15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence |

18844 | You would cripple mathematics if you denied Excluded Middle |

17963 | The facts of geometry, arithmetic or statics order themselves into theories |

17966 | Axioms must reveal their dependence (or not), and must be consistent |

12456 | I aim to establish certainty for mathematical methods |

8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) |

12461 | We believe all mathematical problems are solvable |

9633 | No one shall drive us out of the paradise the Cantor has created for us |

12462 | Only the finite can bring certainty to the infinite |

12460 | We extend finite statements with ideal ones, in order to preserve our logic |

12455 | The idea of an infinite totality is an illusion |

12457 | There is no continuum in reality to realise the infinitely small |

13472 | Hilbert aimed to eliminate number from geometry |

17967 | To decide some questions, we must study the essence of mathematical proof itself |

18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid |

17965 | The whole of Euclidean geometry derives from a basic equation and transformations |

17964 | Number theory just needs calculation laws and rules for integers |

17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience |

17698 | Logic already contains some arithmetic, so the two must be developed together |

12458 | Kant taught that mathematics is independent of logic, and cannot be grounded in it |

10113 | The grounding of mathematics is 'in the beginning was the sign' |

10115 | Hilbert substituted a syntactic for a semantic account of consistency |

12459 | The subject matter of mathematics is immediate and clear concrete symbols |

18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements |

10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions |

9636 | My theory aims at the certitude of mathematical methods |

17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge |