Yes, "Occam's Razor" is just as relevant and just as appropriately applicable when deciding whether or not to believe in a divine being as in any other domain of rational enquiry. Why shouldn't it be? But the principle is a qualified one: it only tells us not to multiply entities beyond necessity (it doesn't say "don't multiply entities", full stop). Applied to the case of religious beliefs, it says: don't postulate djinns or dryads, cherubim or archangels, or fully-fledged gods, unless there is strong reason to do so . But of course, some believers in God (as traditionally conceived) think there are strong reasons for postulating the existence of such a being. And in so far as they think that they ought to have such reasons, they are still conforming their belief-formation to the principle encapsulated in Occam's Razor (but, contra the previous response, I wouldn't say that Occam's Razor is itself a reason for their theistic belief -- their reasons are e.g. an argument from design or...

"In some ways one might welcome the fact that they are being brought up by one parent in such an unusual and distinct manner, as compared with the majority of their peers." Oh, really? I think not. The kids are being subject to child abuse of a rather nasty kind (how else should we describe telling children that their greatgrandmother is going to be damned to hell?). Of course, saying that doesn't settle how you should respond to the abuse. I agree with Oliver Leaman at least in this much: future influences are likely to counteract some of the effects. A healthy teenage dose of sex, drugs, and rock'n'roll will probably do wonders. Still, you don't want your kids getting too caught up in some superstitious farrago in the meantime. What to do? I'd suggest some cheerful urbanity and gentle mockery (after all, kids rarely like to think that they are being uncool and rather silly ). But why not try some philosophy too? Press the obvious questions with wit and good-humour when the occasion arises: ...

This is a straightforwardly empirical question which needs an empirical, data-based, answer (not an arm-chair, philosophical one!). It would be interesting, then, if some panelist knows about any relevant research. I conjecture, though, the answer goes something like this: If by "philosopher" you mean something like "university teacher of philosophy", then yes, as a group they are less religious than the general population. But that isn't especially because they are philosophers, but because there tends to be less religious belief among people educated to PhD level in general. But that is a conjecture, and I await refutation!

Perhaps this just reflects that the notion of fallacy (in the broad sense) is used in a fairly catch-all way. Let's say (as a first shot) that a fallacy is someflaw in the structure of an argument which prevents its givingrationally persuasive support for its conclusion. And let's distinguish that from the narrower idea of a deductive fallacy, a feature of a supposedly deductively valid inference which prevents its being so. Deductive fallacies are fallacies in the broad sense. But many fallacies in the broad sense are of course not deductive fallacies -- for example, fallacies in various kinds of inductive reasoning. The case of a "question-begging" argument like "P, therefore P", is another sort of case where the argument doesn't involve a deductive fallacy, but the structure prevents the argument giving any rationally persuasive support for its conclusion: so it is deemed to be a fallacy in the broad sense.

I'd separate the question whether mathematical statements are (often) existential from the question of the status of set theory. (Sure, we can construct faithful proxies inside set theory for most of the structures that mathematicians are interested in. But it is a moot question whether this makes set theory foundational in any good sense at all.) Now, many mathematical statements are pretty uncontroversially not existential, but have the form "if anything is A it is B ". So the theorem that anything which is a finite division ring is commutative doesn't tell us that there are such things as finite division rings, but only what they must be like if they do exist. But of course many other common or garden mathematical theorems certainly do look existential. "There are an infinite number of prime numbers" looks existential -- and it is naturally read as implying that there are prime numbers (lots of them!). "There are four regular star polyhedra" looks existential --...

Just a footnote to Marc Lange's response (which seems spot on to me). It is worth adding that in serious analytical philosophy there is actually a good deal more agreement on arguments than there might appear to be at first sight, and there is a good deal of pretty secure knowledge. For what often emerges from the to and fro of debate is essentially something of the form "If you accept A, B and C, then you'd better accept D too". Then one party might endorse A, B and C and conclude that D; and another party might think D is unacceptable, and conclude that one of A, B, or C must be wrong. And another party again (me, often!) might not know how to respond. [A trite example. If you accept act utilitarianism plus some other things, it seems that you should sanction the sheriff hanging an innocent man if that is the way to stop a riot in which more innocent people are killed. Some bite the bullett, some think so much the worse for utilitarianism.] Now, there may indeed be a loud disagreement between...

Well, why should an "average" person (whoever she is) care about the history of Venetian convents in the sixteenth century, or about the genetics of mice, or about large cardinal axioms in set theory, or the geology of the Caucasus mountains, or Italian linguistics? No special reason! Why should it be any different for philosophy? Why indeed should the man in the street care about the limits of a priori knowledge, or about whether we should be structuralists about the natural numbers, or what the correct theory of conditionals is, or whether the theory-theory is better than the simulation theory about how we ascribe mental contents, or ... Again, no special reason at all. Of course, philosophers' in-house questions can have their roots in "what is ..?/how is it possible that...?/can we know whether ...?/what should we do ...?" questions of broader appeal. But then in-house questions from historians and scientists, say, ultimately have similar roots. And there is no particular reason...

One thing that can happen is this. Someone asks an inchoate, perhaps rather muddled, question. A respondent -- operating in the approved housestyle of analytical philosophy -- disentangles the issues, and having separated out a crisply formulated question or two, responds briskly to them with clinical precision (well, we try!). And, it can be tempting to think, something important is lost in the process. What lay behind the question -- the depths, so to speak -- are somehow being ignored, and the response doesn't really address the posed worry. So it can seem that the questioner is being fobbed off with BS. Maybe that is your feeling? But one of the hard lessons when you start philosophy is the realization that behind one's inchoate and confused half-formed questions is often just ... confusion. It is usually not so much a question of hidden depths as muddy shallows. And it can take some time before the penny drops that the analytical philosopher's answers are disentangling the real issues. Are...

"To every thing there is a season, and a time to every purpose under the heaven" (Ecclesiastes 3:1). There are occasions when it might be appropriate to talk and argue about atheism, or about vegetarianism, or global warming, or liberalism, or the Welsh rugby team, or Portishead's new record, or whatever else grips you, and other occasions when it certainly wouldn't be. Just going around, trying to convince people of your views, willy nilly, out of season, is not to treat others with much respect, nor is it likely to be very productive. But I take it that isn't what's being suggested! The issue, I imagine, is: if you have come to believe that some widely shared, deeply held, view is wrong (perhaps damagingly wrong), then should you press your contrary arguments on appropriate occasions, even if people are prone to get a bit upset/offended? Should you, for example, when the occasion is suitable, advance your atheistic arguments even if it rocks the boat? Well, why not? It is only through...

Actually, the presumption here is wrong. It isn't the case that "much of philosophy is concerned with providinga rigorous foundation to truths which are otherwise intuitive anduncontroversial". In particular, that isn't the case in the philosophy of mathematics. Of course, famously, Frege tried to show that the basic laws of arithmetic (and hence the proposition 1+1 = 2) can be derived from the laws of logic plus definitions. But he did this in order to defend the claim that arithmetical truths are analytic, true in virtue of logic alone, and so explain why those truths are necessarily true and why they necessarily apply to everything. He didn't claim that, prior to his attempted derivation of 1+1 = 2 from pure logic, no one knew it to be true. Rather we weren't in a good position to see clearly the sort of truth that it is, analytic according to Frege. Unfortunately, one of Frege's putative laws of logic turned out to lead to contradiction, and his foundational edifice crumbled (though neo...