Logic in Russell's Principles of Mathematics
type: Item
instance of: scholarly article
title: Logic in Russell's Principles of Mathematics
zbMATH Open document ID: 0883.03001
author: Gregory Landini
published in: Notre Dame Journal of Formal Logic
publication date: 1998-01-05T00:00:00Z
review text: The author gives a thorough discussion and reconstruction of the logical calculus proposed by Bertrand Russell in his ``Principles of Mathematics'' of 1903. The author starts with considerations on Russell's philosophy of logic. Like Frege before him, Russell advocated a ``syntactic approach'' according to which logic is a universal language with content in its own right. This is opposed to the ``semantic approach'' of Tarski and his precursors in the algebraic tradition regarding logic as the study of uninterpreted deductive calculi which can express a content, if an interpretation over an appropriate domain is provided. The author critically examines Russell's nonstandard view on the propositional calculus as a system which permits bindable predicate variables in subject and predicate positions. He compares it with Peano's universal quantification. After discussing Russell's definitions of logical primitives he proves the completeness of the propositional calculus with respect of the propositional analogs of sentential tautologies, and the semantical completeness with respect to nonpropositional analogs of sentential tautologies. In sum 29 theorems are proved.
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 1093120
zbMATH Keywords: logical calculus
zbMATH Keywords: implication
zbMATH Keywords: propositional calculus
zbMATH Keywords: quantifiers
zbMATH Keywords: completeness
zbMATH Keywords: Russell's philosophy of logic
reviewed by: Volker Peckhaus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040046142
OpenAlex ID: W2076117627
cites work: Russell, logicism, and the choice of logical constants
cites work: Q3235339
cites work: Q3967509
cites work: Q4530611
cites work: Q5588619
cites work: The principles of mathematics. With a new introduction by John Slater
cites work: Logic as calculus and logic as language
cites work: Q3778712
cites work: Q4357731
DOI: 10.1305/NDJFL/1040046142
description: scientific article; zbMATH DE number 1093120