17926 | Rejecting double negation elimination undermines reductio proofs |

17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation |

17924 | Excluded middle says P or not-P; bivalence says P is either true or false |

17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it |

17930 | Axioms are 'categorical' if all of their models are isomorphic |

17928 | Ordinal numbers represent order relations |

17923 | Intuitionists only accept a few safe infinities |

17941 | Infinitesimals were sometimes zero, and sometimes close to zero |

17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths |

17936 | Transfinite induction moves from all cases, up to the limit ordinal |

17940 | Most mathematical proofs are using set theory, but without saying so |

17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it |

17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? |

17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies |

17939 | Mathematics can reveal structural similarities in diverse systems |

17938 | Mathematics can show why some surprising events have to occur |

17933 | Reductio proofs do not seem to be very explanatory |

17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory |

17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems |

17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? |

17937 | Mathematical generalisation is by extending a system, or by abstracting away from it |