However good an argument in philosophy may happen to be, it is generally not good enough.

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

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.

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

However good an argument in philosophy may happen to be, it is generally not good enough.

An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up.

The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they proceed from separate places in the imagination.