10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order |

10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables |

23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical |

10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions |

10638 | A pure logic is wholly general, purely formal, and directly known |

10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? |

10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations |

10635 | Second-order quantification and plural quantification are different |

10636 | Plural plurals are unnatural and need a first-level ontology |

10641 | Traditionally we eliminate plurals by quantifying over sets |

10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise |

10639 | Plural quantification may allow a monadic second-order theory with first-order ontology |

23447 | In classical semantics singular terms refer, and quantifiers range over domains |

23443 | The axioms of group theory are not assertions, but a definition of a structure |

23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms |

23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory |

23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world |

14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality |

14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures |

14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories |

14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets |

14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure |

14083 | Structuralism is right about algebra, but wrong about sets |

14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures |

23441 | Logical truth is true in all models, so mathematical objects can't be purely logical |

23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics |

14091 | There may be a one-way direction of dependence among sets, and among natural numbers |

10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' |

10637 | Ordinary speakers posit objects without concern for ontology |

14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals |

10782 | The modern concept of an object is rooted in quantificational logic |

10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? |