Editing Syllogism (section)

===Boole's acceptance of Aristotle===
[[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|Boole, George]]. [1854] 2003. ''[[The Laws of Thought]]'', with an introduction by J. Corcoran. Buffalo: [[Prometheus Books]].</ref><ref>van Evra, James. 2004. "'The Laws of Thought' by George Boole" (review). ''[[Philosophy in Review]]'' 24:167–69.</ref> Corcoran also wrote a point-by-point comparison of ''[[Prior Analytics]]'' and ''[[The Laws of Thought|Laws of Thought]]''.<ref name=":1">[[John Corcoran (logician)|Corcoran, John]]. 2003. "Aristotle's 'Prior Analytics' and Boole's 'Laws of Thought'." ''History and Philosophy of Logic'' 24:261–88.</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:<ref name=":1" />

# providing it with mathematical foundations involving equations;
# extending the class of problems it could treat, as solving equations was added to assessing [[Validity (logic)|validity]]; and
# expanding the range of applications it could handle, such as expanding propositions of 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 Aristotle's four propositional forms to one form, the form of equations, which by itself was 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."