13 ideas
9944 | We understand some statements about all sets [Putnam] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
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] |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
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] |
9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |