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bogus comments on Rational subjects and rational practitioners - Less Wrong
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Comments (36)
One reason for this is that, generally speaking, non-constructive proofs can in fact be embedded into constructive logical systems. I think there is more controversy about what formal foundations we should endorse for mathematics. ZF(C) is good enough as a proof of concept, but type-theoretical and category-theoretical foundations seem to be better in terms of actually doing formalized mathematics in the real world.
While that may be a reasonable justification for what mathematicians do, I think it is false as a historical claim about what caused mathematicians to do what they did. Mathematicians settled on their foundations ("No one can expel us from Cantor's Paradise," 1926) before they understood power and limits of constructive methods.
I'm curious if you are making a practical claim or a formal one.