What we're trying to get to is the probability, given all the evidence, that A is guilty. Let H be the hypothesis that A is guilty. You're supposing that our initial probability for H is 5%, i.e., .p(H) = .05. Then we get a piece of evidence – call it E – and the probability of E assuming that H is false is 10%, i.e., p(E/not-H) = .1. Your question: in light of E, how likely is H? What's p(H/E)? We can't tell. We need another number: p(E/H). We need to know how likely the evidence is if A is guilty. And we can't infer that from p(E/not-H). Why not? Well, suppose the evidence is that the Oracle picked A's name out of a hat with 10 names, only one of which was A's. The chance of that if A is not guilty is 10%, but so is the chance if A is guilty (assuming Oracles don't really have special powers.) iI this case, the "evidence" is actually irrelevant. The crucial question is this: what's the ratio of p(E/H) to p(E/not-H)? Intuitively, does H do a good job of explaining E? And knowing only one...

One thing is clear: if everyone downloaded for free, content producers wouldnt be able to profit from their labor. One reason why I don't downloaded pirated music, movies, etc. is that I think filmakers, musicians, etc. should be able to make money by doing what they do, and I can't see what's so special about me that I should be entitled to benefit for free from what they do. That's a long-winded way of saying I think it would be wrong for me to download pirated copies. Even though the filmaker would never get Freddy Freeloader's money, if. All did as Freddy does, the filmaker would suffer and in the long run, so would we all. Having said this, I think there's an awful lot wrong with contemporary copyright and intellectual property law. It could even be (though I'm not in a position to say so) that copyright law as it stands does as much harm as good. It could even be (though I doubt it) that we'd be better off if there were no intellectual property laws and we just depended on people's sense...

I'd suggest that there needn't be a determinate answer without adding more detail. In particular, the notion of "mixing" the three collections would need to be spelled out. Suppose the "mixing" works this way: take 10 marbles from the red bag and one from each of the blue bags. Put in an infinite vat and stir. Repeat ad infinitum. (We could imagine the first operation is performed in 1 minute, the second in half a minute, the third in a 1/4 minute…) The intuitive thought is that a "random" draw is most likely to give you a red marble. (10 chances out of 12). This may seem contrived, but only because we have some other loose, unspecified idea of mixing that we're comparing it to. The point is simply that the problem, as stated, doesn't determine the answer.

An interesting question. Without trying to settle the issues you use to raise your question, I'd suggest that there's no sure-fire method to be had here, and that while philosophers have things to contribute, they don't have any sort of magic wand. Ethical conundrums come up when different ways of looking at an ethical question suggest different and incompatible answers, and when the different approaches have some serious plausibility. Many people will agree: there's something to the idea that a woman who wants the Plan B medication ought, other things being equal, to be able to get it. But many of those same people will agree that in general, people shouldn't need to violate their consciences to practice otherwise respectable professions. Put briefly, both sides have plausible starting points. This is true of a good many serious disagreements, ethical or otherwise: the right answer isn't obvious, and different answers are prima facie plausible enough to be taken seriously. So what do...

I'm not sure there's a fundamental difference between science and non-science. But the point about falsifiability isn't that a true theory can be proven false. It's that scientific theories can be tested, and we know what sorts of results would count against the theory in principle Keep in mind that even a theory that's survived a long string of rigorous tests might still be overthrown. The point of the falsifiability requirement is that we know what sorts of results would count against the theory - whether or not they ever turn up. One more point, though. It's one thing to say we know what would count against a theory. It's another to say that some particular bit of evidence would refute a theory conclusively. Things are seldom if ever that simple.

Others can no doubt give more nuanced answers, but most people (I'd be wiling to say virtually all) who earn a living depend either directly or indirectly on government-supported institutions and government-provided infrastructure for the possibility of their livelihood. This includes but is not limited to - military defense against external aggression, a police force, a court system to enforce legal rights, a public education, system, highways... A setting in which a worker can avail him/herself of none of those things is a setting in which very few indeed would prefer to work.

Sure. Even if existence is not a predicate, it's at least arguable that necessary existence is. (As Norman Malcolm pointed out years ago, there really are two versions of the argument, and the second one deals with necessary existence.) We doubt that existence is a predicate because, roughly, saying that something exists tells us nothing about what it's like. Not so for necessary existence. Not just anything could exist necessarily. The computer I'm typing on is the wrong sort of thing to be a candidate for necessarily existing thing. Assuming that some things are of the right sort to exist necessarily, necessary existence would be a predicate. Whether this is a defense of the argument all things considered is another matter. But I think the point made here is fair as far as it goes. A being that merely happened to exist wouldn't be a being than which none greater can be conceived.

How about this? A fallacy is an actual mistake in reasoning. A cognitive bias is a tendency to commit certain sorts of mistakes. Not all fallacies are the result of cognitive biases, and having a cognitive bias doesn't guarantee that you'll commit the corresponding error.

An interesting question. I'd start by suggesting that your "if and only if" is open to challenge. First the less important part for our purposes: the fact that somebody values something doesn't obviously mean it's actually valuable. Some people value terrible thing, after all. There's a chilling scene in James Clavell's novel Shogun in which a samurai takes deep, deliberate and despicable pleasure in the screams of a man being tortured to death by a torturer who specializes in optimal cruelty. The samurai clearly values the experience, but I'm not willing to say that it's therefore valuable . Still, it seems right that value has a deep connection with experiences and the beings who have them. That may seem to be all that your worry needs. In other words it might seem that something is valuable only if someone values it or, more broadly, only if it evokes the right sort of reaction in some sentient being. But this is too strong. Consider: something could be exquisitely beautiful (to take...

Good for you for taking what's right so seriously! As for general advice, a few quick thoughts. First, though utilitarianism undoubtedly provides useful insights, it's not really clear that utilitarianism always gives the best answers. A quick example: the fact that a mafia leg breaker gets satisfaction and enjoyment from his work arguably carries no weight at all in deciding what's morally best. Perhaps the utilitarian can explain this, but only perhaps. And that leads to the second point. It may be that the study of ethics tends to lead people to better moral decisions, but that's very doubtful. (Don't be so sure that the people on this panel know more than you do.) In any case, it's hard to believe studying ethics necessary for being good. Whether I'd turn to someone for moral advice and whether they've studied ethics don't have much to do with one another. But simply trusting one's gut isn't always best either; gut feelings are often wrong. So what's the positive advice? A good deal of...