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Aristotle's Prior Analytics and Boole's Laws of Thought

2003; Taylor & Francis; Volume: 24; Issue: 4 Linguagem: Inglês

10.1080/01445340310001604707

1464-5149

John Corcoran,

Philosophy and History of Science

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. … using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published. Paul Rosenbloom 1950 Acknowledgements For bringing errors and omissions to my attention, for useful suggestions, and for other help, I gladly acknowledge the following scholars : O. Chateaubriand (Brazil), D. Novotny (Czech Republic and USA), B. Smith (Germany and USA), J. Sagüillo (Spain), J. Gasser (Switzerland), I. Grattan-Guinness (UK), S. Burris, D. Hitchcock, G. Reyes and J. Van Evra (Canada), J. Anton, G. Boger, M. Brown, J. Burgess, W. Corcoran, J. Dawson, B. Decker, L. Jacuzzo, J. Kearns, W. Lawvere, K. Lucey, S. Mitchell, S. Nambiar, P. Penner, M. Scanlan, S. Wood, J. Yu and J. Zeccardi (USA). Earlier versions were presented at the Buffalo Logic Colloquium in March 2003 and the University of South Florida in April 2003. This work is gratefully dedicated to Professor Ivor Grattan-Guinness, founding Editor of the international journal History and Philosophy of Logic, who has done more than any other person toward establishing the combined field of history and philosophy of logic as a rigorous, productive, and recognized field of scholarship.