ZFC is inconsistent

Listening to Mikroutsikos – Milva – Volpe d”amore
and Live 1995

Part surprise, part dark fear that this was always a possibility: ZFC is inconsistent.

You can read the paper here.

For who doesn’t get the letter soup: ZFC stands for the Zermelo & Fraenkel & Axiom of Choice system of axioms for set theory. ZFC is supposed to be the foundation for modern mathematics. Alas, mathematics appears to be founded in the minds of mathematicians and not on those axioms.

Around 1900, Gottlob Frege (1848-1925) started the business of axiomising set theory. When he had one of his books ready for print, Bertrand Russell (1872-1970) wrote him about what became known as Russell’s paradox. Frege still wanted his book printed, but hurriedly included a line that Russell’s paradox made him doubt.

“Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion.” (Gottlob Frege, 1903)

Logicomix tells the saga in vivid comics. The problem with Logicomix is that they haven’t read my book ALOE (1981, 2007, 2011), while there now is this new result on ZFC, that puts quite a bit of flavour on the connection between Russell and Cantor and ZFC.

Indeed, there is a new dramatic story to tell, involving the need to boycott Holland.

Also, the authors of Logicomix are all Greek, except for Annie Di Donna: which not only shows the importance of exceptions, but also indicates the surprising links in Europe, say between Holland and Greece – or my admiration for Milva in 1995 in Syracuse (Magna Graecia). But, of course, math is an issue for the whole world, so don’t feel excluded.

Logicomix, cover (Source: wikimedia commons)

Logicomix, cover (Source: wikimedia commons)

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