9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules |

18208 | We regard classes as mere symbolic or linguistic conveniences |

10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element |

10036 | In 'Principia' a new abstract theory of relations appeared, and was applied |

18248 | A real number is the class of rationals less than the number |

18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers |

10025 | Russell and Whitehead took arithmetic to be higher-order logic |

8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic |

10037 | 'Principia' lacks a precise statement of the syntax |

10093 | The ramified theory of types used propositional functions, and covered bound variables |

8691 | The Russell/Whitehead type theory was limited, and was not really logic |

10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains |

8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality |

8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it |

12033 | An object is identical with itself, and no different indiscernible object can share that |

10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory |

18275 | Only the act of judging completes the meaning of a statement |