Editing Term logic (section)

==Boole’s acceptance of Aristotle==
[[File:Alexander - Commentaria in Analytica priora Aristotelis, 1549 - 4725692.tif |thumb|''Commentaria in Analytica priora Aristotelis'', 1549]]
[[George Boole]]'s unwavering acceptance of Aristotle's logic is emphasized by the historian of logic [[John Corcoran (logician)|John Corcoran]] in an accessible introduction to ''Laws of Thought''<ref>[[George Boole]]. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.</ref> Corcoran also wrote a point-by-point comparison of ''Prior Analytics'' and ''Laws of Thought''.<ref>John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261–288.</ref> According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were “to go under, over, and beyond” Aristotle's logic by:

# providing it with mathematical foundations involving equations;
# extending the class of problems it could treat– from assessing validity to solving equations; and
# expanding the range of applications it could handle– e.g. from propositions having only two terms to those having arbitrarily many.

More specifically, Boole agreed with what [[Aristotle]] said; Boole's ‘disagreements’, if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced the four propositional forms of [[Aristotle's logic]] to formulas in the form of equations– by itself a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic– another revolutionary idea –involved Boole's doctrine that Aristotle's rules of inference (the “perfect syllogisms”) must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce “No quadrangle that is a square is a rectangle that is a rhombus” from “No square that is a quadrangle is a rhombus that is a rectangle” or from “No rhombus that is a rectangle is a square that is a quadrangle”.