more on this theme | more from this text
Full Idea
Von Neumann suggested that functions be pressed into service to replace sets.
Gist of Idea
Von Neumann wanted mathematical functions to replace sets
Source
report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23
Book Ref
Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.188
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| 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] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| 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] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |