9550 | We only know relational facts about the empty set, but nothing intrinsic |

9562 | In simple type theory there is a hierarchy of null sets |

9572 | Realists about sets say there exists a null set in the real world, with no members |

9573 | The null set is a structural position which has no other position in membership relation |

9551 | What is special about Bill Clinton's unit set, in comparison with all the others? |

9549 | The set theorist cannot tell us what 'membership' is |

9571 | ZFU refers to the physical world, when it talks of 'urelements' |

9563 | A pack of wolves doesn't cease when one member dies |

18151 | Could we replace sets by the open sentences that define them? |

8758 | We could talk of open sentences, instead of sets |

9561 | The mathematics of relations is entirely covered by ordered pairs |

9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced |

9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum |

9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects |

9553 | Analytic geometry gave space a mathematical structure, which could then have axioms |

10192 | We can replace existence of sets with possibility of constructing token sentences |

10265 | Chihara's system is a variant of type theory, from which he can translate sentences |

8759 | We can replace type theory with open sentences and a constructibility quantifier |

10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' |

9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? |

9566 | No scientific explanation would collapse if mathematical objects were shown not to exist |

9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' |

9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them |

9574 | 'Gunk' is an individual possessing no parts that are atoms |