12 ideas
9944 | We understand some statements about all sets [Putnam] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
9937 | I do not believe mathematics either has or needs 'foundations' [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] |
9941 | Science requires more than consistency of mathematics [Putnam] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
6003 | Galen showed by experiment that the brain controls the body [Galen, by Hankinson] |
6030 | Each part of the soul has its virtue - pleasure for appetite, success for competition, and rectitude for reason [Galen] |