10170 | While true-in-a-model seems relative, true-in-all-models seems not to be |

10166 | ZFC set theory has only 'pure' sets, without 'urelements' |

10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets |

10165 | 'Analysis' is the theory of the real numbers |

10174 | Mereological arithmetic needs infinite objects, and function definitions |

10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' |

10172 | Set-theory gives a unified and an explicit basis for mathematics |

10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures |

10169 | Relativist Structuralism just stipulates one successful model as its arithmetic |

10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) |

10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common |

10182 | There are Formalist, Relativist, Universalist and Pattern structuralism |

10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations |

10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous |

10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model |

10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out |

10171 | The existence of an infinite set is assumed by Relativist Structuralism |

10173 | A nominalist might avoid abstract objects by just appealing to mereological sums |