12 ideas
9944 | We understand some statements about all sets [Putnam] |
15571 | The idea of an atemporal realm of validity is as implausible as medieval theology [Heidegger] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
15581 | Dasein is always only that which it has chosen to be [Heidegger] |