Abstract

George Boole published his account on hypotheticals in his pamphlet The Mathematical Analysis of Logic in 1847. Hypothetical deductions were not as developed as categorical ones by Boole’s time. It was still common practice to reduce hypotheticals to categoricals. Boole innovated by proposing an algebraic method to derive (equations expressing) the conclusions of hypotheticals. He had developed a calculus of classes for categoricals in his first pamphlet chapters and seemingly intended extending it to hypotheticals. Nonetheless, propositions can be only true or false. In contradistinction with his approach for categorical propositions, here it was not possible to consider things or classes of things but only the cases and conjunctures of circumstances in which the propositions are true. Some criticisms have been raised concerning Boole’s view of logic as the solution of algebraic equations. In order to circumvent such criticisms, we construct a deductive system based on Boole's algebraic treatment and apply it to deductions of those hypotheticals analyzed by Boole. We found that Barbara translated in our notation is useful to eliminate symbols in such deductions. The deductive system presented here has the potential to provide a new perspective on Boole’s approach to hypotheticals in The Mathematical Analysis of Logic.