Could questions in the philosophy of language in principle be answered in terms of the structures of the human brain? Might we imagine, for instance, pointing at a certain lobe and saying "Well, this shows that Russell was wrong about denotation"?

Well, I don't know if it could be quite like that, but one dominant approach to contemporary linguistic theory holds that questions like, "How do descriptions work in natural language?" are ultimately questions about the psychology of competent speakers. Assuming that (cognitive) psychology in some sense or other ultimately reduces to facts about the brain, it follows that the question how descriptions work in natural language is, in some sense, a question about the brain. But the nature of the relation between psychology and brain-facts is the difficult question here.

I am an American who has embraced the ideals of the Enlightenment, specifically the inherent value, perspective, and rights all humans on this planet. How do we reconcile these values with contemporary ideologies, specifically Zionism, that posits a racially, religiously unique group with "overriding" rights?

It's no doubt true that Zionism as such doesn't necessarily insist that Jews are "unique" and so deserve "overriding rights". That said, there's a case to be made that "national ideologies" are intrinsically racist, on the ground that the very notion of a "nation" that is being deployed here is intrinsically racist. It is certainly true, for example, that there are people who regard the French as constituting a "nation" that deserves its own homeland, but most of those people would generally be regarded as extremists, and the same goes for British and German nationalists. If so, then nationalism is fundamentally inconsistent with the Enlightenment values the questioner mentions. Whether any of what I've just said is true, however, is hotly debated. In particular, the question to what extent "shared community values" might inform the basic structure of a political system has been much discussed over the last few decades. As good a place to start as any is Michael Walzer's Spheres of Justice .

Having just read Dawkins's The God Delusion I was appalled to learn how reviled atheists are in America. In Europe a person's stance (including politician's) on religion is largely irrelevant unless they draw attention to it. What is going on in America? What should skeptics and atheist philosophers do there to point out that atheism is a reasoned and logical viewpoint that doesn't presuppose immorality, etc.? It beggars belief that all presidential aspirants have to (in some cases as Dawkins remarks) probably pretend to be Christians in order to have any chance of being elected. I know of the Atheist's Wager, acceptance of which seems braver to me than blindly accepting the religious promises of heaven as dictated by those who brought you up. And what place do 'faith-based initiatives' have in an ostensibly secular government where church and state are separate under the constitution?

I agree with Eddy that atheists are indeed regarded with a good deal of skepticism in the United States, and, in particular, that an "out of the closet" atheist would have a hard time being elected to national office. That said, I think his own comments reveal that he is almost as ignorant of the varieties of religious belief as are the believers he is criticizing. I think it's probably safe to say that a majority of the people at my church do not "believe in a God with supernatural powers ... or in special creationor in immaterial souls", with the only question I'd leave open being how many of us believe in some form of continued existence ("life" is probably not the correct term) after death. To borrow from the words of someone who wrote recently in Time discussing Barack Obama's religious beliefs, for many relgious folks, God is more a matter of mystery than of miracles.

The clarification is welcome, but the reason for my remark was simply that I was putting these two remarks together: (i) "I think that an avowed atheist would have absolutely no hope ofelection to President or likely to any major office in any (or almostany) state, regardless of his or her other attributes orviews..."; (ii) "Once one recognizes that atheists can and do believe these [sensible] things, itis difficult to see why choosing not to believe in a God withsupernatural powers...should count against one's ability to bean effective political leader or most anything else." Unless I'm missing something, (ii), read against (i), strongly suggests that an atheist is someone who rejects supernaturalism , etc, which rather strongly suggests that a theist is someone who endorses it. Perhaps (ii) was badly stated, and should have said simply, " is difficult to see why choosing not to believe in a divine being should count against...".

Is this argument valid?: A) The sky is blue. therefore B) 2+2=4 It may not seem that the premise is relevant to the conclusion. But an argument is supposed to be valid if its premises cannot be true without its conclusion being true. B is a necessary truth (we can imagine a world in which the sky is red, but a world in which 2+2=5 is just incoherent). B is always true, therefore B must be true in cases in which A is true. So this must be a valid argument. There's something horribly wrong with this thinking, but I can't figure it out.

It may not help very much, but the argument you describe is not (usually considered to be) logically valid. It's true that 2+2 could not have been other then 4, but almost no-one nowadays would suppose that it was logic that guaranteed that fact. So we might say that the argument is "mathematically valid", since there is no mathematical possibility of its conclusion being false while its premise is true. One other thing worth saying is that one shouldn't confuse the question what implies what with the question what you should infer from what. It does indeed seem silly to infer that 2+2=4 from the premise that the sky is blue (or pink, or green!). But it only follows that "the sky is blue" doesn't imply "2+2=4" if you assume that correct implication should always entail reasonable inference. But you shouldn't assume that.

Logic textbooks which offer a system of natural deduction containing a so called "rule of replacement" restrict this rule to logically equivalent formulae. Only these can replace each other wherever they occur. I have often wondered why this is so. It seems to me that, having e.g. p q and p&r as lines in a proof (as premisses, say), would allow one to soundly infer q&r directly from them by replacement of p by q in p&r, without requiring that p and r be logically equivalent. In less formal situations, for example, when solving a math problem, I find myself (and others) doing this all the time. I've searched the internet for this, but couldn't find any answer so far. Most grateful in advance for a reply.

There's a need for some care here. In classical logic, one certainly does have the rule: From A <==> B and ...A..., infer ...B..., in the sense that the former things will always imply the latter thing, and also in the sense that, in any complete system, applications of this rule could always be replaced by applications of other rules. So, in such systems, this is what is sometimes called a "derived rule". But we do not always have this rule. Indeed, there are plenty of systems in which one does not have it. A simple example is a modal logic that has the additional operator ◊, meaning "possibly". It certainly does not follow from A <==> B and ◊A that ◊B. It does follow (at least in the usual systems) if A <==> B is not just true but a theorem.

Notation: Q : formal system (logical & nonlogical axioms, etc.) of Robinson's arithmetic; wff : well formed formula; |- : proves. G1IT is always stated in the form: If Q is consistent then exists wff x: ¬(Q |- x) & ¬(Q |- ¬x) but we cannot prove it within Q (simply because there is no deduction rule to say "Q doesn't prove" (there is only modus ponens and generalization)), so it's incomplete statement, I don't see WHERE (in which formal system) IS IT STATED. (Math logic is a formal system too.) In my opinion, some correct answer is to state the theorem within a copy of Q: Q |- Con(O) |- exists x ((x is wff of O) & ¬(O |- x) & ¬(O |- ¬x)) where O is a copy of Q inside Q, e.g. ¬(O |- x) is an arithmetic formula of Q, Con(O) means contradiction isn't provable...such formulas can be constructed (see Godel's proof). But I'm confused because I haven't found such statement (or explanation) anywhere. Thank You Very Much

One thing the questioner seems to want to know is in what kinds of theories the first incompleteness theorem can itself be proved. As Peter says, the proof of the theorem is fine given informally, as almost all actual mathematical results are. But still, one might want to know: Where is this theorem provable? The answer is: Not in Q, but in fairly weak theories. It can certainly be proven in PA---full Peano arithmetic---though that hardly counts as a "weak" theory. I am fairly certain, though, that it can be proven in the theory known as "I-Sigma-1"---though I'd have to check that before betting my life on it. Part of the reason I'm sure about this, though, is that I-Sigma-1 is susceptible to the second incompleteness theorem. What you get in such cases is (e.g.) that PA |- Con(PA) --> G PA ; but then, if PA |- Con(PA), then PA |- G PA , and PA is inconsistent, by the first incompleteness theorem, and this works for any theory T that extends Q and is capable of proving: Con(T) --> G T . ...

Most atheists presumably believe that there is insufficient evidence to justify belief in God. What I want to ask is: is there ANY evidence? Or none at all? Is there anything that the panelists might point to and say, "this counts as evidence that God exists"?

Sorry, I didn't see this one, or I'd certainly have said something about it. Unsurprisingly, different people have different views about what the evidence for God's existence might be. And, for that matter, very different conceptions of who or what God is. Most of the suggestions Jasper considers are familiar and ancient, and still popular. And I'll agree with him: pretty unconvincing. But there are other views. Speaking just for myself, I'm not really sure if I'd say there was any "evidence" of God's existence. It's not that I don't think there's any reason to believe that God exists. I do. It's rather that I don't think I could describe my reasons in terms of "evidence". I suppose that much of my own conviction lies in my personal experience of the divine. But of course I don't expect anyone else to find that convincing, and such experiences aren't like (say) visual experiences, where you can just say, "Well, look for yourself". And I wouldn't want to model this, as some philosophers have, on...

Are philosophers generally less religious than the general population? I'm not talking about the old-school ones, just the ones that are still alive.

This is a thorny topic, and I doubt there is any detail concerning philosophers per se. But for some data, see the Harris Poll on Americans' Religious Beliefs , which found that people with post-graduate degress are somewhat less likely to believe in God. But the difference isn't very impressive: 85%, as opposed to 90% for the general population. There are larger gaps concerning belief in miracles, which is perhaps not so surprising, either.

I have an opinion I'd like some feedback on. My view on war is generally that it's a bad idea. Aggression against another country or similar entity is difficult to justify. However the fact remains that an outside force can invade and make war on your country. My opinion on this is that an invader should be destroyed completely. Ruthless exploitation of any weakness, and use of any weapon is completely justified to expel the threat, at least until they have ceased their aggression and given back any territory gained. After that it would be difficult again to justify continuing the use of ruthless tactics in an act of aggression towards your enemy in their own territory. My idea of using complete force against an aggressor comes from that you didn't make war on them. They brought war to you. For example, if you were being violently mugged, it would be justified to kill your assailant. However, it would be unjustified to go out and kill someone just because they might mug you. Or, if you were mugged and...

This much I'd agree with: There's a big difference between defending oneself against aggression and undertaking aggressive action oneself. What's not so clear is that one can (let alond should) do absolutely anything in response to aggression. Take the mugging case. It isn't at all clear that, if you are being violently mugged, then you are justified in killing your assailant. If killing your assailant were the only way you could protect yourself, then it would presumably be justified---or better, excusable. And if that were not the only way, but if you were to defend yourself in other ways that were justified and were to kill your assailant more or less accidentally, then you would not be blameworthy. But you do not get to kill someone just because they are mugging you. (And how violent exactly does the mugging have to be?) The same is true of war, even justified defensive war. Civilized nations have long recognized limits to the conduct of war. The use of chemical weapons, for example, is...

Considering Descartes' malicious demon idea, is it possible that we could be manipulated in such a way so as all our beliefs are false? I'm thinking that we'd already need some true beliefs in order to have false ones. To be fooled into thinking that pig beards are shorter on Tuesdays I'd have to have true beliefs about pigs, beards, length, and Tuesdays for example. Can I infer then that the overwhelming majority of our beliefs must be true?

This kind of argument has been made by many different philosophers. Two that come immediately to mind are Ludwig Wittgenstein and Donald Davidson. Their considerations are broadly along the lines of: To have any beliefs at all about pigs, beards, etc, I must have some (mostly?) true beliefs about them. For Davidson, the argument involves considerations about what he calls"radical interpretation", the process of making sense of anotherthinker. But that just seems to me to answer the wrong question. The issue isn't about what's involved in making sense of someone. Maybe you do have to agree with the person about a lot of things to do that. The issue concerns what it is to have beliefs. Jerry Fodor has written at length about a great conflict between broadly "pragmatist" theories about the contents of beliefs and, uhh, non-pragmatist theories. According to Fodor's view, for example, being able to have beliefs about pigs involves being in the right kind of causal relation with pigs, and there isn't any...