25 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] |
5311 | If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO] |
5312 | A child first sees objects as distinct, and later as members of groups [Wilson,EO] |
5309 | Beliefs are really enabling mechanisms for survival [Wilson,EO] |
5310 | Philosophers study the consequences of ethics instead of its origins [Wilson,EO] |
22187 | Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha] |
5313 | The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO] |
5316 | We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO] |
5318 | Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO] |
5317 | The actor is most convincing who believes that his performance is real [Wilson,EO] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
20662 | The biology of societies: kin selection, parenting, mating; status, territory, contracts [Wilson,EO] |
5308 | The only human purpose is that created by our genetic history [Wilson,EO] |
5314 | Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO] |
5315 | Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO] |
5320 | It is estimated that mankind has produced 100,000 religions [Wilson,EO] |