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13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation |

13883 | The best way to understand a philosophical idea is to defend it |

10142 | The attempt to define numbers by contextual definition has been revived |

9868 | An expression refers if it is a singular term in some true sentences |

13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology |

13892 | One could grasp numbers, and name sizes with them, without grasping ordering |

13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept |

17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are |

13862 | There are five Peano axioms, which can be expressed informally |

17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence |

17854 | What facts underpin the truths of the Peano axioms? |

17855 | It may be possible to define induction in terms of the ancestral relation |

13894 | Sameness of number is fundamental, not counting, despite children learning that first |

17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition |

13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number |

10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic |

8692 | Frege has a good system if his 'number principle' replaces his basic law V |

13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions |

13869 | Number platonism says that natural number is a sortal concept |

13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism |

13873 | Treating numbers adjectivally is treating them as quantifiers |

7804 | Wright has revived Frege's discredited logicism |

13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals |

13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes |

13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms |

13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects |

13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems |

13884 | The idea that 'exist' has multiple senses is not coherent |

13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence |

9878 | Contextually defined abstract terms genuinely refer to objects |

13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals |

13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities |

13866 | A concept is only a sortal if it gives genuine identity |

13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them |

13898 | If we can establish directions from lines and parallelism, we were already committed to directions |

17857 | We can accept Frege's idea of object without assuming that predicates have a reference |

13882 | A milder claim is that understanding requires some evidence of that understanding |

13885 | If apparent reference can mislead, then so can apparent lack of reference |