1. Stella is a woman and she is mortal. 2. Joan is a woman and she is mortal. 3. Liz is a woman and she is mortal...etc How many instances of women being mortal do I need before I can come to the general conclusion that all women are mortal?

the short answer: you need as many instances as there are (or have been, or will be) women. a longer answer: if what you're asking is how many instances do you need before it might be reasonable to infer that all women are mortal -- well there's no absolute answer to such a question (I would say). Partly it's about all such similar forms of reasoning -- in general, how many instances do you need in any inductive argument before it's reasonable to draw the general conclusion. Partly it's about the specific case -- what are the specific biological facts about womanhood (assuming that's a biological category) and mortality, which might govern how many instances are required before the general conclusion is reasonable. Partly it's a matter of social norms -- in the community you inhabit, how many instances will people require of you before they decide you are reasonable etc ..... the short answer has the benefit not merely of being correct but also being clear! hope that helps --- Andrew

How can you be confident that you're an open-minded or free thinker? Doesn't it seem likely that even the most prejudiced, dogmatic individuals view themselves as free thinkers (or, at any rate, appropriately responsive to evidence) with respect to their own views?

Good question. Could use some precision in the terms, i.e. what exactly counts as being "open-minded" or "free thinking"? some of these terms might have very specific meaning in certain contexts, but not clear what meaning you're assigning to them here. Also the heart of your second sentence/question is empirical, really -- we'd have to do a carefully devised survey to find out how people generally self-conceive. One of the really deep philosophical questions you have a finger on here might be this: is it possible to reconcile "open-mindedness" with "having reached a firm rational conclusion" -- since the degree to which you are convinced (rationally) by P is the degree to which you are no longer "open to" not-P. So even if you are initially "open" to all sorts of arguments/evidence, once you've made up your mind you are now "closing yourself" with respect to counter arguments/evidence. Of course, one might hold that an "open-minded" thinker is one who continuously revisits the issue, revisits the...

What do you call this type of argument? Stephen Hawking recently boycotted a prestigious Israeli academic conference, and many were quick to call him a hypocrite: "If you’re going to boycott Israel, please remove the Intel chip that allows you to speak" I was just wondering if there was a name for this type of argument? Thanks in advance.

This is a really excellent question, and a complicated issue. First coming to mind might be the ad hominem fallacy, if you take the argument to be something like "because you are a hypocrite, your position vis a vis boycotting should be rejected." But I don't think that many of the people who have raised this argument mean it in that fallacious sense (though perhaps some do). A deeper analysis might be that this isn't really an argument at all -- it's merely an attack on Hawking's character (w/o inviting others to reach any conclusion about the boycott in question). This seems reasonable: if Hawking truly is committed to some very general boycott of Israel, Israeli achievements, academics, etc., then consistency may well require that he give up his chip ... so this point calls attention to his 'boycott of convenience': portray himself as supportin a general boycott (perhaps to receive acclaim from those on that side) when he fact he doesn't. But then an even deeper analysis (perhaps intended by some of...

In scenarios where the metaphorical glass is either half-full or half-empty, so to speak, are there any compelling rational reasons to come down on one side or the other? Or is a person's optimism or pessimism just a character trait independent of rational thought?

Well, there may be certain ontological commitments or implications of choosing one over the other. (This would be independent of one's "optimism/pessimism"...) For example, in the medievals there was extensive discussion about what constituted "real being" and what only seemed real, but was in fact either derivative or conceptual or negative being. So, for one example, it was argued that light is "real" while shadows, which SEEM real, can be "thought of" as if they were real, in fact are not: shadow is merely the absence of light. A lot could ride on this: all real being (for example) would require a cause of its being, while derivative or non-beings would not. So if there is light you need to explain what causes the light; but if there is darkness, you don't need something which "generates" darkness, since darkness is not a real existent, but the absence of the real existent. That being said, there is something to say for preferring the glass being half-full -- for then you are speaking of what...

Can madness be explained in terms of irrationality?

If so, then we are all mad -- for much empirical research demonstrates the endless ways in which all of us behave irrationally practically all the time ... (see best-selling work by Dan Arielly, for example!) ... And anyway, surely we are familiar with at least the literary/cinematic stereotype of the absolutely even-keeled, coldly rational/logical/calculating supervillain who is simply MAD in his desire to conquer the world etc.... I don't know if there ever have been individuals fitting that description but the sheer fact that it's conceivable suggests that we conceive of "madness" in terms other than "irrationality" .... And finally, perhaps, "irrationality" is a matter of how well the means we pursue are apt to obtain the ends we pursue -- but madness (at least in that stereotype case) is a function only of the status of the ends themselves .... so a mad "end" might be pursued very rationally, or a sane "end" might be pursued very irrationally .... hope that's useful! ap

One popular take on religious belief is that it can only be arrived at through faith, rather than considerations of evidence or reasons. Even admitting there to be a paucity of evidence in favor of god's existence, we are to suppose that one may legitimately believe in him nonetheless. A theist who not only holds this view about, but claims to believe in god in precisely this way, would then seem to claim something like the following: "Although I recognize there to be insufficient evidence for the existence of god, I still believe in him." I want to ask whether we can really take this claim at face value. Set aside the question of whether religious belief is justified from an objective standpoint, and ask whether it is really coherent for someone to genuinely believe both (1) that X, and (2) that there is insufficient evidence for belief in X. To me this notion has a paradoxical flavor, and I wonder if what is really going on in here is something else entirely. That is, I wonder whether theists of the...

Great question! ... Several terms could use more careful specification/definition, esp. the notion of "sufficient" evidence, not to mention "evidence" itself for that matter ... One route might be to explore "comparative confidence" -- eg Descartes claimed via his ontological argument (Med. 5) that he could be as certain of God's existence as he is of mathematical truths -- pretty 'sufficient' evidence (or argument) there! ... More realistically we might explore whether our confidence in God's existence is comparable to our confidence in the dictates of science, or of common sense about the physical world, or even of belief in the existence of a physical world, or the general reliability of our senses -- the latter three in particular have often been challenged by philosophers, and it may well be an open question whether there is "sufficient evidence" to accept any of of those three, so we might compare the degree of evidence in God's belief with degree of evidence there .... (When confronted with...

Are there any logically possible situations in which acting in accord with probability would not be logical? Is probability the ultimate logical guideline?

You might want to google 'newcomb's problem' or 'newcomb's paradox' -- one way of analyzing such cases is to conclude that the rational thing to do (in those circumscribed cases) is to act irrationally ... That sounds sort of close to a kind of case, which I gather you have in mind, where it is rational to pursue the less probable outcome .... (re the latter, I gather you have in mind something like this: you desire outcome x, and path A is more likely to obtain x than path B, all else being equal, and yet it is more 'logical' or rational to pursue path B .....) AP

Is there something fallacious/illogical about how the theist/atheist debate in the west is currently framed? Let me illustrate my point with an example. Consider the Irish legend of Fionn mac Cumhaill. In making sense of this legendary figure we could start by analysing arguments for and against his existence. We could count, for example, the "Giant’s Causeway" in N.Ireland to be evidence in favour of his existence. But this approach seems slightly misguided. We have jumped right into debating his physical existence without first looking at the sources of the Fionn mac Cumhaill tale. A knowledge of Celtic mythology and folklore would reveal to us the mythological nature of this figure and it consequently becomes illogical for us to debate his actual physical existence. Is the same true of the existence of the Biblical god "Yahweh"? Once we analyse the sources of the Bible, particularly noticing the influence of Near-Eastern mythologies and the development of monotheism from its henotheistic context, we...

great point -- I think I largely agree -- but there may, still, be some disanalogy between the two cases (the Irish legend v. 'God') -- namely once you begin describing God's various attributes (omnipotence, creator, goodness, etc.) then it may well be plausible to seek independent/direct evidence of his existence in the world around you, independent that is of the 'source' of the 'tale' itself -- and that might not be equally true, or true to the same degree, as in the Irish legend case -- after all, you may not need to know who thought of the idea of a 'Creator' God first in order to evaluate, perfectly rationally, whether the world around us exhibits any evidence of intelligent design or creation -- of course, when you do learn more about the 'source' of the idea of God that may increase your skepticism about the truth of the claim that God exists, but it does seem to me that claim may also be evaluable independently of its sources -- best, Andrew

How is it that almost anything that any religious preacher says to prove the existence of God turns out to be typical examples of one or the other of the well known logical fallacies? How is it that they don't realise this simple fact when all such fallacies are enumerated in the Web in such sites as the Wikipedia? Are human being basically very irrational creatures ?

just to supplement Charles's very fine response: first, yes human beings are very irrational, but you can find irrational humans in every domain, theist and atheist ... if you're looking for 'rationality,' or at least approximations thereof, or at least 'reasonableness,' you probably don't want to be listening to local preachers (or even local 'atheists', whatever that means) -- you want to be talking to more philosophically inclined people (which is more or less what Charles is getting at) -- and there are plenty of deep, engaging, provocative things to think about, with respect to religion -- not merely the existence of God but many related topics -- even when you constrain yourself to trying to be 'rational' ... (I've tried to collect a number of these in my recent book 'The God Question,' which presents what a lot of famous philosophers have said on the subject of religion ...) hope that's helpful -- best, AP