26 ideas
| 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] |
| 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] |
| 579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
| 23865 | Morality would improve if people could pursue private interests [Weil] |
| 23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
| 23871 | No central authority can initiate decentralisation [Weil] |
| 23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
| 23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
| 23863 | Only individual people of good will can achieve social progress [Weil] |
| 23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
| 23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
| 23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
| 23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |