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If there is a category "Empty Set" it has to have the property "nothingness". Thus it is not propertyless - contradiction?

As far as I can see, the definitive property of the empty set is not nothingness but instead emptiness : It's the one and only set having (containing, possessing) no members at all. The empty set can be empty, in that sense, without itself being nothing. So I see no threat of contradiction here. Indeed, the empty set can belong to a non-empty set, such as the set { { } } , which couldn't happen if the empty set were nothing.

Is their really an objective answer as to where the world came from?

I take it you presume that there is an objectively true answer to your question (otherwise, why ask it?). I can't see how there could fail to be an objectively true answer concerning where the universe came from, and the objectively true answer may be that the universe never came from anything because the universe (in one form or another) has always existed. Of course, the existence of an objectively true answer to the question is, by itself, no guarantee that we will ever come to know the answer.

Does logic rule out the possibility that someone could travel into the past and affect events so that they turn out otherwise than we remember them?

Does logic rule out the possibility that someone could travel into the past and affect events so that they turn out otherwise than we remember them? No, because our memory of those events could be mistaken. But: Does logic rule out the possibility that someone could travel into the past and affect events so that they turn out otherwise than they in fact did? Yes, so far as I can see.

What drives all the squabbles about free will and determinism? Is it anything more than a desire to reward and to punish, especially to punish?

What you're asking is really an empirical, psychological question -- What motivates the various sides in a particular controversy? -- rather than a question that philosophers, as such, are well-equipped to answer. But I'll hazard an answer anyway. Take some carefully, even painstakingly, considered decision, such as U.S. president Obama's decision to order the May 2011 hit on Osama bin Laden. If that decision wasn't one for which the agent is morally responsible -- i.e., morally liable to praise or blame -- then I don't know what could be. But according to the incompatibilist side of the debate, if determinism is true then Obama bears no more responsibility for his decision than someone high on PCP bears for his/her decision to try to fly from the roof of an apartment building. According to incompatibilism, if determinism is true then all decisions are equally unfree, equally lacking in responsibility, regardless of how sober, well-informed, and deliberate the decision-maker is. The philosophical...

Do words only have the power that we give them?

By "power" in this context, I take it you're referring to the psychological, rhetorical, or political power of words. I can't see any source of such power except us humans. That isn't to say that the power is unreal, only that words possess no internal magic, contrary to what humans in general used to (and some still) believe. Nor is it to say that any individual can render words powerless simply by deciding to. A racial slur, for instance, might induce people to physically harm the person targeted by the slur even if the person targeted decides to regard the slur as having no power over him or her.

Has American philosophy lost interest in metaphysics?...thanks, Arnold

No, indeed. I don't know which periods of American philosophy you're comparing when you ask whether American philosophy has lost interest in metaphysics. But if you check the current tables of contents of general American philosophy journals such as Nous , Philosophical Studies , and Philosophy & Phenomenological Research -- to say nothing of more specialized American journals such as The Review of Metaphysics -- you're sure to find articles in metaphysics written by American philosophers. You'll also find plenty of American-authored metaphysics articles in philosophy journals that are headquartered outside America, such as Mind , Analysis , and Erkenntnis . If anything, the interest of American philosophers in metaphysics has increased compared to, say, the middle decades of the twentieth century.

As all logical arguments must make the assumption that the rules of logic work, is there any way to derive the laws of logic?

As you suggest, all logical arguments (and hence all derivations) depend at least implicitly on laws of logic. So I can't see any way of deriving any law of logic without relying on other laws of logic. Nevertheless, we can derive every law of logic, provided we're allowed to use other laws of logic in our derivation. We needn't fret about our inability to derive a law of logic while relying on no laws of logic, because the demand that we do so is simply incoherent.

When a person, and especially a talented one, dies young, people sometimes mourn not just what they have in fact lost, but what might have been. But is mourning what might have been predicated on the belief that things could have been otherwise? And if someone is a thoroughgoing determinist and thinks that there's only one way things ever could have turned out, would it be irrational for such a person to mourn what might have been?

One way to interpret the mourner's state of mind is this: the mourner is thinking (optimistically) about the life the young person would have led had he/she not died young. That state of mind is consistent with believing that the young person's death was fully determined by the initial conditions of the universe in combination with the laws of nature. The deterministic mourner might even recognize that, in mourning the young person's death, the mourner is committed to regretting that the Big Bang occurred just the way it did or that the laws of nature are just as they are: for only if the Big Bang or the laws of nature (or both) had been appropriately different would the young person not have died young. Furthermore, determinism allows that they could have been different. Determinism doesn't say that the initial conditions and the laws of nature are themselves causally determined; that would require causation to occur before any causation could occur. Although the deterministic mourner's regret...

Can we perceive the natural laws, which have shaped our ability to perceive?

I'm not sure I would use quite the verb "perceive" to describe our cognitive grasp of natural laws, but I don't see any reason why we can't discover at least some natural laws, including those that have shaped our ability to perceive (or discover). That is, I don't see any reason why a natural law's having shaped our ability to perceive should make that natural law especially hard for us to discover. It's not as if we should think of natural laws as having purposely shaped our ability to perceive in order to keep themselves hidden from us.