33 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] |
3144 | Everything is what it is, and not another thing [Butler] |
21315 | A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler] |
21317 | Despite consciousness fluctuating, we are aware that it belongs to one person [Butler] |
21313 | If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler] |
21314 | Consciousness presupposes personal identity, so it cannot constitute it [Butler] |
21318 | If the self changes, we have no responsibilities, and no interest in past or future [Butler] |
8066 | Butler exalts conscience, but it may be horribly misleading [Anscombe on Butler] |
7337 | In Mosaic legal theory, crimes are sins and sins are crimes [Johnson,P] |
7339 | Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P] |
7353 | The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P] |
7340 | Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P] |
7338 | Man's life is sacred, because it is made in God's image [Johnson,P] |
7348 | The Jews sharply distinguish human and divine, but the Greeks pull them closer together [Johnson,P] |
7336 | A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P] |
7341 | Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P] |
7342 | Isaiah moved Israelite religion away from the local, onto a more universal plane [Johnson,P] |
7355 | The Torah pre-existed creation, and was its blueprint [Johnson,P] |
7344 | Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P] |
7345 | In exile the Jews became a nomocracy [Johnson,P] |
7347 | Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P] |
7349 | Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P] |
7354 | The main doctrine of the Pharisees was belief in resurrection and the afterlife [Johnson,P] |
7356 | Pious Jews saw heaven as a vast library [Johnson,P] |