How the continuum hypothesis could have been a fundamental axiom

Like many, I greatly admire Joel Hamkins’s terrific combination of technical prowess and expository ability as a mathematician. I’ve learnt a great deal from him. And I hope to learn more: he is promising us a book on ten ways of proving Gödelian incompleteness. Wouldn’t it be great, too, if one day he wrote an introductory book on forcing with his customary verve and insight?

I’m not always as convinced by his more philosophical pieces, but that’s philosophy for you. But I do think that his new approachable piece on “How the continuum hypothesis could have been a fundamental axiom” is particularly interesting and thought-provoking. In a close possible world in which Newton and Leibniz had said more about infinitesimals, there is a natural way our mathematics might have developed in which the continuum hypothesis would have come to be seen as axiomatic. Or so goes his story. You’ll find slides for a talk here.  And a preprint of quite a short paper on the arXiv here. Intriguing.

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