I've heard philosophers talk about "dissolving" problems and questions. What does it mean to dissolve questions/problems and how do philosophers do it?

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...

I have been reading a recently published book about the existence of all things (e.g. addressing the question, "Why is there something rather than nothing?"), and am struck by an interesting issue I see in the book and others like it. The author interviews philosophers (among other professionals) who often speak about the existence of things based on what one can imagine (e.g. one imagining something about possible worlds). It seems to me that there should be some kind of theory about how thoughts relate to the universe before anyone can conclude things about its nature. I know there are philosophers who have raised the question that the "laws" that govern thought/logic may be very different than the physical laws that govern the universe (and hence whatever theories we have about the world may be nothing more than our own ideas); so why is there such emphasis placed on imagination when discussing metaphysical issues? Why is the intelligibility of an idea about the universe (e.g. whether there are many...

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...

I have often heard it argued that moral relativism prevents us from agreeing that our moral advances (e.g. civil rights, Gandhi, etc.) are conclusively good. I was of the belief, however, that moral relativism merely states that morality is a human construct and is defined by individual experience -- not that there is nothing that can be held to be fundamentally good. That is to say, I judge actions based on a utilitarian, distinctly non-theist ethic, but I do judge them. Does this argument refute moral relativism and, then, am I not a moral relativist?

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 understand that mathematical induction is deductive reasoning (but why doesn't it have another name?!). But I wonder if there can be true induction based only on reason. Here is an example: I may think about a possible practical problem and think what I would do in many variants of it. I can also ask other people to imagine other variants and I can ask them help about what to do in all those variants. After all this thinking, it is possible that one notices a general rule about what to do with that problem, and come to believe that that rule would be good for every variant of it, even for those variants we didn't check. Wouldn't that be an inductive conclusion? And do you think that this conclusion would be less acceptable than inductive conclusions in the natural sciences?

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!

Everything needs a cause, right, or it couldn't happen, right? But, if everything needs a cause, how could anything happen? Because the thing that would cause it to happen would also need a cause. So does that means the universe can't happen/could never get to now? Or is time a cause in and of itself? And "drags" things as time goes forward, like a replay in a video game? But then time would need a cause too, right?

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...

Can paradoxes actually happen?

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...

Is it rational to believe that some of my beliefs are false? This seems like a reasonable claim. After all, most people have some false beliefs, and I know that I've had plenty of beliefs in the past which I later learned were false. On the other hand, I obviously believe that each of my beliefs is true (otherwise, they wouldn't be my beliefs). So how could I also believe that some unspecified beliefs among them are false?

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.

Would it be logically coherent to have a world in which everything that happened was bad or have a world in which everything that happen was good? Can good and evil exist independently of each other? Do we need one to define or contrast the other? Can each of them be definable in their own right? Is there any arguments that can be put forth to show that good and evil are not polar concepts?

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.

In mathematics numbers are abstract notions. But when we divide number say we do 1 divided by 2 i.e. ½ does this mean abstract notions are divisible. It gives me a feeling like abstract notions have magnitude but then it comes to my mind that abstract has no magnitude.1=1/2 + 1/2 can we say the abstract notion 1 is equal to the sum of two equal half abstract notions? How should I conceptualize the division? The other part related to abstract notion is that how is the abstract notion of number 1 different from the unit cm? how can we say that the unit cm is abstract when we consider it a definite length. How is the unit apple different from unit cm if I count apples and measure length respectively? I am in a fix kindly help me to sort out this. I will be highly- highly grateful to you.

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...

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