# Aristotle's prior analytics and Boole's laws of thought

*History and Philosophy of Logic.*24 (4):261-288 (2003)

**Abstract**

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.

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Archival date: 2014-11-07

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References found in this work BETA

Critique of Pure Reason.Kant, I.

On Denoting.Russell, Bertrand

Logic, Semantics, Metamathematics.Tarski, Alfred

The Principles of Mathematics.Russell, Bertrand

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Citations of this work BETA

Aristotle's Demonstrative Logic.Corcoran, John

The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.Corcoran, John & Sagüillo, José Miguel

LOGIC TEACHING IN THE 21ST CENTURY.Corcoran, John

Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW]Dutilh Novaes, Catarina & Andrade-Lotero, Edgar

Aristotle’s Prototype Rule-Based Underlying Logic.Corcoran, John

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