The Aussie Anthropoid has posted a lovely quote from William Stanley Jevons who explains why the concept ‘essence’ should be banished from philosophical discourse. Jevons was a 19^{th} century philosopher of science, economist and logician. Now I paid my dues as a historian of science working in a research project on the history of formal logic and my special area was the British algebra of logic, with Jevons as one of my subjects. Jevons’ logic was a modified form of the algebraic logic that George Boole had developed in his *Mathematical Analysis of Logic* (1847) and his *Laws of Thought* (1864). Nowadays everybody knows Boole’s name because of the pervasiveness of Boolean algebra in the world of computers. However there is a famous paper by Theodore Hailperin (famous amongst historian of logic that is) with the title* Boole’s algebra isn’t Boolean algebra*, which points out that Boolean algebra is the modified algebra of Jevons and not the original from Boole. Essentially, Jevons replaced Boole’s exclusive ‘or’ (aut in Latin for the logic experts), i.e. A or B but not ‘A and B’, with the inclusive ‘or’ (vel in Latin), i.e. A or B or ‘A and B’ thus making the De Morgan laws valid in this algebra.

Now I once held a public lecture, in a series on the history of the computer, about Boolean algebra and the life and work of George Boole. In due course I explained Hailperin’s point and went on to say that “the two valued algebra of classes that I have been discussing should not be called Boolean but by rights Jevonian but that sounds more like a geological period than a mathematical discipline!“

I think my professor was the only person of the fifty people present who got the joke.

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That pun isn’t so bad. Also, who were the other 49 people who didn’t get it? I mean, come on, people!

Hah, nice one.

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Some questions about boolean algebras: who was the first to speak about non-binary boolean algebra? And about infinite ones? Boole himself (even in the different version explained in this post) or someone other?

I’m afraid I can’t answer that. Firstly, I left the field of the history of logic a long, long time ago and secondly you’d have to ask someone, who studies the history of twentieth century logic and mathematic, which I have never done.