Teams, surely, cannot exist without individuals to play on them, but it isn't obvious to me, anyway, that teams don't "really" exist. It was the same team that won the World Series in 2004 as had last wonit in 1918, so there has to be something more to a team than just acollection of players. Teams can gain and lose players, change locations and ownership, even change names, and yet it can be the same team. The question you are asking can perhaps be clarified if we introduce the idea of a fusion , which is a notion from merology, the logic of parts and wholes. Suppose we have a bunch of objects, say, a shoe, a tennis ball, and a neutron star. The fusion of these objects is, by definition, simply the "sum" of these three objects. It's tempting to say that it is the object whose only parts are the shoe, the ball, and the star, but that's not quite right, because the parts of the shoe are also parts of the fusion. Moreover, the scattered thing consisting of half the tennis ball and the sole of...

This question could mean two different things, depending upon what's meant by "convincing him that he does". If what's meant is that one convinces the person to want the product, so that, in the end, the person really does want it, then I don't see why that should be objectionable. People change their minds about things all the time. But the tone of the question suggests a different reading, on which, even after being "convinced", the person doesn't really want the product. In that case, it seems as if what one has done is simply to manipulate the person, to arrange the situation so as to make it difficult or impossible for h'er to act on h'er considered preferences. And that, yes, seems very objectionable indeed.

This is an incredibly complicated question. One question we might want to ask is what's meant by "justifying" a law of logic. I'll do my best to ignore that question here. It's tempting to say that one can't justify anything without using the laws of logic, but that is arguably too strong. I think my belief that there is a computer in front of me is justified by my perception of it, and I doubt that the laws of logic have to be invoked there. Moreover, it is not obvious that the laws of deductive logic have always to be invoked even when justification is somehow "inferential". Often, they will, but, again, it's not clear they always must be. What is meant here by "laws of logic"? Do we mean such generalizations as that, if a conditional is true and its antecedent is also true, then its consequent is true? Or do we mean to count what we'd otherwise call instances of logical laws, such as "Either Dubya likes popcorn or Dubya does not like popcorn", as "laws of logic" for the purposes...

Lots! There are certain things for which philosophy obviously would not prepare you terribly well: Graduate study in physics, for example. But beyond these obvious sorts of cases, there is nothing you cannot do. Probably the single most popular career for philosophy majors is the law: A significant proportion of students at Harvard, where I taught for 14 years, went on to law school after graduating. However, in my years of teaching, I have known students who went to business school, who went into business directly, who became writers of fiction or artists, who went to medical school (of course, they also did the pre-med requirements), and so on and so forth. So, as I said, studying philosophy closes very few doors. Studying philosophy prepares one quite well, then, for a whole range of careers. A study done some years ago (I can't remember by whom) showed, in fact, that businesses are particularly keen on philosophy majors. The reason, I believe, is that studying philosophy teaches you how to read...

See question 27 for some relevant remarks.

I'm not sure what's meant by "natural" here. But the numbers e , i , and π are the numbers they are, and are related as they are, quite independently of how we choose to do mathematics, just as the stars are hot balls of fiery gasses whether or not anyone regards them as such. Whether Euler's Equation (see question 393 ) plays any important role in our mathematical theories is, on the other hand, a consequence of how we choose to formulate them, and so one might ask why we should choose to formulate mathematics as we do instead of some other way. But again, this question is no different, in principle, from the question why we should accept the astronomical theories we do. Mathematicians have, and can give, good reasons for formulating analysis in the way they do, and there are sometimes disagreements about how best to proceed. These disagreements get resolved (or not) on broadly mathematical grounds. One or another formulation leads to a fruitful way of conceiving the problem space; others do not...

Dan says that he wouldn't say that whether e i π = -1 isn't "'independent of how we choose to do mathematics' because it does depend on how we choose to define exponentiation for complex numbers". But to what does the emphasized "it" refer? Presumably, to the claim that e i π = -1. But we really should not say that whether e i π = -1 depends upon how we have chosen to define exponentiation. Whether " e i π = -1" expresses a truth depends upon how we define exponentiation, but whether e i π = -1 does not, just as whether "3+4=7" expresses a truth depends upon what "3", "4", "7", "+", and "=" mean, but whether 3+4=7 does not.

There's also this point: If one has shown that, if X is true, then Y is true, then one has proven, without making any assumptions, that, if X, then Y. One might say that, if one has given an argument, then one has assumed that it is legitimate to use whatever principles of argument one applied in the argument. But, as Lewis Carroll once observed in a famous paper titled "What the Tortoise Said to Achilles", that claim leads to the conclusion that argument itself is impossible. We have to distinguish between an argument's justifiably employing certain principles and its assuming that those principles may legitmately be employed. I take it, however, that the question was not concerned with whether we can prove this kind of claim but, perhaps, with whether we can prove anything that would actually be regarded as contentious. Can we prove, for example, that abortion is immoral? or, conversely, that it is morally permissible? In such cases, the answer may well be "No".

One can slightly simplify Mark's case as follows. Suppose one believes that p and also believes that q . One therefore believes that p and q , but also that p or q . The disjunctive belief surely must be "based upon" one's beliefs in the disjuncts, but neither of them is essential: The belief in the disjunction would survive failure to believe either disjunct. Should we say that your knowledge is "based upon" a false belief? It seems to me that, in this case, one has two independent reasons for the disjunctive belief, namely, the beliefs in its disjuncts. The reasons are independent in several senses: (i) one could have each reason even if one did not have the other; (ii) as I'm imagining the case, anyway, one's justification for the beliefs in the disjuncts is independent of one's justification for the othe belief; (iii) each reason is sufficient, on its own, to underwrite knowledge in the disjunction. As it happens, however, only one of the reasons actually underwrites...

For those who do not know (I had to look it up...it's been a while!), this equation follows from a more general equation, known as Euler's Equation: e xi = cos( x ) + i sin x . Complex analysis is applied in many parts of physical science, and it would be surprising if such a fundamental relation did not have some physical interpretation in, say, fluid mechanics. But I don't know to what extent complex exponents are in play there. There is another question that arises simply within mathematics and that might have an interesting answer, namely: Is there some natural geometrical interpretation of Euler's equiation. I don't know the answer to that question, either.

There need be nothing inconsistent about this position. The first view, that abortion is morally impermissible, is a moral or ethical view. The second view, that each woman should be permitted to choose for herself whether to have an abortion, is a political view, one about what laws a state ought to have. The combination istherefore consistent so long as one denies that, if it is morallyimpermissible to do A, then it ought to be illegal to do A. Whymight one deny that claim? One might well ask why one should endorseit, but there is a better answer. Suppose one believed the following: Alaw must be justifiable on the basis of principles that cannotreasonably be rejected by any citizen, where a rejection is"unreasonable" if it is flatly irrational or, more interestingly, basedupon too many particulars of one's actual situation. Inparticular, religious doctrine cannot figure in the justification ofany law, since one's finding the appeal to any religious doctrineconvincing depends...