10 ideas
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
4366 | We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse] |