31 ideas
192 | Only one thing can be contrary to something [Plato] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
20184 | The only real evil is loss of knowledge [Plato] |
191 | Everything resembles everything else up to a point [Plato] |
23111 | If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
23059 | Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray] |
188 | Socrates did not believe that virtue could be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
4129 | It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick] |
20588 | Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf] |