5750 | Consistency is modal, saying propositions are consistent if they could be true together |

5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets |

5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) |

5740 | Second-order logic needs second-order variables and quantification into predicate position |

5741 | If every model that makes premises true also makes conclusion true, the argument is valid |

5735 | Maybe names and predicates can capture any fact |

5736 | No sort of plain language or levels of logic can express modal facts properly |

5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities |

5738 | We may be sure that P is necessary, but is it necessarily necessary? |

5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions |

5739 | Sometimes we want to specify in what ways a thing is possible |

5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives |

5742 | In possible worlds semantics the modal operators are treated as quantifiers |

5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal |

5749 | Possible worlds could be real as mathematics, propositions, properties, or like books |

5751 | The truth of propositions at possible worlds are implied by the world, just as in books |

5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility |