George Boole's Deductive System
Frank Markham Brown
Source: Notre Dame J. Formal Logic Volume 50, Number 3
(2009), 303-330.
Abstract
The deductive system in Boole's Laws of Thought (LT) involves both an algebra, which we call proto-Boolean, and a "general method in Logic" making use of that algebra. Our object is to elucidate these two components of Boole's system, to prove his principal results, and to draw some conclusions not explicit in LT. We also discuss some examples of incoherence in LT; these mask the genius of Boole's design and account for much of the puzzled and disparaging commentary LT has received. Our evaluation of Boole's logical system does not differ substantially from that advanced in Hailperin's exhaustive study, Boole's Logic and Probability. Unlike the latter work, however, we make direct use of the polynomials native to LT rather than appealing to formalisms such as multisets and rings.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1257862040
Digital Object Identifier: doi:10.1215/00294527-2009-013
Zentralblatt MATH identifier: 05657221
Mathematical Reviews number (MathSciNet): MR2572976
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