If by "empirical reasoning" you mean non-deductive reasoning, then your brother is incorrect. That the truth of the premises guarantees the truth of the conclusion is a hallmark of deductive reasoning.

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.

If you have difficulties actually getting or buying books, you might also look at Paul Teller's A Modern Formal Logic Primer. The book is now out of print, but Teller has made it completely available for downloading from the Web. You can find it here .

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."

See here for some similar questions and their answers.

You might find this recent opinion piece by Martha Nussbaum, a philosopher at Chicago, to be of interest.

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...

For a related discussion of the notion of randomness see Question 264 .

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...

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.