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18395 | Sets are mereological sums of the singletons of their members |

15496 | We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton |

15500 | Classes divide into subclasses in many ways, but into members in only one way |

15499 | A subclass of a subclass is itself a subclass; a member of a member is not in general a member |

15498 | We can accept the null set, but there is no null class of anything |

15502 | There are four main reasons for asserting that there is an empty set |

15503 | We needn't accept this speck of nothingness, this black hole in the fabric of Reality! |

15497 | We can replace the membership relation with the member-singleton relation (plus mereology) |

15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets |

15506 | If we don't understand the singleton, then we don't understand classes |

15511 | If singleton membership is external, why is an object a member of one rather than another? |

15513 | Maybe singletons have a structure, of a thing and a lasso? |

15507 | Set theory has some unofficial axioms, generalisations about how to understand it |

10191 | Set theory reduces to a mereological theory with singletons as the only atoms |

15508 | If singletons are where their members are, then so are all sets |

15514 | A huge part of Reality is only accepted as existing if you have accepted set theory |

15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it |

15525 | Plural quantification lacks a complete axiom system |

15518 | I like plural quantification, but am not convinced of its connection with second-order logic |

15524 | Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory |

15517 | Giving up classes means giving up successful mathematics because of dubious philosophy |

15515 | To be a structuralist, you quantify over relations |

15520 | Existence doesn't come in degrees; once asserted, it can't then be qualified |

15504 | Atomless gunk is an individual whose parts all have further proper parts |

15501 | We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture |

15516 | A property is any class of possibilia |

14748 | The many are many and the one is one, so they can't be identical |

6129 | Lewis affirms 'composition as identity' - that an object is no more than its parts |

15512 | In mereology no two things consist of the same atoms |

15519 | Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power |

15521 | Given cats, a fusion of cats adds nothing further to reality |

15522 | The one has different truths from the many; it is one rather than many, one rather than six |

10660 | A commitment to cat-fusions is not a further commitment; it is them and they are it |

14244 | Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions |

10566 | Lewis prefers giving up singletons to giving up sums |

15509 | Some say qualities are parts of things - as repeatable universals, or as particulars |