thoughts out there, but the puzzle you have asked about encourages philosophers to try to work out how we can know this.

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.

Sensations are real in my book while I am having them, but you are right that it is not easy to use them to build a table. The trouble is that the table has a continuous existence, while it is only intermittently observed. One standard way around this problem is to fill in the apparently unobserved periods by having God observe the table all the time. That was George Berkeley's suggestion. Another way is to fill in the gaps between actual table sensations with merely possible sensation. This too is suggested by Berkeley in one remarkable passage, and figures centrally in John Stuart Mill's phenomenalism, acccoring to which tables are, in his memorable phrase, 'permanent possibilities of sensation'. The idea is that even when nobody is looking at the table, it is still true that if someone were to come into the office, they would see the table. Phenomenalism is a clever solution to the gap problem, but like many other philosophers (not to mention ordinary people) I find it incredible to...

You won't be suprised to hear that philosophers disagree a lot about the reality of times. Some say that time is a lot like space, and that all times are equally real at all times. On this view, the present is where we happen to be at the moment, but right now the past and the future are also equally real, much as here is the place we are, but other places are equally real even though we are not at those places. At the other extreme, there are those, appropriately called 'presentists', who think that only the present is real: the past has gone out of existence and the future has yet to come into existence. Your view is intermediate: the past and present are real but the future is not. This too can be seen as a kind of spacial view of time, but in an expanding universe. If it helps, think of the universe as an inflating balloon: on your view the temporal dimension is inflating too, so there are more and more real times. I too find the expanding view of time attractive, in part because...

Take the concept of apples. There is no cosmic connection between that concept and the term 'apple'. It's just a convention, and indeed it's only a convention for those who speak English. Among English speakers, however, it does seem important for the sake of communication that we are following the same convention. Otherwise when you ask me for an apple I might give you a hamster. There is however a deep philosophical worry about how it is possible for you to entertain a concept. The issue here is not how you know that other people's concepts are the same as yours, but how you can have any general concept at all. Take the concept of apple again. How do you manage to think, not just of this or that apple you may have seen, but of the set of all apples, the great majority of members of which you will never encounter? The trouble is that the apples you have seen are not just a subset of the set of apples, but also a subset of innumerably many other sets, such as the set consisting of apples...

We naturally think of the world as made up of things with properties. Take my black pen: the pen is the thing and being black is the property. But metaphysicians disagree about whether at the end of the day there are things entirely distinct from properties. Some say you need some kind of substance to have properties; others say that a pen is really just bundles of properties: its colour, weight, shape, composition, etc. It's the same with our mental life. I have a headache: "I" is the thing, and having a headache is its property. But some philosophers would say that although we distinguish between the thought and the thinker, at the end of the day the "I" -- the thinker -- is really just a bundle of thoughts. (Insofar as it exists at all.) In that case, I suppose that the "I" would be located in the same place as those thoughts. Other philosophers may wish to insist however that the "I" must be distinct from the thoughts it has: it must be some kind of substance. It might be a physical...

Indeed it seems that we don't even know what it means to say that modern mathematics is correct. Does it mean that it contains no hidden contradictions, that it accurately describes 'the world of numbers', that it supports empirical science, or what?

I take it that the Euthyphro dilemma against divine command theory involves the choice between saying that something is right because God says it is right and saying that God says something is right because it is right. The former claim seems false, since it seems to entail the falsehood that if God simply said torturing kittens was right, that would make it right to torture kittens. And the latter claim does not seem strong enough for divine command theory, since it does not make God's command the source of moral value. I'm no expert on this topic, but there seem to be two obvious rejoinders. One would be to bite the bullet and allow that God is the source of morality, so the first horn of the dilemma is correct. If God commanded kitten torture, then that would in fact be the right thing to do. Our strong initial intuition to the contrary is just due to the fact that we have been brought up on the basis of what God actually commands, which (let's suppose) includes a command to be kind to animals....

Even if they are not so inclined, people should avoid fallacies, roughly because it makes them less likely to acquire new beliefs that are false. But you are not asking what people ought to do, but rather what will in fact lead them to want to avoid fallacies. Maybe we just need to know more about these people to answer this question. Thus perhaps they are inclined to accept pretty much any claim if it is presented in the form of a song, to the tune of 'Happy Days are Here Again'. In that case, I suggest you sing them 'Avoid fallacies, if you can' to that tune. The trouble is that if we try to imagine people who are completely unresponsive to logical force, then who knows what will move them? But actually it's not clear that such a supposition is coherent, because any creature that would count as thinking at all must at least be somewhat responsive to logical force, if their thoughts are to have content. (Of course they may still be prone to various fallacies, and not much bothered by them.)...

This is an excellent and hard question. Balanced coverage is a problem in science journalism, since there sometimes is a tendency to go for a 50/50 approach, even if one side of the debate is much better supported by the scientific evidence than the other. In that case 50/50 seems clearly unbalanced, and it looks like one might be able to come up with some principle of balance in terms of the weight of evidence or the weight of opinion in the qualified professional community. Of course this won't be easy to work in practice, but at least there are some principles one might have. In the case of political balance, the situation is much more difficult: difficult to work out what 'balance' means and, as you say, difficult to see how we could recognize balance and imbalance, even if we knew in the abstract what they mean.