Russell's Metaphysical Logic

by Bernard Linsky

Overview

This study reconciles distinct aspects of Russell's thought long 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 in the Introduction to Principia Mathematica. This account, which interprets Russell as being a realist about both universals and propositional functions, while distinguishing the two, provides a defense of some problematic features of the logic of PM 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.

Product Details

ISBN-13:	9781575869575
Publisher:	CSLI
Publication date:	01/15/2017
Series:	Lecture Notes , #101
Sold by:	Barnes & Noble
Format:	eBook
Pages:	176
File size:	4 MB

About the Author

Bernard Linsky is professor of philosophy at the University of Alberta and a fellow of the Royal Society of Canada. He is the author of The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition.

Table of 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 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