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11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions |

10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' |

11004 | Necessity is provability in S4, and true in all worlds in S5 |

11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers |

11011 | Same say there are positive, negative and neuter free logics |

11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets |

10986 | Not all validity is captured in first-order logic |

10972 | The non-emptiness of the domain is characteristic of classical logic |

11024 | Semantics must precede proof in higher-order logics, since they are incomplete |

10985 | We should exclude second-order logic, precisely because it captures arithmetic |

10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques |

10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square |

10973 | A theory is logically closed, which means infinite premisses |

11007 | Quantifiers are second-order predicates |

10978 | In second-order logic the higher-order variables range over all the properties of the objects |

10971 | A logical truth is the conclusion of a valid inference with no premisses |

10988 | Any first-order theory of sets is inadequate |

10975 | Compactness does not deny that an inference can have infinitely many premisses |

10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset |

10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) |

10976 | Compactness makes consequence manageable, but restricts expressive power |

11014 | Self-reference paradoxes seem to arise only when falsity is involved |

11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us |

10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic |

10980 | Second-order arithmetic covers all properties, ensuring categoricity |

10997 | Von Neumann numbers are helpful, but don't correctly describe numbers |

11016 | Would a language without vagueness be usable at all? |

11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments |

11019 | Supervaluations say there is a cut-off somewhere, but at no particular place |

11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations |

10995 | A haecceity is a set of individual properties, essential to each thing |

11001 | Equating necessity with truth in every possible world is the S5 conception of necessity |

11002 | Equating necessity with informal provability is the S4 conception of necessity |

10992 | The point of conditionals is to show that one will accept modus ponens |

11017 | Some people even claim that conditionals do not express propositions |

10989 | The standard view of conditionals is that they are truth-functional |

10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics |

10982 | How can modal Platonists know the truth of a modal proposition? |

10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) |

10981 | A possible world is a determination of the truth-values of all propositions of a domain |

11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts |

10998 | The mind abstracts ways things might be, which are nonetheless real |

11005 | Negative existentials with compositionality make the whole sentence meaningless |

10966 | A proposition objectifies what a sentence says, as indicative, with secure references |