10482 | The logic of ZF is classical first-order predicate logic with identity |

10492 | A few axioms of set theory 'force themselves on us', but most of them don't |

18192 | Do the Replacement Axioms exceed the iterative conception of sets? |

7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections |

10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves |

10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first |

13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) |

10699 | Does a bowl of Cheerios contain all its sets and subsets? |

14249 | Boolos reinterprets second-order logic as plural logic |

10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems |

10225 | Monadic second-order logic might be understood in terms of plural quantifiers |

10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic |

10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic |

10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets |

10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus |

10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed |

13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology |

10267 | We should understand second-order existential quantifiers as plural quantifiers |

10698 | Plural forms have no more ontological commitment than to first-order objects |

7806 | Boolos invented plural quantification |

10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences |

13841 | Why should compactness be definitive of logic? |

10491 | Infinite natural numbers is as obvious as infinite sentences in English |

10483 | Mathematics and science do not require very high orders of infinity |

10833 | Many concepts can only be expressed by second-order logic |

10490 | Mathematics isn't surprising, given that we experience many objects as abstract |

10700 | First- and second-order quantifiers are two ways of referring to the same things |

10488 | It is lunacy to think we only see ink-marks, and not word-types |

10487 | I am a fan of abstract objects, and confident of their existence |

10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. |

8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect |