## From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege's Frege's book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Of the forty-five contributions here collected all but five are presented |

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### Contents

DEFINITION OF THE SYMBOLS | 10 |

Inference The Aristotelian modes of inference | 17 |

Peano 1889 The principles of arithmetic presented by a new method | 83 |

Dedekind 1890a Letter to Keferstein | 98 |

BuraliForti 1897 and 1897a A question on transfinite numbers | 104 |

Cantor 1899 Letter to Dedekind | 113 |

Russell 1902 Letter to Frege | 124 |

Zermelo 1904 Proof that every set can be wellordered | 139 |

Skolem 1922 Some remarks on axiomatized set theory | 290 |

Skolem 1923 The foundations of elementary arithmetic established | 302 |

Brouwer 1923b 1954 and 1954a On the significance of the principle | 334 |

Schonfinkel 1924 On the building blocks of mathematical logic | 355 |

von Neumann 1925 An axiomatization of set theory | 393 |

Kolmogorov 1925 On the principle of excluded middle | 414 |

Finsler 1926 Formal proofs and undecidability | 438 |

Hilbert 1927 The foundations of mathematics | 464 |

Konig 1905a On the foundations of set theory and the continuum | 145 |

Zermelo 1908 A new proof of the possibility of a wellordering | 183 |

Zermelo 1908a Investigations in the foundations of set theory I | 199 |

Descriptions | 216 |

Wiener 1914 A simplification of the logic of relations | 224 |

Skolem 1920 Logicocombinatorial investigations in the satisfiability | 252 |

Post 1921 Introduction to a general theory of elementary | 264 |

Fraenkel 1922b The notion definite and the independence of | 284 |

Weyl 1927 Comments on Hilberts second lecture on the foundations | 480 |

Ackermann 1928 On Hilberts construction of the real numbers | 493 |

Skolem 1928 On mathematical logic | 508 |

The properties | 525 |

Godel 1930a The completeness of the axioms of the functional | 582 |

Herbrand 193Ib On the consistency of arithmetic | 618 |

657 | |