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

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.

I do not know whether any of this is true. I am certain that the scientific community does not know that it is false.

In the end, every scheme and every science is justified by itself or it is not justified at all.

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.

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

The calculus is the story this [the Western] world first told itself as it became the modern world.