“Truths are illusions about which one has forgotten that this is what they are”
An apt description of what is at work when mathematicians are in ‘Platonic’ mode…when foundations that in fact are not solid are deemed sufficiently so.
A quote:
According to Weyl 1946, “Brouwer made it clear, as I think beyond any doubt, that there is no evidence supporting the belief in the existential character of the totality of all natural numbers … the sequence of numbers which grows beyond any stage already reached by passing to the next number, is a manifold of possibilities open towards infinity; it remains forever in the status of creation, but is not a closed realm of things existing in themselves. That we blindly converted one into the other is the true source of our difficulties, including the antinomies – a source of more fundamental nature than Russell’s vicious circle principle indicated. Brouwer opened our eyes and made us see how far classical mathematics, nourished by a belief in the ‘absolute’ that transcends all human possibilities of realization, goes beyond such statements as can claim real meaning and truth founded on evidence.”
—Kleene 1991, pp. 48–49
But then again, we have the atom bomb. Oh, the wonders mathematics has wrought. Yes, we have the CAT scan.
What a strange mix.
21st Century Paradox 