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Logic

Is there any single genuinely correct logic or so called all-purpose logic? If not, why should we find it?

I presume that you would dismiss out of hand the following answer to your first question: "Yes, there is a single genuinely correct, all-purpose logic, and there is no such logic, and there is more than one such logic." So I take it that your question presupposes that no correct logic could allow that answer to be true. If you're asking whether there's any good reason to abandon the standard, two-valued, "classical" logic routinely taught to university students in favor of some non-classical logic, then I'd answer no . Some philosophers say that we ought to adopt a non-classical logic in response to such things as the Liar paradox or the Sorites paradox, but their arguments for that conclusion have never struck me as persuasive. I think that the Liar and the Sorites can be solved using only classical logic (and bivalent semantics), or at least it's too early to conclude that they can't be. For a much more detailed answer, you might consult Susan Haack's book Deviant Logic, Fuzzy Logic:...
Physics

Assuming that the multiverse account of the universe is true -- and every possible reality is being simultaneously played out in an infinite number of parallel universes -- am I logically forced into accepting a nihilistic outlook on life? Or is it still possible to accept the truth of the multiverse account and still rationally believe that the pursuit of life goals is both meaningful and valuable, despite the fact that every possible outcome -- or potential reality -- is unfolding somewhere in another parallel universe?

I don't think that the multiverse account implies that it's irrational to pursue life goals or irrational to believe that pursuing life goals is meaningful or valuable. For even if the multiverse theory is true, I take it that you yourself are confined to one universe, our universe. The beings very similar to you who inhabit other universes are at best "counterparts" of you, which leaves open the question "What will you do with your life?" It may be well and good if one of your counterparts works hard to achieve wisdom, promote justice, or whatever, in some other universe. But his/her hard work isn't yours and doesn't occur in your universe. We need your shoulder to the wheel here!
Knowledge

what are the requirements for knowledge?

You'll find your question very thoroughly taken up in the SEP entry on the analysis of knowledge . As you'll see there, some philosophers go so far as to reject your question on the grounds that knowledge can't profitably be analyzed into other concepts. Enjoy!
Ethics

If it is not immoral to shoot dead an intruder into one's house without asking questions, why would it be immoral to shoot dead an intruder into one's country?

I presume that by "an intruder into one's country" you mean an illegal immigrant rather than, say, an invading enemy soldier. Otherwise, I'd answer differently. Does one own one's country in the way in which one owns one's house? I think not, or else I own much more real estate than I thought. Moreover, an intruder into one's house can plausibly be assumed to be a serious threat to oneself. I don't think this assumption is as plausible in the case of an illegal immigrant, all else being equal.
Identity

Does it actually make any sense when someone claims that they wish they were born in a different era or location or to a different family? Sometimes, someone will say that they wish they'd been born in, say, 1950. Without thinking too hard about it, it seems to make sense. But if I do think about what they said, it really doesn't. Let's say we have two timelines. We have the first one in which the person says they wish they were born in 1950. And then we have the second one in which, for whatever reason, there was one more person born in 1950 that wasn't born that year in the first timeline. The problem I see is that there's really no way of linking these two people. Who's to say if they're "the same"? They'd have different experiences, different looks, and probably different personalities. I could see this maybe being resolved by throwing in the concept of a soul, but that doesn't really seem like a logically-sound option (if you and I (as souls) switched bodies for the day, would either of us be...

Excellent questions. They engage the issue of whether one's biological parentage or the time of one's birth are essential to one's identity . I doubt I can do any better than to refer you to two SEP entries that are relevant to this issue: "Essential vs. Accidental Properties" "Arguments for Origin Essentialism" I hope you find them helpful.
Identity

As far as I can tell western and Buddhist philosophers would probably agree that if at noon Jones is in London and Brown is in Paris, then Jones and Brown are not identical people, because they are discernible (in this case by location). However it seems like they would disagree in the case of Jones in London at noon and in Paris at 6 PM. A western philosopher might say that while Jones in London can be discerned from Jones in Paris, this discernment is cancelled out by the fact that the two situations don't happen at the same time, as in the example with Jones and Brown, and so Jones in London at noon is still identical to Jones in Paris at 6. Whereas a Buddhist philosopher might say that Jones in London at noon and Jones in Paris at 6 can't be identical people, not only because they are discernible by location, but also because they are discernible by time. Mustn't there be something wrong with one of these views, or both perhaps? If they're both correct then Jones in London at noon is both identical...

One thing to ask is what is being referred to by the expressions "Jones in London at noon" and "Jones in Paris at 6pm." Whatever, if anything, is referred to (denoted by) those expressions would seem to be strange: a "time slice" of Jones or a "space-time slice" of Jones. Now, some philosophers do say that such things exist, which are usually called "temporal parts" of Jones. Other philosophers say that there's no good reason to believe in the existence of temporal parts. Defenders of temporal parts would agree that the two temporal parts referred to aren't identical. But, they say, those two temporal parts can belong to a single individual, Jones, provided that the temporal parts are related (perhaps causally related) to each other in the right way. On the other hand, opponents of temporal parts can say that a single individual, Jones, has both the property of being in London at noon and the property of being in Paris at 6pm . Jones doesn't have those properties literally at the same time but...
Identity

Does the identity of indiscernibles principle indicate that, for example, a person with N number of hairs, who then loses a hair, is not identical to the person with N -1 number of hairs? Unless I'm mistaken the principle is basically that entities having all of their properties in common are identical entities, but is it also true that two entities not having all of their properties in common (like Bill with N hairs and Bill with N -1 hairs) are not identical? Can entities with different properties nevertheless be identical? If so, how can we determine that Bill and Sally aren't identical, since merely not having all of their properties in common does not exclude the possibility of identity?

You're correct that the Identity of Indiscernibles says that qualitative identity (i.e., identity of properties) implies numerical identity (i.e., just one individual rather than more than one). You then asked about the converse principle, which says that numerical identity implies qualitative identity: in other words, any individual has all and only the properties that it has. This converse principle, the Indiscernibility of Identicals, is even more secure than the Identity of Indiscernibles. Even those who challenge the Identity of Indiscernibles (such as Max Black, in his classic dialogue "The Identity of Indiscernibles") tend to accept the Indiscernibility of Identicals. As for Bill with n hairs and Bill with n -1 hairs: The defender of the Indiscernibility of Identicals would probably insist on describing Bill's properties in a more fine-grained way. For example: Bill has the property of having exactly n hairs at time t1 and the property of having exactly n-1 hairs at...
Freedom
Biology

If neuroscience were to prove that one particular person has free will, does that imply that everyone else in the world would have to have free will as well? If neuroscience tests show that not everyone has free will, how would philosophers explain that other than redefining free will?

I notice that your question leaves "free will" undefined, so let me propose the definition found at merriam-webster.com: "the ability to choose how to act; the ability to make choices that are not controlled by fate or God." I presume that no one imagines that neuroscience will prove that some of our choices are controlled literally by fate or God. So if neuroscience is to show that some or all of us lack free will, neuroscience must show that some or all of us lack the ability to choose how to act or the ability to make choices. I don't think we need neuroscience experiments to show us that some people lack free will in the sense just defined: for example, people who are in the midst of drug-induced mania or a psychotic episode. To show us something we didn't already know, neuroscience would have to show that people in general typically or routinely lack free will. Some neuroscientists do claim to have shown that, but their arguments are woefully unpersuasive (in my judgment and in the...
Logic

Recently I asked a question about logic, and the answer directed me to an SEP entry, which then took me to two other SEP entries, on Russell's paradox and on the Liar's paradox. Frankly, after having read through those explanations, there was a glaring omission from every cited philosopher, and I wondered if everyone was overcomplicating things: I don't see how there is any "paradox" at all. Consider the concept of a "round square" or a "six-sided pentagon." Those are nonsensical terms, because of the structural nature of the underlying grammar. They are neither logical nor illogical, they are merely grammatically inconsistent at the fundamental level of linguistic definition. The so-called "paradox" of Russell and the Liar seem to me to be exactly the same kind of nonsensical formulations: the so-called "paradox" is merely a feature of the language, these concepts also are grammatically inconsistent at the fundamental level of linguistic definition. Russell's "paradox" is just as "paradoxical" as...

If I may, I think you're being a bit too dismissive of Russell's paradox. We start with the observation that some sets aren't members of themselves: the set of stars in the Milky Way galaxy isn't itself a star in the Milky Way galaxy; the set of regular polyhedra isn't itself a regular polyhedron; and so on. It seems that we've easily found two items that answer to the well-defined predicate S: is a set that isn't a member of itself . Naively, we might assume that a set exists for every well-defined predicate. (For some of those predicates, it will be the empty set.) But what about the set corresponding to the predicate S? This question doesn't seem, on the face of things, to be nonsensical or ungrammatical. But the question shows that our naive assumption implies a contradiction, and therefore our naive assumption can't possibly be true.
Science

My question is: does naturalism lead to scientific anti-realism? From a naturalistic perspective, there does not seem to be any Archimedean point from which to get an objective view - there is no ultimate meaning maker who can offer a “God’s eye view” of reality. Therefore, if one assumes philosophical naturalism, one must also deny the ability of science to provide objective information about the world. To quote Hannah Arendt, from a naturalistic perspective, “man can only get lost in the immensity of the universe, for the only true Archimedean point would be the absolute void behind the universe.” I really don’t see any way around this. Science, if understood as the pursuit of objective knowledge, can only stand on the shoulders of theism.

I confess I don't see a skeptical problem here. It's true that any perspective I could occupy, no matter how broad, will be my perspective when I occupy it. But that truth is just a tautology: it's implied by everything, including by theism as much as by naturalism. It makes no difference to either of those positions. Importantly, it doesn't imply that I can't achieve objective knowledge. From my perspective, elephants are bigger than mice: I perceive them that way. The fact that I perceive things that way doesn't imply that elephants aren't objectively bigger than mice, i.e., bigger than mice regardless of anyone's perception of them. Nor does it imply that I can't know that they're objectively bigger. To the objection, "But how can you know that you know this about elephants and mice?" one can reply with one's favorite theory of knowledge, which will explain how one knows anything, including how one knows that one knows that elephants are bigger than mice. In short, I don't see...

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