I’ve run into a problem in philosophy recently that I do not completely appreciate. Certain sets are said to be “too big” to be sets. In Lewis’ Modal Realism, the set of all possible worlds is said to be one such set. These are sets whose memberships is composed of infinite individuals of a robust cardinality. I (purportedly) understand that not all infinities are equal. But I don’t quite see why there can be a set of continuum many objects, but not a set of certain larger infinities. Am I misunderstanding what it is to have “too big” a set?

As Alex says, in Lewis's case, he's really pointing towards an idea familiar from the philosophy of set theory. Not all "collections" of objects can form sets: The assumption that they do leads to contradiction. (Of course, we need some logical assumptions to get that contradiction, and these could be denied. And one might also not think contradictions are all that bad. But let's not go there now.) And given the standard axioms of set-theory, we can prove that there is no set containing every object and, moreover, that there is no set that can be put in 1-1 correspondence with all the objects there are. But the standard concept of set, as embodied in Zermelo-Fraenkel set-theory, is not in any way motivated by the idea that a set cannot be "too big". It is based upon a very different idea, called the "iterative"conception of set, though there is some question about whether the Axiom ofReplacement (which was Fraenkel's distinctive contribution) is really motivated by the iterative conception or...

What is the current take on Chomsky's 'language acquisition is hard-wired into the brain' theory? I remember reading ten years or so ago that a scientist had isolated a gene that led to kids having trouble learning to speak normally (I have no citation, unfortunately). Would this be proof that Chomsky was right?

No, that wouldn't be proof that Chomsky was right. No one ever denied that something innate was involved in language acquisition. And for all we've been told, it might be that the gene in question had something to do with a child's ability to dissect the acoustical stream at a stage far prior to anything linguistic. That said, the empirical evidence continues to suggest that some very general linguistic principles and categories are genetically provided.

I opened up your website and encountered a philosophical discussion of a bent spoon in a glass of water. Which prompts my question: Why hasn’t there been a scientific revolution in philosophy as there has been in physics, chemistry, biology, physiology, historiography, astronomy, music, political science, the social sciences, medicine, er... well just about everything else? Here's my point. When a college student studies ANY of those other subjects, there is scant attention paid to what people thought before the Enlightenment or at best before the Renaissance (except as a historical curiosity). And that's a good thing, BECAUSE =phlogiston has no place in modern physics; =Air, Fire, Water and Earth in Chemistry =the Great Chain of Being in Biology =Bodily Humors in physiology =the Great Man Theory in historiography =Astrology in astronomy =Celestial number sequences in Music theory =belief in the Divine Right of Kings in Poly Sci =belief in possession by demons, the caste system, or the Noble...

I hate to be overly defensive but, frankly, for someone asking this kind of question, and making these kinds of accusations, the questioner displays quite astonishing ignorance. Rigor? Methodology? Math? I would have thought that twentieth century analytic philosophy was almost defined by its obsession with these things. Now that said, the next question---whether philosophy is a branch of literary criticism---rather suggests that the questioner has relatively little familiarity with analytic philosophy. Perhaps a good suggestion, then, would be that the questioner should read Bertrand Russell's Problems of Philosophy . Or Carnap's Logical Syntax of the World . Or Quine's Word and Object (though read Carnap first). Or, perhaps best of all, Frege's Foundations of Arithmetic . And have a look at question 1416 . Besides which: The concern about the bent spoon is a concern about the nature of perceptual representation, a concern that is continuous with the concerns of visual...

When something disastrous happens, like Katrina, "logic" says: so much the worse for a loving God. But for the believer, what comes out, instead, are things like "God never gives us more than we can handle" and "We have to praise the Lord, and thank him, that we are OK." Why? (Or is this just a psychological or sociological question? Or did I watch too much Fox news?)

Let me start by thanking Louise for her contribution, and especially for mentioning Hume's Dialogues ,which remains my single favorite philosophy book. Hume's dismantling ofthe argument from design probably should be cited as often as possiblein the current climate. Having said something nice, I'll now proceed todisagree with Louise on one point. But I'll then agree with her aboutanother. It is not entirely obvious that there is any such thing as the 'Judeo-Christian' conception of God. The various Problems of Evil,logical and "evidential" (as I've seen the one Louise emphasizescalled), attack a particular combination of claims---omnipotence,omniscience, and benevolence, typically---that, to be sure, has figuredsignificantly in Christian theology but whose relation to Jewishthought is really quite unclear. Moreover, even within Christianthought, there are many conceptions of the divine, and not all of themwould subscribe to those three claims. Nonetheless, it probably is truethat most...

If you are just wondering why people respond in such different ways,then perhaps your question is just psychological. But there are deeperissues here, too. Natural disasters raise, in a very impressive way,the so-called Problem of Evil. It goes like this. Suppose that God isomnipotent, omniscient, and benevolent. Then it would seem that Godwould had to have known what sort of suffering Katrina would cause,want to prevent that suffering, and be able to do so. But God didn't,so God must not be all those things. And if you think that, if Godexists at all, then God has to be all those things, then you get theconclusion that God does not exist. It will not surprise you thatthe Problem of Evil has been much discussed. There is a very nicecollection edited by Marilyn Adams on it. Ican't end this note,however, without saying one more thing, namely, that there are manydifferent ways "believers" respond to such events. It is true that thereactions you mention are commonly encountered, but they are not...

Have there been any systematic attempts to determine what the most difficult language(s) to learn as a second-language may be? Is the difficulty of second-language acquisition necessarily tied to the second-language's similarity to one's first language, or otherwise dependent on some inherent or acquired capacity of one's brain to learn a given second-language? Or are there some languages which are more difficult to learn as a second-language across the board, so to speak? If so, what sort of formulae might be used to determine the difficulty of the acquisition of a given second-language?

Human beings and human languages are made for each other. So far aswe have reason to believe, any (normal) human being can learn any humanlanguage as his or her first language, and young children are capableof learning many languages, if they are exposed to them.It seems that, as one matures, the part of one's brain devoted tolanguage-learning more or less shuts off (much as, in many people, theenzymes devoted to digestion of milk cease to be produced). And so, atthat point, one's language-learning no longer proceeds in quite the way it would have when one was younger. So it's possible, to be sure, that some languages yield more easily to the methods of acquisition we are forced to employ as adults. But it's hard to imagine there would be any absolute measure here. It is, famously, not particularly difficult for native speakers of Portuguese to learn Spanish, but I doubt Spanish would be terribly easy for a native speaker of Japanese or even of German. So it seems plausible that there is some...

Dear all, Am I right in thinking that what William Paley's mistake in his design argument, was not to suggest a designer but he was mistaken to 'specify' how design came about, so he came up with the concept of 'special creation' i.e. design coming instantaneously. Therefore that was his pitfall, not that the design argument is wrong, but just that he was stipulating conditions on how God should create. I think it was Bohr who said 'Don't tell God what to do'. I think to further show my point is where some argued that this creation was special because the earth was the center of the universe, and when this was proven wrong, certain religous figures acted violently because this assumption was proven wrong. Am I right in the above? Many thanks :) Kind regards!

I'm not sure I fully understand that question being asked here, and I should say, straight off, that I'm not familiar with Paley's particular version of the argument from design. (The argument goes back, in one form or another, a very long way.) But it's certainly true that, if the argument shows anything, it shows only something very abstract: The universe was created by some form of "intelligence". Indeed, part of Hume's criticism of the argument from design is precisely that it can show so little: The argument gives us no reason whatsoever to suppose that the intelligence that created the universe, if such there be, has any of the attributes traditionally associated with divinity. (In fact, Hume goes farther and argues that, if one is really proceeding by analogy here, one should conclude that the intelligence has few, if any, of those attributes.)

I hope you can help me answer a question I've been thinking about for some time... How do we really know if objective reality exists at all and, even if it does, what is to say that our view on objective reality is correct?

What do you mean by an "objective" reality? Do you mean a reality that exists outside of my mind? It isn't obvious to me that there is any better answer than that given by the British philosopher G. E. Moore: I know that I have two hands, and my hands are certainly not inside my mind but attached to my arms. So, well, there you go. There are all kinds of questions about what, exactly, Moore's argument shows and what it doesn't show. But one of Moore's points, I take it, was that the question whether there exists a world outside my mind is one that is to be answered, if at all, in terms of whether there is anything outside my mind, and my hands are as good an example as any there could be. And that just seems right. Regarding the second question, nothing guarantees that our view of the world is correct. I can imagine, just barely, that I do not have two hands but seem to myself to have two hands because of some weird brain injury. I suppose that is, in some sense, possible. But the mere fact...

My question will be introduced at the end of this post. I have thought on this question for some time now. But first off let me say that I do not know all there is to know about the theory of Solipsism. From what I gather, the definition can be summed up in the phrase: The theory that only the self exists, or can be proved to exist. Holding this to be true, person A kills himself. Moments before doing so, he scribbles down on a sheet of paper: If You can read this when I am dead, the theory of Solipsism is false. This seems to be a great way to find out if the theory of Solipsism is true or not, but I have come up with a counter: Person B discovers person A's body and the note. If Person A kills himself, having written down what he did, then he would have only been acting in person B's perception of the world; hence, the theory of Solipsism would be true to person B, because person B can still only be sure of his own existence- and cannot be sure that person A ever did exist. This brings up yet...

I would suggest that the problem here is that the term "Solipsism" is being applied to more than one view. Solipsism, as I understand it, is the view that only I exist. This is obviously true. Nonetheless, my experience contains streams of sensations that I am able to organize, for my convenience, into sequences I call "persons", and I have sometimes encounted some of these "persons" discussing another view that they call "Solipsism", which they claim is the view that only they exist. I find this both confusing and amusing. These "persons" don't exist at all, except as streams of sensations, and so they certainly don't exist in the way I do (as I am not a stream of sensations). So it's not at all clear to me what view this other Solipsism is supposed to be. Is it that only the streams of sensations that constitute them exist? What a silly view! As if sensations could exist without someone whose sensations they were! But, well, I suppose it's not surprising that the view should be so silly, since...
Sex

Why is it that homosexuality is not accepted in general? In society there is only the role model of man and woman to build a family and that the family is the foundation of the society. But has this necessarily to be so? Is there an ethical or philosophical argument to not accept homosexuality?

See questions 1223 and 1221 for some relevant reflections. Your question is slightly different, perhaps, but I'm not sure. The other questions largely concern same-sex relationships, whereas you talk of "homosexuality", which is either a form of behavior---having sex with someone of the same gender---or a "sexual orientation"---being inclined to be sexually attracted to members of one's own gender. These are very different from anything involving relationships , even (for lack of a better word) "romantic" ones, which may or may not involve sex and do not, in any event, need to be defined by it. For this reason, I'd much prefer to speak of people who are homoamorous : people who are inclined to develop feelings of romantic love towards members of their own gender and, as a result, inclined to become involved in romantic relationships with people of their own gender. Of course, now that we've distinguished the sexual question from the question of relationships, we can see clearly that,...

A friend of a friend of mine posed a really odd problem regarding our beliefs that I’ve not really been able to answer to my own satisfaction. If we believe that X is the case, then it seems to go without saying that we also believe that we believe X is the case. It would be odd to say that we believe X but don’t believe we believe it. But then if that has to be so, it also seems that we must also believe that we believe that we believe that X is the case. And if that’s so then it seems we must believe that we believe… You get the picture. What’s going on here? We’re finite beings so we can’t have an infinite number of beliefs, can we? I’d put forward some of the thoughts I had about it, but I’m not entirely sure that I think I had them.

The standard way to resolve this problem is to distinguish explicit from implicit beliefs. Suppose, just for illustration, that believing that p , in the explicit sense, is having a sentence that means that p written on a blackboard in your head. So believing that snow is white, for example, is having a sentence that means that snow is white written on a blackboard in your head. (You can think of this as meaning, roughly, that this information is explicitly stored in memory somehow.) Now, suppose I have the sentence "I have two arms" written on my mental blackboard and that I also have the sentence "two is less than three" written on my internal blackboard. Suppose, further, that I am capable of simple reasoning. Then, if the question were to arise, it seems reasonable to suppose I would conclude, from those explicit beliefs, that I have fewer than three arms. So we might say, in this case, that I implicitly believe that I have fewer than three arms. And so on. It is not an easy...

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