10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning |

10713 | Usually the only reason given for accepting the empty set is convenience |

13044 | Infinity: There is at least one limit level |

10708 | Nowadays we derive our conception of collections from the dependence between them |

13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects |

10707 | Mereology elides the distinction between the cards in a pack and the suits |

10704 | We can formalize second-order formation rules, but not inference rules |

10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional |

10711 | Russell's paradox means we cannot assume that every property is collectivizing |

10712 | If set theory didn't found mathematics, it is still needed to count infinite sets |

17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms |

13043 | A relation is a set consisting entirely of ordered pairs |

13042 | If dependence is well-founded, with no infinite backward chains, this implies substances |

13041 | Collections have fixed members, but fusions can be carved in innumerable ways |

10709 | Priority is a modality, arising from collections and members |