At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.

Some philosophers see into themselves, and some into their times; still others forge an alliance with the future.

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

Every computer divides itself into its hardware and its software, the machine host to its algorithm, the human being to his mind. It is hardly surprising that men and women have done what computers now do long before computers could do anything at all. The dissociation between mind and matter in men and machines is very striking; it suggests that almost any stable and reliable organization of material objects can execute an algorithm and so come to command some form of intelligence.

No distinction in kind rather than degree between ourselves and the chimps? No distinction? Seriously, folks? Here is a simple operational test: the chimpanzees invariably are the one behind the bars of their cages.

Darwinism is not a sufficient condition for a phenomenon like Nazism but I think it's certainly a necessary one.

If moral statements are about something, then the universe is not quite as science suggests it is, since physical theories, having said nothing about God, say nothing about right or wrong, good or bad. To admit this would force philosophers to confront the possibility that the physical sciences offer a grossly inadequate view of reality. And since philosophers very much wish to think of themselves as scientists, this would offer them an unattractive choice between changing their allegiances or accepting their irrelevance.