I think I could do little better than to point you to what Descartes himself says about this. It's quite right that, in the First Meditation, he does seem to bring even logical (or mathematical) reasoning into the scope of his sceptical doubt: "What is more, since sometimes I believe that others go astray in cases where they think they have the most perfect knowledge, may I not similarly go wrong every time I add two and three or count the sides of a square, or in some even simpler matter, if that is imaginable?" (CSM II, 14; AT VII, 21). And then, at the start of the Second Meditation, we get the Cogito which, on the face of it, certainly seems to have the form of a logical deduction of existence from thought. So is he really entitled to it at all? Couldn't he similarly go wrong there too? Well, Descartes would say no, and the clue to his solution is to be found in the Second Replies: "when we become aware that we are thinking things, this is a primary notion which is not derived by means of...

To begin with a slightly pedantic point: logic doesn't actually give us very much knowledge at all. Logic tells us things like that, if A is true and B is true, then A & B is true. But, in order for us to be in a position to draw that conclusion, we first need to know that A is true and B is true. And, for most ordinary A s and B s, logic isn't going to tell us that. We need to turn instead to our senses. We have five external senses -- sight, touch, hearing, smell, taste -- which tell us about the qualities of objects in our environment. And, if we use these in a cautious and regimented way, and maybe start to draw logical inferences once we do first have the raw data to work from, then we can achieve an awful lot of knowledge. But now to turn to your question: can meditation give us additional knowledge, besides that which we can get through the external senses? Yes, it surely can. Meditation can teach us what it feels like to meditate. Indeed, it might enable us to...

According to the view that Berkeley is here criticising, there are, in effect, two worlds. Indeed, there are two corporeal worlds. There is an ideal world, constituted by perceptions that have been placed directly into our minds by God, and including perceivable tables, chairs, and even human bodies (including our own), complete with all of their familiar colours, textures, shapes, sizes and other sensible qualities. Then, distinct from and causally unrelated to this, and yet in some mysterious way corresponding to it, there is a world of material substances, including one that corresponds to our sensible body, but which cannot themselves be perceived, and which have no colours, no shapes, etc. Now, on this two-worlds view, how can we be so sure that our material bodies do survive? We can't perceive them, after all: how would we ever know? Maybe our material bodies got destroyed long ago: we'd be none the wiser, and it's not clear why we should even care, because God could perfectly well carry on...

I read the question rather differently: can any amount of past and present evidence falsify a claim about the future, insofar as it still remains the future ? Of course, past and present evidence can give us ample reason to doubt certain claims that might be made about the future: but could it ever demonstratively disprove such claims? I'm not at all sure that it could. An instance of an F that isn't G can falsify the proposition that all Fs are currently G, but it can't similarly falsify the proposition that all future Fs will be G. Current evidence tells us about what is currently true or false, and to project this onto the future for the purposes of falsification is as problematic -- no more so, but also no less so -- as projecting it onto the future for the purposes of verification. And, as David Hume showed us more than 250 years ago, that there are genuine grounds for concern about the latter. The 'problem of induction' suggests that there is a certain logical circularity in any ...

I've been racking my brains over this one -- it's a tricksy little question! -- and I'm still not sure what the answer should be. Of course Nicholas Smith would be correct, if the question was about the proposition that I am being systematically deceived. But it isn't. I take it that the question is how we know that it is possible that I am being systematically deceived. Admittedly, Descartes himself does ultimately conclude that this isn't even so much as possible: but he reaches this conclusion via a rather idiosyncratic and unconvincing argument, resting on the nature of God; and, in any case, even he acknowledges that it certainly does seem to be possible. He sets up his methodological scepticism in the First Meditation (as I'm sure you know), pointing to things like optical illusions, dreams, and the possibility of an evil demon. Many of the same points could be made about each of these arguments: but, for simplicity's sake, I shall just take the one about illusions. So, for...

I'd certainly agree that qualities like goodness and badness aren't really features of the world as it is in itself, so much as attitudes that we project onto it. And it does indeed follow from this that such attitudes are neither accurate nor inaccurate, since there is no objective quality out there to which they might either conform or fail to conform. So, if optimism and pessimism simply meant regarding the world as mostly good or mostly bad, then they would not generate any inaccuracy. But there's more to optimism and pessimism than that: they also tend to give rise to specific expectations about the future. Optimism might lead you to believe that you're going to win the lottery, land your dream job, find your soulmate, and live happily ever after. Pessimism might lead you to believe the opposite. And those beliefs about future events certainly will be objectively accurate or inaccurate, depending on how things actually turn out. My suspicion is that excessive optimism and pessimism are both likely to...

One suggestion that philosophers have come up, for measuring people's degrees of certainty, is to relate it to their willingness to place bets. Of course, there are all kinds of factors that undermine this approach: in the real world, some people avoid gambling altogether for ethical or religious reasons; some might not regard it as worth the effort of betting at all, when the prospective reward is tiny; and, in certain cases, it is hard to conceive who could possibly qualify as the arbiter of whether the bet had been won or lost. But, abstracting away from all of those problems, suppose that we agree that a person's betting inclinations are an accurate guide to their level of confidence. If someone is only willing to place a bet on the truth of a certain proposition when the offered odds are very long, that shows that they are very unconfident. They need the prospect of a very large return to justify risking their stake. On the other hand, if someone is willing to place a bet at very short odds, that...

The argument of the Meditations goes as follows: first, Descartes establishes his own existence as a thinking thing; then, purely by considering the content of his thoughts, he establishes the existence of God; then, by reflecting on the nature of God and discovering that He is not a deceiver, he finally establishes the existence of other things. He still concedes that his senses might not reliably show him the way bodies really are, but he feels that he can at least rest assured that they do indeed have properties like size, shape and motion or rest. "They may not all exist in a way that exactly corresponds with my sensory grasp of them, for in many cases the grasp of the senses is very obscure and confused. But at least they possess all the properties which I clearly and distinctly understand, that is, all those which, viewed in general terms, are comprised within the subject-matter of pure mathematics." Now, there is plenty of scope for criticising this or that step in Descartes' overall...

There is a certain irony in seeing such a question posted online, typed in via a computer (or, for all I know, maybe some even more cutting-edge piece of handheld technology). Because, if wise men and women, the best part of a century ago, hadn't developed the principles of quantum mechanics, there could be no such things. At least not in anything like their current form: we'd still be on valves and transistors, or even cogs and pulleys... themselves the off-shoots of yet earlier scientific research. As for those hospitals you mention, had it not been for scientific research into human biology, they wouldn't have any treatments to offer their patients (in which case, it really wouldn't matter if their budgets were to be taken away altogether!). Gene therapy, for instance, clearly would not have been able to get off the ground if its developers had not possessed any conception of a 'gene' or understood the structure of DNA. But that is something that we owe to state-funded scientific research. It is...

We have to take care over the interpretation of positive assertions about fictional characters. Consider the sentence "Harry Potter wears glasses". There seems to be a sense in which this is true. We might wish to say, for instance, that Harry Potter wears glasses but Ron Weasley does not. But there seems to be a different sense in which it is not true. We might wish to say that John Lennon really wore glasses, but Harry Potter doesn't. He can't really wear glasses, because he isn't a real person at all. The second kind of claim is just the literal sense we use in ordinary discourse about real things. When we make the first kind of claim, by contrast, we are indulging in a sort of verbal make-believe, pretending to go along with the fiction for the sake of our discourse. We might sometimes opt to make this explicit by prefacing our claims with an expression like "Within the fiction..." or "According to the story...". Of course, most of the time we'll leave this unspoken, but only because we are...