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The Project Gutenberg EBook of The Algebra of Logic, by Louis Couturat This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net Title: The Algebra of Logic Author: Louis Couturat Release Date: January 26, 2004 [EBook #10836] Language: English Character set encoding: TeX *** START OF THIS PROJECT GUTENBERG EBOOK THE ALGEBRA OF LOGIC *** Produced by David Starner, Arno Peters, Susan Skinner and the Online Distributed Proofreading Team. 1 THE ALGEBRA OF LOGIC BY LOUIS COUTURAT AUTHORIZED ENGLISH TRANSLATION BY LYDIA GILLINGHAM ROBINSON, B. A. With a Preface by PHILIP E. B. JOURDAIN. M. A. (Cantab.) Preface Mathematical Logic is a necessary preliminary to logical Mathematics. Mathematical Logic is the name given by Peano to what is also known (after Venn ) as Symbolic Logic ; and Symbolic Logic is, in essentials, the Logic of Aristotle, given new life and power by being dressed up in the wonderful almost magical armour and accoutrements of Algebra. In less than seventy years, logic, to use an expression of De Morgan's, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians would not recognize it, and many old-fashioned logicians will not recognize it. The metaphor is not quite correct: Logic has neither grown nor altered, but we now see more of it and more into it. The primary signi cance of a symbolic calculus seems to lie in the economy of mental e ort which it brings about, and to this is due the characteristic power and rapid development of mathematical knowledge. Attempts to treat the operations of formal logic in an analogous way had been made not infrequently by some of the more phi