I posted a reply simultaneously with David's excellent one: it is perhaps just about worth leaving these two remarks here. (1) An atheist certainly need not "take a position on god's existence ahead of time and argue it dogmatically". Someone can reject theism because they come to think that we have no good reason to accept the theistic hypothesis, and very good reasons to reject it. In fact, that is a common enough intellectual trajectory for people brought up in some religion: their eventual atheism is (at least by their lights) the result of weighing up the arguments, pro and con. Such an atheist might be misguided in her assessment of the weight of the arguments, but is hardly being dogmatic. (Nor indeed need every theist count as dogmatic, either.) (2) "Must a philosopher, in order to maintain integrity, put every principle on the chopping block?" Well, certainly we should stand willing to revise cherished views, if that's where the preponderance of evidence and argument takes us....

Indeed, there are all kinds of commentaries written on the works of the Great Dead Philosophers, at various levels of sophistication. But it isn't clear to me why "the average person" would particularly want to read the works of the Great Dead Philosophers -- unless gripped by the idea that those works are somehow full of timeless pearls of wisdom. But that's not a happy idea. Those old works are, of course, very much creatures of their times, responding to intellectual concerns of their times (concerns which might overlap with ours, but which are also very different in subtle and complex ways), and typically bringing to bear all kinds of hidden assumptions of their times. That's why the Great Dead Philosophers can often be so baffling: they can seem to talking about issues that we half-recognize, but often in ways that initially make little sense. And that's why we need the commentaries, to help us see where our predecessors were coming from. (Think for example just how much philosophy over the...

It is rather difficult to believe that you have correctly describe your assigned task -- is it really to write at length about the notion of being in the Sophist without consulting any commentaries or interpretative essays? Well, not to beat about the bush, that project strikes me as simply ludicrous . You need all the help you can get if you are to work your way into a text some two and half thousand years old (in fact, I take it you are relying on a translation which has already made some interpretative moves that themselves raise issues): it is just absurd to pretend otherwise. Unless, I suppose, the point is to reveal to you the impossibility of the enterprise and make you appreciate that relative beginners need the commentators and the philosophical interpreters -- but then that is a pretty dumb way of getting you to see what is already an obvious truth.

You certainly don't need to be able to do original research in maths to be able to work on the philosophy of maths. But you will need to be able to follow whatever maths is particularly relevant to your philosophical interests. How much maths that is, which topics at which levels, will depend on your philosophical projects. For example, compare and contrast the following questions (not exactly a random sample -- they all happen to interest me!): "Is our basic arithmetical knowledge in any sense grounded in intuition?" Evidently, you don't need any special mathematical knowledge to tackle that . "Can a fictionalist about mathematics explain its applicability?" Again, I guess that acquaintance with the sort of high school mathematics that indeed gets applied is probably all you really need to know to discuss this too. "Just what infinitary assumptions are we committed to if we accept applicable mathematics as true?" Here you do need to get more into the maths, and know quite a lot about...

I'm not quite sure what is meant by "sublime insight"! But anyway, serious philosophy involves negotiating your way around thickets of argument . Philosophical originality is a matter of finding new moves to make (or breathing new live into old moves) in argued debates that have usually been developing and deepening for many years, in some cases for thousands(!) of years. Generations of philosophers have explored the options on (as it might be) the liar paradox, or the free-will problem, or the nature of consciousness, with ever-more sophistication, piling distinction upon distinction, argument upon argument. And yes, of course, lots of progress is made -- refining the options, working out their costs and benefits, and often engaging with the relevant science (or work in logic, etc.) as that develops. Now, it is hard enough for graduate students who've devoted five, six, or more years studying philosophy to start making much progress -- they have to get to grips with so much first, in order...

I'd say: if you've done a maths course or two already, then you should have learnt some lessons about arguing rigorously and giving absolutely clear gap-free proofs. Doing further courses won't teach you any more about that. So if you are not going to specialize in the philosophy of mathematics, a little maths in addition to some logic is already enough. If you want to work eventually in the philosophy of mind and language, then much better to do some courses on scientific psychology, neuro-biology, and linguistics.

Jennifer Church points out a couple of types of a case where irrationally formed beliefs (or degrees of belief, in the over-confidence case) can promote our welfare. Sure there are such cases. But that doesn't affect the original point at stake. There being a few cases doesn't undermine the point that in general false beliefs (because of their content!) are unlikely to lead to successful action,* and so irrationally formed beliefs -- being likely to be false -- are not in general likely to lead to actions which get us what we want. And that is enough to explain why we should in general care a lot about forming our beliefs in a rational way. Which in turnis enough to counter the original questioner's worry that philosophy"uses as its main tool a mechanism [rational thought] that is theopposite of what is most important to us": in general ,rational belief-formation matters for getting whatever is important tous. *Indeed, some attractive views about ascribing content to belief...

Just a footnote to Mark Collier's helpful post. I actually said that irrationally formed beliefs are not likely to lead to actions which get us what we want (rather than cannot get us what we want). And that claim is enough to explain why we should in general care a lot about forming our beliefs in a rational way . Which in turn is enough to counter the original questioner's worry that philosophy "uses as its main tool a mechanism [rational thought] that is the opposite of what is most important to us": in general , rational belief-formation matters for getting whatever is important to us. Even if pockets of irrationality, episodes of self-deception, etc. can -- by good fortune -- happen to promote our welfare.

"Often the questions seem to me of the utmost seriousness, but a serious response doesn't seem fashionable." The implication seems to be that serious answers aren't much in evidence here. Which is an extraordinary thing to say. For there is a really remarkable amount of good, patient, serious, philosophy here in the answers from my co-panellists. To be sure, their answers are often enviably zippy, witty, done with a light touch, with memorable examples. But seriousness in philosophy isn't at all the same as solemnity. As to the question: facts aren't the sort of thing that are rational or irrational. It's beliefs, belief-forming policies, methods of argument, desires shaped by our beliefs, the actions they lead to, and the like (and the people who have beliefs, belief-forming policies, etc.) which are rational or irrational. But the facts are the facts, and that's that. Some facts are really difficult to get our heads around intellectually (like the facts of quantum mechanics). Some facts,...

There's no settled usage for the term "naturalism" in philosophy. But I guess that most of those who think of themselves as naturalists would say that we should recognize the sciences as the best way of finding out about the world and "refuse to recognize the authority of the philosopher who claims to know the truth from intuition, from insight into a world of ideas or into the nature of reason or the principles of being, or from whatever super-empirical source. There is no separate entrance to truth for philosophers."* On this view, philosophy's questions may be more sweeping than those of the special sciences or concern the relationships between different special sciences (and perhaps other forms of enquiry), but the methods of good philosophy are continuous with those of science. Now, that's still not very specific, but you can already see that naturalism understood this way involves something a lot more than just unfriendliness towards the supernatural. You could cheerfully endorse the...