## Logic from Russell to ChurchThis volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights |

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### Contents

1 | |

29 | |

77 | |

Chapter 4 Thoralf Albert Skolem | 127 |

Life Logic and Automated Deduction | 195 |

Chapter 6 The Logic of the Tractatus | 255 |

Chapter 7 Leśniewskis Logic | 305 |

Chapter 8 Hilberts Proof Theory | 321 |

Chapter 10 Gödels Logic | 449 |

Chapter 11 Tarskis Logic | 511 |

Chapter 12 Emil Post | 617 |

Chapter 13 Gentzens Logic | 667 |

Chapter 14 Lambdacalculus and Combinators in the 20th Century | 723 |

Chapter 15 The Logic of Church and Curry | 819 |

Chapter 16 Paradoxes Selfreference and Truth in the 20th Century | 875 |

1015 | |

### Common terms and phrases

abstract algebra arithmetic axiom axiom of choice axiomatic Barendregt Böhm Boolean Brouwer Church classical combinatory logic complete Computer Science concept consistency proof construction defined definition derivation disjunction domain editors epsilon calculus epsilon terms equivalent expression finite finitist first-order formal system formula Frege Gentzen geometry Gödel Heijenoort Herbrand Heyting Hilbert and Bernays implected incompleteness theorem induction infinite interpretation intuitionistic logic Jacques Herbrand Journal of Symbolic Kleene Kreisel L. E. J. Brouwer language lectures Logik Löwenheim Math Mathematical Logic Mathematik Meinong’s Meinongian metamathematical method natural deduction natural numbers negation normal form notion number theory objects paper paradox Philosophy Post Post’s predicate logic problem proof theory propositional logic propositions provable proved quantifiers real numbers recursive functions relation result rules Russell Russell’s semantics sentence sentential sequence sequent calculus set theory Skolem Symbolic Logic Tarski thesis translation truth undecidable University variables Wittgenstein