Boole: From calculating numbers to calculating thoughts

Abstract

We are often taught in a first course in the history of logic or in the philosophy of mathematics that Frege singlehandedly invented second-order logic, and that there was no one close to his achievements before him. In a slightly more sophisticated version of the same course, a qualifying nod is made in the direction of Boole, who did "bring quantifiers to logic". But the student is given the impression that Boole, like Frege, rose ex nihilo from the weedy wasteland of Aristotelian syllogistic reasoning. While this is not a wholly mistaken impression, it is misleading, and should be corrected. Boole was working in the context of a revival of logic-where "logic", especially as it was being taught in England, was gradually being prised away from the doxa of Aristotelian syllogistic reasoning. It is in this context that Boole made innovative contributions by bringing together a number of ideas. The combination brought us closer to our modern conception of logic. © 2010 Springer-Verlag Berlin Heidelberg.