History of Logic Seminar Series - Talk: Stanley Burris, "Justifying Boole's Algebra of Logic" (11.02.2026)
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We are pleased to announce the fourth session of the second annual cycle of the History of Logic Seminar Series. The session will be held on Wednesday, February 11, from 3 to 5 p.m. CET.
We will meet via Zoom. To have the Zoom link, please reach out to us at historyofl...@gmail.com.
On this occasion, we will host a talk by Stanley Burris (University of Waterloo). His talk is titled Justifying Boole's Algebra of Logic. Here is a short abstract:
Although Boole's algebra of logic was greatly admired for its ability to derive correct conclusions from premises, his use of uninterpretable terms in derivations did not sit well with scholars. He had given two radically different foundations for his work in The Laws of Thought: (1) an axiomatic approach based on laws used in the algebra of numbers plus his special law x^2 = x, and rules of inference; (2) a numerical decision procedure to determine which statements were correct in his algebra of logic. Neither were convincing to others, and within a decade Jevons had initiated changes to eliminate uninterpretable terms, leading eventually to modern axiomatic Boolean algebra. Boole's foundations were ignored for a century, until the 1970s when Hailperin showed how to perfect Boole's axiomatic approach (1), introducing models based on signed multisets instead of classes – this eliminated the
problem with uninterpretable terms. It was (2) that Boole said was the real foundation of his work, but it continued to be ignored until it was made precise in 2013 by Burris and Sankappanavar, showing that Boole's decision procedure applied to Horn sentences. Using this, one can verify that Boole's algebra of logic is correct.
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Kind regards,
Antonio