from the Writings of

David Hilbert

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek. | |

Letter to Frege, 1899 |

If the arbitrarily established axioms do not contradict each other with all their consequences, then they are true, then the things defined through the axioms exist. That is for me the criterion of truth and existence. | |

Letter to Frege, Dec. 29, 1899 |

© created 1997-05-10 modified 2011-07-18