All human activities seem to have dramatic, defining, pivotal moments. Take basketball : 1987 Game 5 Celtics v. Pistons. Dennis Rodman rejects Larry Bird with 5 seconds left. Pistons take the ball. All they need to do is inbound the ball and hold it and they take a 3-2 series lead home. Instead, Larry steals Isiah's inbound pass and the Celtics win. Wow. Of course there are many such moments in sports. What are the equivalent moments in Philosophy? What Philosopher, finally, in what paper, knocked down a prevalent theory held for 1,000 years? That kind of thing. Can a few of you contribute your favorite moments in the history of philosophy?

David Hume's Enquiry Concerning Human Understanding (1748) contains a discussion of induction that I would like to say qualifies – except I don't know that the position he argues against was going for 1,000 years. In fact, I don't even know if the question he addresses would have been a live one during that time. Perhaps better, then, would be Gottlob Frege's Begriffsschrift (1879), which doesn't directly argue against a logical analysis of natural language sentences which I gather had been kicking around for well over 1,000 years but which effectively demolishes it by articulating, elaborating and defending a far more powerful analysis – one which continues to be presented at every university or college in the world that offers a course on formal logic.

Does Quine's argument that there is no real boundary between analytic and synthetic statements include purely mathematical statements such as 1 + 2 = 3? Granted, sentences in everyday languages contain both analytic and synthetic elements, but cannot formal languages support purely analytical statements? Or does mathematics, being a human creation, inextricably model the natural world around us, and thus contain synthetic information? I'm trying to understand the short and (very difficult for me) book "Knowledge and Reality: A Comparative Study of Quine & Some Buddhist Logicians" by Kaisa Puhakka, which seems to represent Quine's thinking faithfully, but my training as a scientist leaves me ill-prepared for much of it. Thank you.

Richard's response is helpful and interesting, but perhaps I would put matters a bit differently. He makes it sound as if Quine accepts the distinction between analytic and synthetic truth and goes on to argue that nothing counts as a truth of the first kind (perhaps "mellowing" his view about this later on). But Quine's position (early, middle, and late) is rather that he can make no sense of the distinction at all. His challenge isn't to the analyticity of logical or mathematical truth; it's rather to the intelligibility of sorting truths into these categories – to the very categories themselves – as the traditional philosopher conceives of them. Your thought that the distinction can be given some sense in the context of an artificial language is a natural one. Quine explicitly turns to this suggestion in section 4 of "Two Dogmas of Empiricism."

So, it's my understanding that Russell and Whitehead's project of logicism in the Principia Mathematica didn't work out. I understand that two reasons for this are (1) that some of their axioms don't seem to be derivable from pure logic and (2) Gödel's incompleteness theorems. However, particularly since symbolic logic and the philosophy of mathematics are not my area, it's hard for me to see how 1 & 2 work and defeat the project.

To follow on some of Richard's observations: I have never found it at all a compelling argument against logicism that it would have the existence of infinitely many natural numbers be a logical truth. That is not an argument against logicism so much as a restatement of the claim that it is incorrect. Richard's discussion of Boolos reminds me of Gödel's own caution with regard to what his Incompleteness Theorems establish with respect to Hilbert's Program (roughly, Hilbert's attempt to show that if a basic, or finitary, proposition of mathematics can be established using the powerful, or infinitary, methods of classical mathematics, then it could already have been established using very basic, or finitary, reasoning). [For more on Hilbert's Program, you might see here or here .] I don't myself think that the phenomenon of incompleteness puts paid to Hilbert's project (as divorced from certain other beliefs that Hilbert may have held, such as the belief that all true mathematical...

I have trouble understanding what people mean when they use a phrase with the word exception. To me it sounds like a contradiction. So my question has two parts: A) Is using the term exception ever legitimate? B) Does the term "except" usually contradict the general rule that comes before it? For example, All ice cream should be taxed, except vanilla. This seems that the quantifier "all" is false if a member is excluded. For example, All students passed the final exam except Roy. Seems to me this means only Roy failed the final exam and the quantifier "all" makes the sentence false. Please help me make sense of the term exception. Thanks for your help.

I see what you're thinking: that in sentences such as: (1) All teams lost except Spain we give in one hand what we take with the other. We are affirming that all teams lost and also that Spain did not lose. You're right that this would indeed be a contradiction. But I don't think the logical structure of such sentences is as you propose. The issue depends on what logicians call the relative scope of the terms "all" and "except". You understand (1) to mean: (2) (all teams lost) and (Spain did not lose) which is indeed a contradiction. Logicians would actually make a few changes to bring out more clearly the logical structure of (2): (2') (each team is such that it lost) and (it is not the case that Spain lost) Again, this is a contradiction. But a more accurate analysis of how the sentence (1) is usually meant is this: (3) all teams except Spain lost where a more perspicuous representation of the logical structure of this is really: (3') each team is such that...

Why students checking facebook on class are regarded disrespectful, while a professor who checks his facebook on a symposium as another professor is reading his paper is said to be cute and cool? Are there absolute boundaries between righteous and evil, right and wrong?

I wouldn't regard such a Facebook-checking colleague as "cute and cool". Besides the fact that wanting to check a Facebook page already disqualifies one from being cool, it is disrespectful. I don't allow my students to use computers, cell phones, etc. during class, and if I were organizing a conference I'd strongly discourage those in the audience from doing so as well.