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Full Idea
I do not believe mathematics either has or needs 'foundations'.
Gist of Idea
I do not believe mathematics either has or needs 'foundations'
Source
Hilary Putnam (Mathematics without Foundations [1967])
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.295
A Reaction
Agreed that mathematics can function well without foundations (given that the enterprise got started with no thought for such things), the ontology of the subject still strikes me as a major question, though maybe not for mathematicians.
| 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] |