Notre Dame Journal of Formal Logic

Logic in Russell's Principles of Mathematics

Gregory Landini


Unaware of Frege's 1879 Begriffsschrift, Russell's 1903 The Principles of Mathematics set out a calculus for logic whose foundation was the doctrine that any such calculus must adopt only one style of variables–entity (individual) variables. The idea was that logic is a universal and all-encompassing science, applying alike to whatever there is–propositions, universals, classes, concrete particulars. Unfortunately, Russell's early calculus has appeared archaic if not completely obscure. This paper is an attempt to recover the formal system, showing its philosophical background and its semantic completeness with respect to the tautologies of a modern sentential calculus.

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Notre Dame J. Formal Logic Volume 37, Number 4 (1996), 554-584.

First available in Project Euclid: 16 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03-03: Historical (must also be assigned at least one classification number from Section 01)
Secondary: 01A60: 20th century 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B05: Classical propositional logic


Landini, Gregory. Logic in Russell's Principles of Mathematics . Notre Dame J. Formal Logic 37 (1996), no. 4, 554--584. doi:10.1305/ndjfl/1040046142.

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