I used to be very interested in the philosophy of mind. And the fascination was in trying to understand how our ordinary talk about the mind ("folk psychology" as we sometimes say) fits together with what explorations in neurobiology, cognitive science and artificial intelligence tell us. These days, I spend most of my time thinking about the philosophy of mathematics. And again the fascination is trying to see how technical work in various areas of logic (and set theory, category theory, etc.) interrelates and throws on questions about the nature of the world of mathematics and our knowledge of it. How does it all hang together? Some of us just like plugging away at pretty narrow areas of enquiry (doing specialist neurobiology, or the technical work in some area of set theory, say): others among us get gripped by the project of standing back a bit and trying to fit things from a number of narrow areas together into bigger pictures. The American philosopher Wilfrid Sellars said that the task...

"I have been to my university's department, talked with philosophy grad students and felt that they do not care genuinely about philosophy really." Then your feeling is almost certainly wrong. The great majority of graduate students care passionately about philosophy. After all, they are usually particularly smart people who have chosen not to go on to law school or do MBA s or whatever (leading to some very lucrative career), but decided to try to stay on in academia, trying to work on some tough philosophical problems that have gripped them. Why else do that other than because they care about the subject?! What may be true is that the grad students you talked to don't seem to care much about what you think of as "philosophy". And there is indeed something of a disconnect between some of the connotations of "philosophy" in the everyday use of the word, and the academic discipline that most of those grad students are engaged in. (There are connections too, of course: the varied use of...

In my experience, philosophers -- I mean, at least, those earning a crust as professionals in universities -- are a pretty cheery bunch. And why not? We are actually being paid good money to have intellectual fun . We like talking and arguing. A lot. Preferably, in the excellent tradition of The Symposium , over a drink or three. (I've been at more than one philosophy conference where the beer has run out, unaccustomed as the bar staff were to academics with our level of boozy argumentative conviviality.) And indeed, what we are having fun doing is mostly not that worth taking too solemnly: nothing very serious in life hangs on getting the ontological status of numbers right, or deciding whether there is a mereological sum of any collection of objects, or wondering whether knowledge is special state of mind, or whatever your favourite current philosophical problem is. So, as they say, just enjoy!

Perhaps there are three different issues hereabouts, There's the question of whether the best route in for beginners is via texts (written material) or via lectures and other media. There's the question of whether first to struggle with " original " texts (meaning articles or books which were/are supposed to be making novel contributions, whenever they were written) or to approach issues via textbook treatments and other works more or less intended for beginners ("supplements", to borrow Lisa Cassidy's word). There's the question of whether to approach things via " original " historical texts (meaning now, in particular, writings by the Great Dead Philosophers) or to start with more contemporary materials. On (1), lectures might be fun and helpful because they tend to be more relaxed and unbuttoned than written texts: but if you are going to study philosophy then, inevitably, you are going to be doing a lot of reading from the very start....

You are quite right that Gödel's (first) incompleteness theorem attracts all kinds of bizarre "interpretations". Various examples are discussed and dissected in Torkel Franzen's very nice short book, Gödel's Theorem: An Incomplete Guide to its Use and Abuse , which I warmly recommend. My guess is that a main source for the whacky interpretations is the claim that has repeatedly been made that the theorem shows that we can't be "machines", and so -- supposedly -- we must be something more than complex biological mechanisms. You can see why that conclusion might in some quarters be found welcome (and other technical results in logic generally don't seem to have such an implication). But as Franzen explains very clearly, it doesn't follow from the theorem.

Apart from the fact that we have pairs each time, I'm not sure I see any other pattern here (even a "family resemblance"). But one thing is clear, the pairs are certainly not all "dichotomies" -- for a dichotomy divides things into two non-overlapping kinds. And while, if we believe Frege, objects ("referents") and concepts are different quite kinds of things, sets and their members can of course be the same kind of thing (since a set can have other sets as its members). Again, while we might suppose physical objects and their appearances are different kinds of things, wholes and their parts needn't be.

It is perhaps worth asking whether our commonsensical beliefs that the regularities in nature will be much the same tomorrow as today and that it is wrong to murder someone actually need 'underwriting' or 'justifying' by philosophical theories? What could that possibly involve? And what would underwrite those philosophical theories? If you are a sceptic about induction, say, why not equally be a sceptic about any theory that purports to justify it? If I come up with some long involved argument whose conclusion is that, indeed, we are right to believe that the regularities in nature will be much the same tomorrow as today -- as occasionally philosophers have tried to do -- would that actually increase your confidence in that belief, or make it any more sensible? Will the premisses from which the long involved argument starts -- if they don't in fact already smuggle in the assumption that the future will be like the past -- actually be any more secure than the belief that they are supposed to...

Plato famously thought that you should master mathematics before you turn to philosophy. No one would quite think that these days (though it is interesting that, among my faculty colleagues, over a quarter of us in fact have first degrees in mathematics, and turned to philosophy later). But perhaps Plato has a point. For a start, it is good to first hone your skills of sharp accurate reasoning, and to practice intellectual humility in the face of really difficult problems, when working on matters that aren't too conceptually tangled (let alone often bound up with your emotions or with cultural/religious prejudices). Not that doing serious mathematics is the only way of getting in the practice, of course: doing a degree in classics is another well-trodden route! Further, outside moral and political philosophy, a great deal of the best work -- philosophy that isn't just the higher arm-waving waffle -- is closely bound up with science, in the broadest sense. To do serious philosophy of...

Read some good introductory books. Here's a list that I really must get around to updating.

A philosopher of mathematics is interested in questions like: what are numbers? what kind of necessity to arithmetical truths have? how do we know the basic laws of arithmetic are true? what about sets -- do they really exist over an abover their members? is there a universe of sets? there are various set theories, how can we decide which is true of the universe of sets? And so on. You don't have to be a working mathematian to think about these matters (though obviously you have know a little about the relevant mathematics you want to philosophize about). Nor do you have to be a logic-expert. Most mathematicians aren't interested in the philosophy of mathematics (just as most scientists aren't interested in the philosophy of science, and most lawyers aren't interested in the philosophy of law). They just go about doing their maths. And among mathematicians, a serious interest in logic is a rarity: you can certainly be a mathematician without being a logician (e.g. by being a fluid-dynamicist or an...