George Boole's Deductive System

Authors

• Frank Markham Brown, Air Force Institute of Technology

Document Type

Article

Publication Date

7-2009

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.

Comments

Copyright © 2009 University of Notre Dame

The "Link to Full Text" opens the full article as hosted at Project Euclid.

MathSciNet: MR2572976

DOI

10.1215/00294527-2009-013

Source Publication

Notre Dame Journal of Formal Logic (ISSN 0029-4527)

Recommended Citation

Brown, F. M. (2009). George Boole’s Deductive System. Notre Dame Journal of Formal Logic, 50(3), 303–330. https://doi.org/10.1215/00294527-2009-013