10 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
9944 | We understand some statements about all sets [Putnam] |
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] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |