I read about the sorites paradox, especially "what is a heap?" and was a bit puzzled about the reasoning. Isn't it fairly straightforward to say, "fiftenn grains is not a heap" and "fifteen thousand grains is a heap" and then say, "even if we cannot give a single precise number where "not a heap" ends and "is a heap" begins, we can narrow down the range within which it occurs, right? In other words, a sort of "bounded fuzziness" applies, where we know for sure what is a heap and what is not a heap (the "bounded" part) while we cannot say exactly where the transition occurs (the "fuzziness" part). It also reminds me of Alexander the Great's solution to the Gordian Knot problem, in a way. People are getting confused because they are using the wrong tools, not because of the nature of the problem itself. the argument seems reminiscent of the supposed paradox about achilles and the tortoise, you can calculate the exact time at which Achilles catches and passes it.

The sorites paradox -- the paradox of the heap and similar paradoxes exploiting more important concepts than heap -- is a terrific topic. It's great to see people thinking about it. You wrote, "we cannot say exactly where the transition occurs." Some philosophers would respond, "It can't occur exactly anywhere, because heap (or bald or tall or rich ...) isn't a concept that allows exact status-transitions. To say that there's an exact point of status-transition, even a point we can't know or say, is to misunderstand what vague concepts are." Some philosophers would also object to your suggestion that the fuzziness can be "bounded," if by that you mean "sharply bounded." They'd say that any boundary around the fuzzy cases must itself be a fuzzy boundary: like the boundary between heap and non-heap , the boundary between definitely a heap and not definitely a heap isn't precise to within a single grain. (This phenomenon is usually called "higher-order...

According to the Stanford Encyclopedia of philosophy Schopenhauer was one of the first philosophers to advocate for the idea that the universe was not something "rational" What is an "irrational" universe then? Is there a difference between a universe being beyond the grasp of human reason and saying that the universe is "irrational"? Does he mean to say that the universe can do things that are illogical such as have square triangles?

I'm also no scholar of Schopenhauer, but from what I remember he's claiming that our universe is at bottom non-rational -- fundamentally arising from causes rather than from reasons . The universe isn't, on this view, irrational if that means 'capable of reasoning but bad at it' or 'containing logical inconsistencies'. I take it that Schopenhauer is rejecting a theistic or deistic view that sees reason (and not causation) as fundamental to our universe. I agree with Professor Manter that neither Schopenhauer's view nor the view he's rejecting allows for inconsistent things such as square triangles. Can I take this opportunity to grind an axe? Advocates of a supernatural (theistic or deistic) origin of our universe often claim that only their view -- rather than metaphysical naturalism -- gives us hope of achieving a rational understanding of the universe by investigating it. They say that only if the universe was rationally intended can we hope to understand it. I think the...

I'm just getting into philosophy, thanks in no small part to this site! I was discussing it with a friend recently - a friend I admire as hard-working, intelligent and someone who challenges himself - and found out that he was actually a philosophy major in college (now he's a businessman). Naturally I was excited, but I was quickly discouraged as he explained that he had given up doing philosophy long ago and had no interest in it. When I asked him why, I received the following explanation, which confused me and I'm hoping to gain some clarity on it from this site. I hope it's not offensive to any of the professional philosophers who read this site, though it is of course anti-philosophy, since it was his reason for abandoning it. In any case, he said that he gave up reading/doing/thinking about philosophy - and he specified "analytic philosophy" as the culprit - saying that, although he found that the material he read was highly intelligent, he was nagged by a persistent feeling (one he ultimately...

As hard as it was for your friend to explain his dissatisfaction with philosophy, it's even harder for me to be confident that I really understand just what his complaint is. But I do think that a philosophical work fails to a significant degree if an intelligent reader comes away feeling that the author missed the boat or can't speak to anyone but specialists. Indeed, I support this website because I think philosophy is far too important not to be better understood by the general public. I'd encourage your friend to try harder to articulate the reasons he came away dissatisfied by this or that particular work of philosophy: to translate his feelings as carefully as he can into reasons and examine them. That exercise by itself very much counts as philosophizing. From time to time (although not as often as the public probably supposes), contemporary academic philosophers take up an age-old human concern like the meaning of life. An outstanding example, if by no means always easy reading, is...

Can a white male ever legitimately speak about racism or sexism?

As a white male myself, I guess I'm answering your question in the affirmative by even presuming to post an answer to it at all. Surely the question you asked is so broad that no one could reasonably answer it in the negative. Racism exists: some people or practices are racist. Sexism exists: some people or practices are sexist. There: I've said it, and I defy any reasonable person to deny my assertions or call them "illegitimate." Now, it's a harder and more interesting question exactly how much a white male can say about racism or sexism without losing credibility on those issues, but I'm inclined to think that a white male could, in principle, become the world's foremost authority on racism and sexism, and the burden of proof would rest with anyone who said he couldn't speak legitimately on this or that particular aspect of those issues: we'd be owed an explanation why not.

Is modern philosophy too abstract? I mean when it asks questions about being does it ask questions that about any kind of being when perhaps it could be asking question about the particular kind of being that we live in? I guess you could say the answer is no because philosophers deal with questions about science and science is about the world we live in. But is the kind of being of science the only "concrete" form of being that philosophers can ask about? I personally think that their is more to being than either physics or hyper-abstractions that only look at being in terms of temporarily, causality and quantity, etc. Is a disagreement about what we think is "being" perhaps one of the central splits between analytic and "continental" philosophy?

I tend to use the noun 'being' as a count noun: You and I are both beings; maybe the number seven is also a being (although of a different kind from you or me). I'll therefore use the words 'existence' or 'reality' for what you seem to refer to by 'being' in your question. When it asks questions about existence or reality, modern-day philosophy -- including analytic philosophy -- ranges as broadly as you like. Philosophy doesn't confine itself to the world described by natural science. Often philosophy asks about the existence or reality of non-natural beings such as abstract objects (maybe numbers, properties, propositions) or concrete, non-natural beings (maybe immaterial minds or souls, maybe God). It's true that analytic philosophers tend to respect natural science, but they shouldn't (and largely don't) think that all legitimate questions are questions for natural science. Furthermore, contemporary philosophy -- perhaps especially analytic philosophy -- asks about ways that reality could...

I seem to remember the "heap paradox" being a very old one (given a heap and repeatedly removing a single grain of sand, when does it stop being a heap?). Yet I don't ever recall hearing a solution to it. No doubt there are different views of things, but is there at least a generally accepted solution to this paradox?

You asked, "Is there at least a generally accepted solution to this paradox?" Not by a long shot! The paradox of the heap (and its cousins that use other vague concepts) is in my opinion one of the greatest unsolved intellectual problems. It has generated a huge philosophical literature, and it's very much a topic of current philosophical debate, but I have yet to see a proposed solution that even comes close to being satisfactory. For starters, you might take a look at these entries from the Stanford Encyclopedia of Philosophy: SEP, " Sorites Paradox " SEP, " Vagueness " Best wishes as you work your way through this daunting -- but inescapable -- problem! I think you'll find it repays your careful thought even if you don't end up much closer to a satisfying solution.

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