Boole's logic

  • Dale Jacquette
  • Published 2008 in British Logic in the Nineteenth Century

Abstract

The development of modern symbolic logic has involved steady progress from a few extraordinary episodes. Among the handful of outstanding insights and innovations that have contributed most dramatically to the progress of contemporary logic must be included George Boole's algebraic analysis of traditional Aristotelian syllogistic logic. Although Boole's logic was at most a forerunner and not yet a prototype of first-order propositional and predicate-quantificational logic or the so-called functional calculus, Boole, independently of but partially in agreement with parallel advances by Augustus De Morgan, introduced several conceptual breakthroughs that paved the way for the formalizations of mathematical logic as they came to fruition in the work of C.S. Peirce, Gottlob Frege, and, especially, A.N. Whitehead and Bertrand Russell's Principia Mathematica. Boole was trained as a mathematician and in particular as an algebraist. In The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning [1847], The Calculus of Logic [1848], and An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities [1854], Boole revolutionized the logic of his day, which was an enhanced four-term syllogistic logic that with minor improvements had remained essentially unchanged since its formulation in Aristotle's Prior Analytics and popularized in Antoine Arnauld's The Port Royal Logic [1662]. Thus, Immanuel Kant, in his Critique of Pure Reason [1787], was able to report a mere sixty years before the publication of Boole's Mathematical Analysis of Logic, that: 'It is remarkable.. . that to the present day this [Aristotelian] logic has not been able to advance a single step, and is thus to all appearance a closed and completed body of doctrine'. 1 Kant 's pronouncement remained appropriate until Boole discovered how to symbolize logic as a specialized interpretation of a more general algebra of variables and values. Boole afterward echoes Kant 's words when in the Laws of Thought he relates that: 'In its ancient and scholastic form, indeed, the subject of Logic stands almost exclusively associated with the great name of Aristotle. As it was presented to ancient Greece in the partly technical, partly metaphysical disquisitions of the Organon, such, with scarcely any essential change, it has continued to the present day. '2

DOI: 10.1016/S1874-5857(08)80011-8

Cite this paper

@inproceedings{Jacquette2008BoolesL, title={Boole's logic}, author={Dale Jacquette}, booktitle={British Logic in the Nineteenth Century}, year={2008} }