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Full Idea
According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
Gist of Idea
It is untenable that mathematics is general physical truths, because it needs infinity
Source
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.202
A Reaction
I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |