# I have a question about "solved" games, and the significance of games to artificial intelligence. I take it games provide one way to assess artificial intelligence: if a computer is able to win at a certain game, such as chess, this provides evidence that the computer is intelligent. Suppose that in the future scientists manage to solve chess, and write an algorithm to play chess according to this solution. By hypothesis, then, a computer running this algorithm wins every game whenever possible. Would we conclude on this basis that the computer is intelligent? I have an intuition that intelligence cannot be reduced to any such algorithm, however complex. But that seems quite strange in a way, because it suggests that imperfect play might somehow demonstrate greater intelligence or creativity than perfect play. [If the notion of "solving" chess is problematic, another approach is to consider a computer which plays by exhaustively computing every possible sequence of moves. This is unfeasible with...

This is a very good question. It is reminiscent of the debate over the so-called "Turing Test", in particular, of an objection to the Turing Test made by Ned Block: his "Blockhead". See the SEP article on the Turing Test for more on this. In the case of chess, it is generally believed that chess is solvable in principle. There are only finitely many possible moves at any stage, etc. So, in principle, a computer could check through all the possibilities and determine the optimum move at each stage. Practically, this is impossible at present, as there are too many moves. But if chess had been solved, and if a computer were simply programmed to make the best move at each stage, then it seems quite clear that no "intelligence" would be involved. Of course, this does not by itself show that "intelligence cannot be reduced to any...algorithm", and the question whether it could be is hotly disputed. There are some famous (or infamous) arguments due to Lucas and Penrose that attempt to establish...

# In writing mathematical proofs, I've been struck that direct proofs often seem to offer a kind of explanation for the theorem in question; an answer the question, "Why is this true?", as it were. By contrast, proofs by contradiction or indirect proofs often seem to lack this explanatory element, even if they they work just as well to prove the theorem. The thing is, I'm not sure it really makes sense to talk of mathematical "explanations." In science, explanations usually seem to involve finding some kind of mechanism behind a particular phenomenon or observation. But it isn't clear that anything similar happens in math. To take the opposing view, it seems plausible to suppose that all we can really talk about in math is logical entailment. And so, if both a direct and an indirect proof entail the theorem in question, it's a mistake to think that the former is giving us something that the latter is not. Do the panelists have any insight into this?

Anyone with any mathematical training will be familiar with the fact that proofs in mathematics do much more than just show that the statement proved is true. One way this manifests itself is that we often value different proofs of the same theorem. Thus, as Jamie Tappenden once pointed out, Herstein's Topics in Algebra , which was the standard algebra text when I was a student, contains three different proofs of the Stone Representation Theorem . Boolos, Burgess, and Jeffrey's Computability and Logic , one standard text for an intermediate logic course, similarly contains multiple proofs of several of the key results, including Church's Theorem on the undecidability of first-order logic and Goedel's First Incompleteness Theorem. And, oddly enough, I myself have just re-proven an existing result in a way that, I think, is clearly better. But not because the original proof wasn't convincing! It's an interesting question, though, why we value different proofs. Somehow, they seem to throw...
I probably should have noted before that, in the case of the different proofs of the first incompleteness theorem in Boolos, Burgess, and Jeffrey, the first proof they give is indirect or, as it is sometimes put, non-constructive: The proof shows us that, in any given consistent theory of sufficient strength, there is an "undecidable" sentence, one that is neither provable nor refutable by that theory; but the proof does not actually provide us with an example of an undecidable sentence. The second proof, which is closer to Gödel's own, is direct and constructive: It does give us such a sentence, the so-called Gödel sentence for the theory. By doing so, it gives us more information than the first proof. It shows us, in particular, the there will always be an "undecidable sentence" of a very particular form (a so-called Π 1 sentence). This is a good example of why constructive proofs are often better than non-constructive proofs: They often give us more information. But it does not directly...

# Is it wrong to fantasize about sex with children? If a pedophile never acts on their fantasies are they still guilty of having evil thoughts, assuming that their abstinence comes out of a genuine desire not to do harm?

So far as I can see, there's nothing wrong with fantasizing about sex with children. There's nothing wrong with fantasizing about anything you like. If that seems crazy, then it's probably because you are thinking that someone who fantasizes about something must actually wish to do that thing. But that is just not true. As Nancy Friday makes very clear in My Secret Garden , her classic and groundbreaking study of female sexual fantasy, fantasy is not "suppressed wish fulfillment". The point runs throughout the book, which you can find on archive.org , but maybe the best statement is on pp. 27-8, though see also the poignant story that opens the book (pp. 5-7). I'd post an excerpt, but the language maybe isn't appropriate for this forum! As Friday's studies reveal, people fantasize about all kinds of things. Some women fantasize about being raped. It's a very common fantasy, in fact. That does not mean these women actually want to be raped, on any level. As Friday remarks, "The message...

# Do philosophers avoid figures of speech in peer reviewed philosphy journals? What about in everyday life; is there a lower standard of conduct when talking to non-philosophers?

By "figures of speech", I'll assume you mean something like metaphor. And, if so, then, no, philosophers do not avoid metaphor, at least not entirely. Here is one of my favorite philosophical metaphors, from W. V. O. Quine: "The lore of our fathers is a fabric of sentences. ...It is a pale gray lore, black with fact and white with convention. But I have found no substantial reasons for concluding that there are any quite black threads in it, or any white ones." Quine would later describe that lore as a "web", which has proven very fruitful. What is true is that philosophers (at least the philosophers I know) try not to settle for such metaphors. One tries to "unpack" the metaphor, and make the underlying point as explicit as possible. But it is, I think, pretty widely appreciated that there is a limit to how far one can go in that direction. Really good metaphors are, as people who work on metaphor say, "inexhaustible", in some sense. There's always more you can dig out of them. That's maybe not...

# I recently heard someone make an argument, something like- "if you accept that there is morality in sex, for example that a father having sex with his daughter is wrong, you can't say gay sex isn't immoral because people should be able to do whatever they want because it causes no harm to others" Is this argument or proof begging the question? Philosophically, what is wrong with this argument.

The main thing wrong with the argument is that it is terrible. Don't we think it's wrong for parents to have sex with their children precisely because we think that it is harmful to the children? One might also think that children have no genuine capacity to consent to sex, an issue that also arises in other settings, such as between a boss and an employee. In such a setting, there are always issues about coercion, even if such coercion is not explicit. Presumably the thought is supposed to be that there are forms of sex that are morally suspect, even though they do not cause any sort of harm. But then one wants to know what those are supposed to be. Then we could consider whether and why they are morally suspect. The example given, as I said, is a very bad one.

# First, I want to clarify that indeterminism is there exists no fact to the matter about future events. It is different than saying that the future is extremely hard to predict. In other words, some say that a coin flip in indeterministic. However, assuming that all particles (atoms, and molecules, etc) behave in mathematically predictable ways, then an omniscient being, knowing the physical properties of all relevant matter (the coin, air current, force of flip, etc) should be able to predict the outcome. Therefore, a simple coin flip is not evidence of indeterminism, because its out come is theoretically (though not practically) possible to determine. Is this a correct way to interpret the view? Second, where do indeterminist think that indeterminism can come from, given the standard view that all matter follows predictable laws of physics?

I don't work on these things myself, but I'll make one point quickly. Nowadays, it isn't at all obvious that you could predict what will happen when the coin is flipped if you knew all the relevant physical facts about the present, for the simple reason of quantum indeterminacy . It may be that the current physical facts make it overwhelmingly likely, say, that the coin will land heads. But quantum mechanics tells us that it is possible, still, that, when you flip the coin, it will turn into a dove and fly away, let alone that it will land tails. So many people think that physics itself speaks against determinism, not in favor of it. Not everyone, mind you, but plenty of people.

# Why don't analytic philosphers in the Anglosphere take a stronger stand against continental psychoanalysis which is divorced from medical findings?

The question seems to presume that it is the job of philosophers as such to take such stands, and that seems wrong to me. Whether psychoanalysis is a helpful form of treatment, and for what conditions, just isn't the kind of question philosophers are well-placed to answer. In particular, whether psychoanalysis is or is not consistent with "medical findings" is presumably something one would have to answer by looking into the relevant medical and psychological literature. That's not what a job that philosophers, for the most part, are trained to do.

# Many people immediately dismiss the following claim: Either something lacks subjective experience, or it does not. Of course, I am talking about consciousness--but I am specifically referring to Nagel's wording, "something it is like to be." Intelligent zombies may not apply. Being such an unpopular claim, it should not be difficult to cite literature refuting it. What are the first two articles and the first two books I should look to in hopes of finding the refutation? Could you begin to refute the claim here? What literature might I read in defense of this claim?

I'm a bit confused. The claim you say "people immediately dismiss" looks like an instance of the law of excluded middle: Either P or not-P. People are often tempted to deny excluded middle in cases of vagueness, but I don't recall a lot of people saying that it can be vague whether a creature is conscious. Anyway, I suspect that either I'm misunderstanding something, or else there's a bad typo, or something. Feel free to write me and we can try to clarify.

# If knowledge is defined as justified true belief, why is it necessary to include "justified" in that definition. If I have a belief that corresponds with an objective state of affairs, why doesn't that count as knowledge regardless of justification? In the Theaetetus, Socrates seems to consider it self-evident that if one forms a belief based on unreliable testimony, that belief is not knowledge even if it true. I don't see why this is the case. If a delusional person tells me it is going to rain tomorrow, and I form the belief (which happens to be true) that it is going to rain tomorrow, why would that not be considered knowledge? Especially if I can use that belief to successfully guide my activity in the world? One more clarification: I can understand why justification matters with respect to the psychological process of forming a belief. I am talking about the definition of knowledge, which is already presupposed to be true.

Different philosophers would answer this sort of question different ways, depending upon how they approach epistemology. On one sort of view, we might think that this is a question about the meaning of the ordinary English verb "to know". And in that case, there seems to be good evidence that English speakers are not always willing to describe someone as "knowing" something just because they believe it and it is true. For example, the Super Bowl is tomorrow. I know nothing about football, but suppose I firmly believe that the Seahawks are going to win. If they do win, would you want to say that I knew they would? A more interesting question, though, to my mind, is simply whether we think there is an important distinction to be made here, whether or not it is one that is made in English. And that, obviously, has to be decided by seeing what work "knowledge", in that sense, can do. It's not at all clear, actually, that all one's true beliefs can "successfully guide...activity in the world" in the same...

# Are there any philosophers who deny that the principle of explosion is a valid principle while at the same time both being not accepting of a paraconsistent logic and being accepting of the Law of Non Contradiction?

According to the article on paraconsistent logic at the Stanford Encyclopedia of Philosophy : "A logical consequence relation, ⊨, is said to be paraconsistent if it is not explosive." So denying explosion just is accepting a paraconsistent logic.