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

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

Authors
John Corcoran
State University of New York, Buffalo
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.
Keywords ARISTOTLE  SYLLOGISM  NATURAL DEDUCTION  GEORGE BOOLE  BOOLEAN-INTERPRETATION FALLACY  EXISTENTIAL IMPORT  ALFRED TARSKI  FORMAL ONTOLOGY  FORMAL EPISTEMOLOGY  UNDERLYING LOGIC
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DOI 10.1080/01445340310001604707
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References found in this work BETA

Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Logic, Logic and Logic.George Boolos & Richard C. Jeffrey - 1998 - Studia Logica 66 (3):428-432.
The Oxford Dictionary of Philosophy.Edward Craig & Simon Blackburn - 1996 - Philosophical Review 105 (2):250.

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Citations of this work BETA

Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
LOGIC TEACHING IN THE 21ST CENTURY.John Corcoran - 2016 - Quadripartita Ratio: Revista de Argumentación y Retórica 1 (1):1-34.

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