Types, Tableaus, and Gödel’s God: 12 (Trends in Logic, 12) - Hardcover

Fitting, M.

Hardcover

ISBN 10: 1402006047 ISBN 13: 9781402006043

Publisher: Springer, 2002

Synopsis

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 safelyskip 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).

About this title

Synopsis

Godel'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 Godel argument is fully formalized. Objections to the Godel argument are examined, including one due to Howard Sobel showing Godel'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 Godel'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).

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 1402006047
• ISBN 13: 9781402006043
• Binding: Hardcover
• Number of pages: 196