16 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] |
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] |
22179 | Explanatory facts also predict, and predictive facts also explain [Hempel, by Okasha] |
21507 | Scientific explanation aims at a unifying account of underlying structures and processes [Hempel] |
6755 | For Hempel, explanations are deductive-nomological or probabilistic-statistical [Hempel, by Bird] |
17083 | The covering-law model is for scientific explanation; historical explanation is quite different [Hempel] |
13052 | Hempel rejects causation as part of explanation [Hempel, by Salmon] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |