 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.