more on this theme | more from this thinker
Full Idea
Mathematics might be 'empirical' in the sense that one is allowed to try to put alternatives into the field.
Gist of Idea
Maybe mathematics is empirical in that we could try to change it
Source
Hilary Putnam (Mathematics without Foundations [1967], p.303)
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.303
A Reaction
He admits that change is highly unlikely. It take hardcore Millian arithmetic to be only changeable if pebbles start behaving very differently with regard to their quantities, which appears to be almost inconceivable.
| 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] |