Dissolving a philosophical problem involves challenging the presuppositions -- often unrecognized presuppositions -- that give rise to the problem. Consider two examples near to my own heart. Newcomb's Problem in decision theory has generated enormous controversy since it was first brought to the attention of philosophers in 1969, and the dispute over the "correct solution" to the problem shows little sign of being settled anytime soon. But some philosophers think the problem is unsolvable because it's ill-posed . On their view, it's a pseudo-problem, perhaps because it's based on the false presupposition that we can understand the set-up of the problem in the first place . They think the problem is therefore one to be dissolved rather than solved. A second example is the perennial question "Why is there something rather than nothing at all?" Many philosophers have spent tremendous energy concocting elaborate metaphysical answers to that question. But I think the question, as it's usually...

You asked, among other things, "Why is the intelligibility of an idea about the universe...a criterion for determining the truth-value of the idea?" I wouldn't say that an idea's being intelligible to us is a criterion for its being true: that would be thinking too highly of ourselves! But an idea's being intelligible to us is necessary for our determining (i.e., ascertaining) its truth-value and even for our entertaining the possibility that it's true. If an idea is unintelligible to us -- if we can't make any sense of it -- then we can't make sense of the assertion that the idea is true, or even possibly true, or false, or even possibly false. I think we can understand the claim that some unspecified aspects of reality are unintelligible to us. But we can't understand the suggestion that some particular unintelligible claim about reality might be true (or false, for that matter). That limitation applies to science just as much as to philosophy. I suspect that the book you're reading is...

It sounds to me as if you're not a moral relativist according to the usual definition of the term. I don't know any utilitarians who classify themselves as moral relativists. On the contrary, utilitarians regard the moral status of actions, institutions, etc., as objective rather than relative to individuals or cultures. For example, many utilitarians condemn the factory-farming of animals as objectively immoral because of the suffering it causes, even though the practice is widely accepted in at least the developed nations. By contrast, moral relativism says that any moral assertion, such as the assertion "Factory-farming is wrong," is true or false only relative to the culture (or maybe the individual beliefs) of whoever makes the assertion.

I recommend reading the SEP entry on "Supertasks" available at this link . It contains helpful answers and references to further reading.

It's not clear to me how your example counts as "induction based only on reason." As I understand it, the process you imagine involves asking other people to think about the problem and then share with you their advice. Even if you stick entirely to your own thoughts about the problem, they'll no doubt be informed by your experience with practical problems of a similar kind. Either of those methods is at least partly empirical rather than "based only on reason." You would indeed be drawing conclusions inductively rather than (purely) deductively. As for the reliability of the results, I prefer a method in which various possible solutions to a type of practical problem are actually tried out rather than merely thought about. As anyone who's tried DIY renovations can tell you, there's a world of difference between thinking about how a practical problem should be solved and seeing how it actually gets solved once you put your thoughts into practice!

Many quantum physicists say that lots of events occur without being caused to occur. But let's assume that they're wrong and that every event needs a cause. One way to answer your challenge is to allow for an infinite regress of contingent events: a series of events stretching back endlessly in which no member is logically or metaphysically required to happen. I don't see what's wrong, in principle, with an infinite regress of events. One might reject such a regress on the grounds that "time couldn't stretch back forever," but I see no good reason to say that it couldn't. But even if time couldn't stretch back forever, you can still squeeze infinitely many events into a finite time if they "telescope" so that the time between them decreases geometrically as you go back. We needn't treat time itself as a cause in any of this. Indeed, if (as almost all philosophers have held) some events are contingent, and if every event has a sufficient explanation why it occurred rather than not, then an...

Yes! But bear in mind that a paradox is an apparent contradiction, an apparent inconsistency, that we're tasked with trying to resolve in a consistent way. For example, a particular argument implies that the Liar sentence ("This sentence is false") is both true and false, and a similar argument implies that the Strengthened Liar sentence ("This sentence is not true") is both true and not true. Usually it's our conviction that those arguments can't be sound that impels us to seek out the flaw in each argument. So too for other famous paradoxes, such as the Paradox of the Heap. Paradoxes abound! But that doesn't mean that contradictory situations do. Now, some philosophers, such as Graham Priest, say it's a mistake to demand a consistent solution to every paradox. Priest says that the Liar Paradox has an inconsistent solution, i.e., the Liar sentence is both true and false: it's both true and a contradiction. So Priest would say that not only do paradoxes actually occur but inconsistent...

It certainly looks like the height of rationality for you to believe that at least some of your beliefs are false. Yet, as you point out, there's no particular belief of yours that you regard as false. Any given belief of yours you regard as true; otherwise, it wouldn't be a belief of yours. This pair of attitudes gives rise to what's usually called the "Paradox of the Preface." One place to start looking is the SEP entry on "Epistemic Paradoxes," available here , which contains both discussion and references.

You've raised a large and complex set of issues. I'll address just one part of one of your questions. It seems to me that the burden of proof rests with whoever claims that good can't possibly exist without evil. For one thing, the claim implies that the monotheistic God is impossible, since God is supposed to be perfectly good and independent of anything distinct from himself (or at any rate independent of evil). Moreover, it's not as if every property is instantiated only if its complement is instantiated. The property of being self-identical is instantiated by everything, but necessarily its complement, the property of being self-distinct, is instantiated by nothing. The property of being physical is instantiated by many things, but it's at least controversial whether the property of being nonphysical is instantiated at all.

You asked, "Does this mean that [these particular] abstract notions are divisible?" I'd say yes . But that doesn't mean they're physically divisible; instead, they're numerically divisible. Abstract objects have no physical magnitude, but that doesn't mean they can't have numerical magnitude. The key is not to insist that all addition, subtraction, division, etc., must be physical. I'd say that the number 1 (an abstract object) is different from the cm (a unit of measure) in that the cm depends for its existence on the existence of a physical metric standard: for example, a metal bar housed in Paris or the distance traveled by light in a particular fraction of a second (where "second" is defined in terms of the radiation of a particular isotope of some element). In a universe with no physical standards, there's no such thing as the cm and nothing has any length in cm. By contrast, the number 1 doesn't depend for its existence on anything physical. Apples are physical, material objects. Units...