# Can the "real world" provide evidence that mathematical knowledge is legitimate? I think its many peoples' intuition that the successful application of math to science and engineering (e.g., that we can use math to build bridges) shows that math is true.

The question is whether what we find in the physical world could tell us whether math is true. Let's consider two sorts of cases. One is what we might call mathematical laws -- 1+1=2 is a particularly simple example. An algebraic law like x 2 - y 2 = (x+y)(x-y) is another. The second sort of case includes things like Newton's law of gravitation -- F 12 = G(m 1 m 2 )/r 2 -- or some mathematical description of the characteristics of steel beams used for bridges. This may be closer to what you have in mind. Start with the first sort of case. Suppose we have two 1-liter beakers of water. We pour them together, measure the volume and find that it's two liters. Have we confirmed the mathematical claim that 1+1=2? If so, what do we make of the fact that if we put pure alcohol rather than water in one of those beakers, when we put the two together we get about 1.94 liters? Does that count against 1+1=2? It's pretty clear that neither experiment tells us anything about whether 1+1 equals 2;...

# What exactly is the nature, scope, and origin of "methodological naturalism"? What are the most authoritative sources to learn about the origin and nature of methodological naturalism as it is employed in the sciences? I would appreciate any reply to this question. Thanks!

On the one hand... There's some controversy here, but a nice, readable paper by Bradley Monton argues that methodological naturalism neither is nor should be a presupposition of science. Monton provides further references to the literature. To see the paper, click here . I think Monton makes a case that we can't use methodological naturalism as a criterion of demarcation between science and non-science. But then there may not be much we can say by way of offering strict criteria of demarcation between science and other activities. Even if science isn't, as it were ,"by definition" naturalistic [aside: when someone says that something is so "by definition, you should be suspicious] it's not an accident that across the sciences, researchers almost always start with and end up with naturalistic hypotheses. That includes researchers who count themselves as religious believers. There's no one simple reason for this; it's partly a matter of history, partly a matter of shared intellectual values, partly...

# At the moment, I'm particularly concerned about the 'personal heresy' in philosophy. Recently, Thabo Mbeki, the South African president, gave a speech in which he quoted several racist statements by key philosophers of Western civilisation. David Hume, for instance believed that "of all the 'breeds' of man, the darkest breed was inferior.."(quote from Mbeki's speech) and it's also believed that Kant believed black people were 'beasts'(again, Mbeki's belief). Whether these quotes are accurate or not, it's indubitable that the milieu in which these philosophers formed their various normative frameworks was a deeply prejudiced one. If philosophy proceeds from deductivism, i.e a set of axioms are laid out, rules of inference determined, and from these various judgements made, is it possible that inherent within western thought is a kind of racial prejudice? And if so, is it possible to account for it, using some kind of 'personal equation' of the kind invoked by Gauss in his work with astronomy?

I'll have to leave the bit about Gauss aside. All I know about the "personal equation" was that astronomers had noticed certain sorts of systematic variations among observers. But there was a different theme in your question that I'd like to address. A preamble: Yes, Hume, Kant and other western philosophers, no doubt all on this panel included, operate in a mileu that's saddled with various prejudices. I'd add that I'm not aware of any large cultural mileu that's exempt from this sad fact, and Africa, like the west, provides its own set of depressing illustrations. But I'm a bit uncomfortable with using a term like "Western Thought" (or, for that matter, "Eastern Thought" or "African thought" or even "South African thought") as an analytical concept. (I'm uncomfortable for similar reasons when my students write papers with sentences that begin "Society holds that...") As noted, the history of the west embodies a good many prejudices and false ideas. Some of these make their way into political and...

# Is it emotionally difficult to be a professional philosopher? Sometimes philosophical questions and subject matter seem so disturbing and intense, that it must surely be taxing psychologically. Does non-philosophical subject matter become pale and boring in comparison? Are professional philosophers socially isolated because of boredom with the non-philosophical, concomitant with the disturbing nature of the philosophical (so that it may not be acceptable in non-philosophical company)? Thanks.

I'll have to admit that most of the Sturm und Drang in my life hasn't got a lot to do with what I think about professionally. Questions like "do quantum states support measurement counteractuals?" or "does indeterminism serve any real function in Professor X's account of libertarian free will?" or "is there an acceptable notion of objective probability that explains how probabilities can be action-guiding?" aren't exactly the stuff from which high monthly psychoanalysts' bills are made. All of those questions are very interesting (No. Really!) but they aren't high on the angstometer. And I have a feeling that if you thumbed through the typical philosophy journal, you'd find much the same for much of what you saw. This isn't a criticism of my chosen profession and first intellectual love. Many of the questions that philosophers wrestle with are deeply fascinating if you have the taste for them, but they often abstract, often not very closely connected with the things in the world that really worry...

# It is generally accepted that certain intervals in music sound "harmonious", i.e. 3rds, 4ths and 5ths. Why is this so? Why do these certain intervals constitute a pleasant sounding harmony, as opposed to jarring, dissonant intervals like 2nds and 7ths? I do not believe it is a matter of taste - most people, even those with no musical training will uniformly identify a harmony as harmonious (or in tune) or dissonant (or out of tune, I suppose). However, I am open to being disproved on this point.

It's an intriguing phenomenon. And it turns out, so I gather, that it's not confined to humans. Various animals differ in their responses to what we label consonant and dissonant intervals. Why this should be isn't something that a philosopher, as such, is in a good position to say. It clearly has some physiological basis and seems to have something to do with the phenomenon of "beats" (something you can actually experience as pulses when two high-pitched notes that differ slightly in pitch are played together.) One study I discovered (by Jonatan Fishman et al. of Albert Einstein medical college) looks at the neural correlates of dissonance in macaques and in humans. If you're able to follow the neurophysiological details (I'm not) you can have a look at the link. There are also references to earlier work. There are still some things left over that a philosopher might want to puzzle about. One is the sort of thing that physiology might straightfowardly help us understand: why is it that...

# Can you be punished for planning a crime? Say your planned to do forgery and you called up friend who has the 'talent.' The friend say she wouldn't do it. Another person knew about you planning to forge and tells the school authorities. Does the school authority have the right to impose punishment on you for contemplating to do forgery? When you think evil things such as stealing does that already make you immoral? What do philosophers say about planning to do evil?

Sometime you can be punished for planning a crime: if it's a case of criminal conspiracy. That's an agreement with at least one other person to commit a crime. Just what the standard of proof might be is a question that I'd have to leave to a lawyer, but conspiracy has long been illegal. If a single person plans to commit a crime, this wouldn't count as criminal conspiracy. One reason for the difference, perhaps, is that people can't be prosecuted for their thoughts, and proving that I really planned to do something wrong, rather than merely fantasized about it, would be hard. When you plan together with someone else, however, you've gone past the stage of merely thinking. The school case is complicated; schools are allowed to discipline students for conduct that isn't criminal. Best to ask someone who knows the relevant law. But I think your underlying question wasn't legal. You asked if thinking evil thoughts makes a person evil, and you asked about planning to do evil things. I'd make a...

# I remember reading some decades ago wile in college, that Plato proposed that humans were originally created as four armed, four legged beings, and that is why we always search for our other half. Is there some book or citation you can direct me to, to re-learn about this? I have been sarching on line and think it's in Timaeus but can't find anything for sure.

It's in the Symposium , in a speech by Aristophanes. The speech is posted separately here .

# The 'State of Nature' is often appealed to in order to make systematic the justification of the state and the extent of our political obligations to it. What option does the present day anarachist have if he refuses to accept the force of these arguments and genuinely wishes to live a stateless, obligation-free, apolitical existence ? Surely he didn't 'choose' to be born into a modern state and yet it seems that there is little he can do to live an alternative life. Is this a significant restriction of his freedom ?

Here are some options: (i) pick a country where there's not much in the way of rule of law and go off and live there. Or (ii) do as the founders of Sealand did, and try to set up shop on an oil rig or some such offshore. (But you might want to pick your territory a little more cleverly than they did.) Or (iii) raise up an army of like-minded people, overthrow some government, and set up a stateless, er, "state." (iv) Moving to another planet doesn't seem to be much of an option, but in principle, I suppose... A more practical compromise might be to (v) fake your death and disappear into the wilderness. If it sounds as though I'm (a) being facetious, and (b) am not entirely sympathetic, I'd have to say that on (a), I don't really see much in the way of other options. [And for the record: I'm against overthrowing legitimate governments; I can't condone (iii). I'm also not big on (v), since it calls for fraud.] On (b), I'm afraid it's true. I think there are lots of interesting questions...

# Do you believe in the socratic method in the teaching of children?

It partly depends on what the method is supposed to be. In reading some of the Socratic dialogues, one gets the strong impression that it was a technique for walking the person being questioned into a pre-determined and sometimes peculiar answer. (Do we really think that Meno's slave boy had learned about triangles in his life before birth?) But the goals people claim to have in mind when they use the Socratic method are good ones: to encourage critical thinking, to get students to take ownership of their ideas, and to see that easy answers are often not forthcoming. Starting with a question -- especially a provocative one -- seems like a plausible way to get people thinking. But we all know that things with the grammatical form of questions can sometimes serve the same purpose as simply making a claim; sometimes it's not hard for students to pick up on the answer they're supposed to go for. Perhaps the real question is what methods work best for getting people to be critical thinkers. That's a...