17 ideas
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| 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] |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |