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Types, Tableaus, and Gödel’s God

  • Melvin Fitting

Part of the Trends in Logic book series (TREN, volume 12)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Classical Logic

    1. Front Matter
      Pages 1-1
    2. Melvin Fitting
      Pages 3-10
    3. Melvin Fitting
      Pages 11-32
    4. Melvin Fitting
      Pages 33-42
    5. Melvin Fitting
      Pages 43-68
    6. Melvin Fitting
      Pages 69-76
    7. Melvin Fitting
      Pages 77-79
  3. Modal Logic

    1. Front Matter
      Pages 81-81
    2. Melvin Fitting
      Pages 83-104
    3. Melvin Fitting
      Pages 105-114
    4. Melvin Fitting
      Pages 115-130
  4. Ontological Arguments

    1. Front Matter
      Pages 131-131
    2. Melvin Fitting
      Pages 133-143
    3. Melvin Fitting
      Pages 145-172
  5. Back Matter
    Pages 173-181

About this book

Introduction

Gödel's modal ontological argument is the centrepiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Objections to the Gödel argument are examined, including one due to Howard Sobel showing Gödel's assumptions are so strong that the modal logic collapses. It is shown that this argument depends critically on whether properties are understood intensionally or extensionally.
Parts of the book are mathematical, parts philosophical. A reader interested in (modal) type theory can safely skip ontological issues, just as one interested in Gödel's argument can omit the more mathematical portions, such as the completeness proof for tableaus. There should be something for everybody (and perhaps everything for somebody).

Keywords

corpus identity issue logic modal logic semantic semantics sound

Authors and affiliations

  • Melvin Fitting
    • 1
  1. 1.Lehman College and the Graduate CenterCity University of New YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-0411-4
  • Copyright Information Kluwer Academic Publishers 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-3912-3
  • Online ISBN 978-94-010-0411-4
  • Series Print ISSN 1572-6126
  • Buy this book on publisher's site