more on this theme | more from this thinker
Full Idea
Surely the mere fact that we may never know whether the continuum hypothesis is true or false is by itself just no reason to think that it doesn't have a truth value!
Gist of Idea
You can't deny a hypothesis a truth-value simply because we may never know it!
Source
Hilary Putnam (Mathematics without Foundations [1967])
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.305
A Reaction
This is Putnam in 1967. Things changed later. Personally I am with the younger man all they way, but I reserve the right to totally change my mind.
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] |
9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
9944 | We understand some statements about all sets [Putnam] |