22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something |

22301 | The Identity Theory says a proposition is true if it coincides with what makes it true |

22324 | It has been unfortunate that externalism about truth is equated with correspondence |

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 |

22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents |

22291 | Deductivism can't explain how the world supports unconditional conclusions |

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

22295 | Modern logical truths are true under all interpretations of the non-logical words |

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 |

22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth |

22298 | Why is fictional arithmetic applicable to the real world? |

22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete |

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

22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers |

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 |

22281 | A material conditional cannot capture counterfactual reasoning |

22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process |

22273 | Traditionally there are twelve categories of judgement, in groups of three |

22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated |

22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components |

22282 | 'Direct compositonality' says the components wholly explain a sentence meaning |

22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) |