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Full Idea
Science demands much more of a mathematical theory than that it should merely be consistent, as the example of the various alternative systems of geometry dramatizes.
Gist of Idea
Science requires more than consistency of mathematics
Source
Hilary Putnam (Mathematics without Foundations [1967])
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.302
A Reaction
Well said. I don't agree with Putnam's Indispensability claims, but if an apparent system of numbers or lines has no application to the world then I don't consider it to be mathematics. It is a new game, like chess.
| 9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
| 9941 | Science requires more than consistency of mathematics [Putnam] |
| 9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
| 9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
| 9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
| 9944 | We understand some statements about all sets [Putnam] |