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Metaphysical Logic cover

Russell's Metaphysical Logic

Bernard Linsky

This volume reconciles distinct aspects of Bertrand Russell's views commonly thought to be incompatible: the metaphysics of universals and facts from Russell's Logical Atomism period and the philosophical justification of the ramified theory of types found in the Introduction to Principia Mathematica. Linsky's account, which is unique in treating logical and metaphysical issues with equal attention, provides a defense of some problematic features of the logic of Principia Mathematica including the Axiom of Reducibility and the Vicious Circle Principle. Russell's seemingly ambivalent attitude towards propositions and functions is explained by interpreting both with a broadened notion of logical construction. Contrary to other recent interpretations, this account follows Alonzo Church's technical formulation of the ramified theory of types and interprets the quantifiers as objectual, ranging over functions as entities, while being consistent with the “multiple relation” theory of judgment.

Bernard Linsky is a professor of philosophy at the University of Alberta

Contents

  • 1 Russell's Changing Ontology
  • 2 Universals and Propositional Functions
    • 2.1 Universals
    • 2.2 Propositional Functions
    • 2.3 Universals and Types
  • 3 Propositions
    • 3.1 Russell Abandons Propositions
    • 3.2 The Unity of Propositions
    • 3.3 Complex Entities
  • 4 The Ramified Theory of Types
    • 4.1 The Church's r-types
    • 4.2 The Paradox of Propositions
    • 4.3 Other Formulations
  • 5 Types in Principia Mathematica
    • 5.1 The Vicious Circle Principle
    • 5.2 Predicative Functions and Matrices
    • 5.3 Logical Form and Logical Type
  • 6 The Axiom of Reducibility
    • 6.1 Objections to the Axiom
    • 6.2 The Origin of the Axiom
    • 6.3 Doubts About the Axiom
    • 6.4 Principia Mathematica as Intensional Logic
    • 6.5 Grelling's Paradox and the Axiom
    • 6.6 The Identity of Indiscernibles
  • 7 Logical Constructions
    • 7.1 Definite Descriptions
    • 7.2 The Multiple Relation Theory
    • 7.3 The No-Class Theory
    • 7.4 Constructing the Numbers
    • 7.5 Constructing Matter
    • 7.6 Constructions and Formal Semantics
  • 8 Postscript on Logicism
  • References

9/15/99

ISBN (Paperback): 1575862107 (9781575862101)
ISBN (Cloth): 1575862093 (9781575862095)
ISBN (Electronic): 1575869578 (9781575869575)

Subject: Philosophy; Russell, Bertrand; Logic

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