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] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 23814 | Every human yearns for an unattainable transcendent good [Weil] |
| 23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
| 23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
| 23823 | Life needs risks to avoid sickly boredom [Weil] |
| 23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
| 23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
| 23819 | Deliberate public lying should be punished [Weil] |
| 23818 | We have liberty in the space between nature and accepted authority [Weil] |
| 23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
| 23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
| 23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |