Russell's Hidden Substitutional Theory
1st Edition
Published on 20. August 1998
350 pages
978-0-19-535372-3 (ISBN)
Description
This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism.
More details
Other editions
Additional editions
Gregory Landini
Russell's Hidden Substitutional Theory
Book
09/1998
Oxford University Press Inc
€286.90
Shipment within 15-20 days
Content
- Intro
- Contents
- Introduction
- Quodlibet Ens Est Unum
- Overview
- PART I: THE UNRESTRICTED VARIABLE
- 1 Russell's Logicist Program
- Two Conceptions of Logicism: Frege and Russell
- Arithmetization
- Russell's Principle of Abstraction
- Logic as a Science
- 2 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
- 3 The New Theory of the Variable
- On Fundamentals" Against Denoting Concepts
- An Argument Against Frege?
- The Variable as Primitive
- The Road to Substitution
- PART II: TYPES AS LOGICAL GRAMMAR
- 4 The Logic of Substitution
- Russell's Original Principles of Substitution
- The Basic Logic of Propositions
- Substitutional Principles
- Identity
- Proofs of Propositional Identities
- 5 The "No Propositional Functions" Theory
- Substitution and Definite Descriptions
- Multiple Substitutions
- Comprehension and Identity
- Types as Logical Grammar
- 6 The "No-Classes" Theory
- Classes as Extensional Propositional Functions
- Complex Prototypes and Extensionality
- The General Theory of Classes
- Comparison with Principia Mathematica
- 7 The "No-Relations[sub(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
- PART III: RAMIFICATION
- 8 Les Paradoxes de la Logique
- Three Paradoxes of Propositions
- Substitutional Manuscripts of April/May 1906
- Poincaré's Vicious Circle Principle
- Logic without General Propositions
- The Statement Liar
- The König, Dixon, Berry, Richard, and Grelling Paradoxes
- Russell's "Mitigating Axiom
- The Demise of "Les Paradoxes
- 9 Mathematical Logic as Based on the Theory of Types
- Orders of Propositions
- Substitutional Logic cum Orders of Propositions
- Predicativity and Reducibility
- Paradoxes of Propositions Avoided
- 10 The Logic of Principia Mathematica
- The Formal System of Principia (cum *10)
- The Perils of Typical Ambiguity
- Orders within Types or Types within Orders?
- The Doctrine of the Unlimited Variable
- Poincaré's Vicious Circle Principle
- The Philosophical Justification of the Type Part of an Order/'Type Index
- The Philosophical Justification of the Order Part of an Order/Type Index
- The Multiple-Relation Theory of Judgment
- What Is Logic?
- What Logic Is Not
- Appendix A: Proof of the Peano Postulates
- Appendix B: Axioms, Theorems, and Definitions
- Bibliography
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Z
