Logic in russell’s principles of mathematics

Abstract

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 re- cover the formal system, showing its philosophical background and its semantic completeness with respect to the tautologies of a modern sentential calculus. © 1996 by the University of Notre Dame. All rights reserved.