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Programs, Proofs, Processes Conference on Computability in Europe

CiE 2010: Programs, Proofs, Processes pp 172-179 | Cite as

Boole: From Calculating Numbers to Calculating Thoughts

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)


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.


Natural Kind Modern Conception Declarative Sentence Logical Calculation Syllogistic Reasoning

I should like to thank the reviewers of this article for many helpful comments on the draft version.








Friend M. (2010) Boole: From Calculating Numbers to Calculating Thoughts. In: Ferreira F., Löwe B., Mayordomo E., Mendes Gomes L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg



