More than sixty years ago, mathematical logicians, by defining precisely the concept of an algorithm, gave content to the ancient human idea of an effective calculation. Their definitions led to the creation of the digital computer, an interesting example of thought bending matter to its ends.

No man is obliged to be what he might have been.

Commentators who today talk of 'The Dark Ages' when faith instead of reason was said to ruthlessly rule, have for their animadversions only the excuse of perfect ignorance. Both Aquinas' intellectual gifts and his religious nature were of a kind that is no longer commonly seen in the Western world.

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.

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

While science has nothing of value to say on the great and aching questions of life, death, love, and meaning, what the religious traditions of mankind have said forms a coherent body of thought... There is recompense for suffering. A principle beyond selfishness is at work in the cosmos. All will be well. 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.