Research Catalog

Title

Russell's hidden substitutional theory / Gregory Landini.

Author

Landini, Gregory.

Publication

New York : Oxford University Press, 1998.

Items in the Library & Off-site

Details

Description

xi, 337 pages; 24 cm

Summary

In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two works. The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions.

Subject

• Russell, Bertrand, 1872-1970
• Russell, Bertrand, (1872-1970)
• Russell, Bertrand
• 1900-1999
• Proposition (Logic) > History > 20th century
• Logic, Symbolic and mathematical > History > 20th century
• 31.02 philosophy and theory of mathematics
• Logic, Symbolic and mathematical
• Proposition (Logic)
• Sprachlogik
• Mathematische Logik
• Propositielogica
• Wiskunde
• Filosofia da matemática
• Lógica
• Proposition (logique) > 20e siècle
• Logique symbolique et mathématique > 20e siècle

Genre/Form

History.

Bibliography (note)

• Includes bibliographical references (p. 325-332) and index.

Contents

The Unrestricted Variable -- Russell's Logicist Program -- Two Conceptions of Logicism: Frege and Russell -- Arithmetization -- Russell's Principle of Abstraction -- Logic as a Science -- The Logic of The Principles of Mathematics -- The Calculus for the Logic Propositions -- Russell's Definitions -- The Theory of Implication -- Quodlibet Ens Est Unum -- Denoting Concepts -- The Analysis of the Variable -- The New Theory of the Variable -- "On Fundamentals" Against Denoting Concepts -- An Argument Against Frege? -- The Variable as Primitive -- The Road to Substitution -- Types as Logical Grammar -- The Logic of Substitution -- Russell's Original Principles of Substitution -- The Basic Logic of Propositions -- Substitutional Principles -- Identity -- Proofs of Propositional Identities -- The "No Propositional Functions" Theory -- Substitution and Definite Descriptions -- Multiple Substitutions -- Comprehension and Identity -- Types as Logical Grammar -- The "No-Classes" Theory -- Classes as Extensional Propositional Functions -- Complex Prototypes and Extensionality -- The General Theory of Classes -- Comparison with Principia Mathematica -- The "No-Relations[subscript e]" Theory -- Relations-in-Extension in Principia Mathematica -- Relations-in-Extension in the Substitutional Theory -- Cantor's Paradox of the Greatest Cardinal -- The Burali-Forti Paradox -- Ramification -- Les Paradoxes de la Logique -- Three Paradoxes of Propositions -- Substitutional Manuscripts of April/May 1906 -- Poincare's Vicious Circle Principle.

ISBN

• 0195116836
• 9780195116830

LCCN

97022750

OCLC

• ocm37246630
• 37246630
• SCSB-9454799

Owning Institutions

Princeton University Library