How do we know if we are reasoning correctly? Consider, for example, this witty “proof” that a ham sandwich is better than eternal bliss: Nothing is better than eternal bliss. But, surely, a ham sandwich is better than nothing (despite Leviticus 11:7). Therefore, a ham sandwich is better than eternal bliss! Admittedly, the error in *this* argument may be easy to see. But, of course, in more subtle lines of reasoning it is much harder to check for bugs. How, then, can we be confident, in general, that our arguments are fallacy-free?

I've generally become pretty good at detecting fallacious reasoning, both my own and that of others. I'm not perfect, to be sure, but pretty good. So, overall, it seems that, in any given case, my chances of having committed an undetected fallacy are fairly small. How small depends upon the complexity of the reasoning. If I'm trying to prove a complicated theorem, I may have to go over the proof repeatedly, spell out all the details, etc, before I can convince myself that the proof is correct. So maybe in those cases, at least initially, the chances I'd committed a fallacy are higher than they would be otherwise. But that seems all right. It just means that, to be justifiably sure that I've not committed a fallacy in any given case, I may have to do different things: a lot in some cases, maybe nothing in others. But if I have done those things and come to the belief that my reasoning is correct, then I see no particular reason the belief should not count as knowledge. Of course, one can push...

Richard Dawkins has written: That which can be asserted without evidence, can be dismissed without evidence. Is this valid, logically? If not, what are the consequences? He is talking about religious belief, i.e., belief in some God or other. Dawkins' statement makes sense to me but can any logical argument invalidate it? Would he then have to retract his statement, or is there a gray area between semantics and logic?

I don't know the context of this claim, nor why Dawkins thinks---I take it he does think this---that no-one has any "evidence" for religious belief. Most theistically inclined epistemologists of religion, in the analytic tradition, anyway, think we do have certain kinds of evidence for belief in God. Dawkins might not find the evidence impressive, or he might disagree as to the evidential facts themselves, but it would be a parody of religious faith to think people believe on absolutely no basis. Just for example, suppose one is some kind of coherentist. Then you might think belief in God forms part of an overal "theory" of the world, and the evidence one has for it is that this theory is coherent, more successful than alternative theories, etc. You've got the same kind of evidence for your belief in God, ultimately, as for anything else you might believe, though belief in God, in such a system, will be deeply embedded, like very high-level theoretical claims, rather than towards the periphery, where...

When is somebody a "competent speaker" with a certain word? For instance, what do I have to know or do to be "competent" with the word "water"? I suppose I don't have to know that it is H2O.

Well, there's no short or agreed answer to this question. Not even some kind of a vague consensus. On one end, you have people who think that having once upon a time heard the word "water", and as a result having added it to your vocabulary, is sufficient for competence. On the other end, there are people who think that there is a sense of "complete" or "independent" competence, which is supposed to be the basic sense, on which you have to be able to individuate (distinguish, more or less) water from all other things in order to be competent. This doesn't mean that you in practice have to be able to do this but rather that you know distinguishing characteristics of water. There's another view, too, probably mine, according to which there's no such thing as a "competent speaker". This phrase seems to suggest that there is some norm of competence that some of us meet and some of us do not, and I don't myself know where this norm is supposed to come from. Of course, if one wants to stipulatively introduce...

Does there exist a type of thing which could be called a mathematical fact? That is, are there true entities which would exist even if there were no minds to do the maths to discover and describe them? In other words, it is the understanding of all numerate human beings that the square root of 81 is 9. Would the square root of 81 still be 9 if there were no minds, human, numerate or otherwise?

There are lots of physicists who study the history of the universe: how the universe began, for example. When they do their calculations concerning, say, the evolution of the universe in the few seconds following the big bang, they do seem to assume that the square root of 81 was 9 even then, when there were no minds. And more generally, it's rather hard to see how the existence or non-existence of minds could affect what the square root of 81 is. Might 81 itself not have existed had there been no minds? How precisely did the existence of minds bring it into being? Was it just impossible before there were minds for there to be 81 stars in a certain region of space? I think not.

My question is about analytic philosophy. Is it true that analytic philosophy aims to approach philosophy ahistorically, and that when asking questions like "what's the meaning of life" it considers itself to be dealing merely with language puzzles and not with a legitimate question that actually matters in real life? If so, it would seem a strange place for philosophy to have evolved to. Then again, I'm sure strange mutations have happened in philosophy in the past, and have gained a large following. Is it possible that the people who practice analytic philosophy today, especially those who don't question it rigorously as a method and simply see it as the only lucid approach - is it possible that these people will ever come to see it differently, as containing some sort of fundamental mistake within itself?

There are really several questions here, and there isn't really any simple answer, since "analytic philosophy" isn't sufficiently unified for there to be any single approach. If there is such a thing as "analytic philosophy", then it is more a tradition than a school. Some analytic philosophers do approach philosophical questions with little regard for history. Not all do, and I guess I'd be something of an example. Some analytic philosophers have also regarded most, or even all, philosophical questions as the result of some kind of linguistic or conceptual confusion. And there was a time---half a century ago now---when that was the dominant approach. But times have changed, and there are now few analytic philosophers who would endorse it. What is widely believed is that making progess on philosophical problems often depends upon getting clear about the concepts involved, and experience has taught that close attention to the language used to express those concepts can be invaluable. But that's...

This is more a technical than a philosophical question, I think. When referencing Greek philosophers, what is the significance of providing the original Greek word(s)? (e.g., “Your eagerness [PROTHUMIA] is worth much if it should have some right aim.”) Is there something about Greek (as opposed to other foreign languages) or about philosophy that makes this useful? As a reader, what am I supposed to be doing with these?

The original words are there because translation is an exceptionally tricky business, and it's often important, from a scholarly point of view, to know what the original words were, so that one can judge the correctness of a translation, or note that two words that are cognates in English are also (or are not) cognates in the original. This is more common, I think, in classical philosophy, though you certainly will see it in any sort of historical study of sources originally in another language. But if so, then that is only because classical Greek is an old language. It's not because Greek is particularly difficult.

Are there any interesting arguments for the existence of God from the existence of beauty? i.e., because there is beauty, we know there is God?

My understanding is that Kant argued in something like this fashion. Or, at least, that Kant thought that it was through the contemplation of beauty that we could experience the divine. I don't myself see that any sort of real argument will be forthcoming along these lines, but I do understand the sentiment. Certainly there is music that makes me particularly conscious of God: Plenty of Coltrane, for example. But for myself, I think my deepest sense of the divine emerges from contemplation of the men and women who have made great contributions towards the emergence of justice in the world. To me, that is, the best argument for the existence of God is the existence of people like Dr Martin Luther King, Jr. I don't expect that to be convincing to anyone else, though.

If my mum hadn't got pregnant with me and I'd never been born, would I be someone else? Sorry that isn't very well phrased, I hope you understand what I mean.

I think most philosophers nowadays would say, no: If your mother had never gotten pregnant, then you simply would not have existed. It's not a pleasant thought, at least not for you, but there you have it.

There is a lot of evidence that reincarnation is a fact, yet the proposition and evidence are ignored or rejected by western society. What evidence would have to be presented for it to be accepted?

I can well imagine that there could be such evidence. But for the evidence to be truly trustworthy, it would have to be collected by people who were neutral, more or less, on what it was supposed to demonstrate, and the evidence would have to be in some sense replicable, and to stand up to critical scrutiny by reasonably neutral parties. So far as I'm aware, there is no evidence for reincarnation that meets anything like this sort of standard, however.

Consider a first-order axiomization of ZFC. The quantifiers range over all the sets. However, we can prove that (in ZFC) there is no set which contains all sets. can we make a _model_ for ZFC? The first thing you do when you make a model for a set of axioms is specify a domain, which is a set of things which the quantifiers range over......this seems to be exactly what you can't do with ZFC. So what am I missing?

This kind of concern has had a good deal of influence on research in logic over the last several decades. It was, for example, a major force behind Boolos's work on plural quantification. More recently, there has been an explosion of research on what is called "absolutely universal" quantification: quantification over absolutely everything, including all the sets there might be. As you note, there is no "model" of such discourse, in the usual sense; that is, the "intended interpretation" of such discourse cannot be a model, in the usual first-order sense. As Dan noted, one can talk about proper class models, but there is another line of inquiry, deriving from Boolos. One way to develop this approach is to take the domain of the interpretation to be a `plurality', so that the quantifiers range over the sets ---not the set ofall sets, or a class of all sets, but simply over the sets, whatever sets there may be. The details have to be worked out here, but it can be done, and in a reasonable way, too...