Racist Bullshit in Mathematics

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Robin Gandy’s “On the Axiom of Extensionality–Part 1”, Journal of Symbolic Logic, Vol. 21, No. 1 (Mar., 1956) quotes Alan Turing using a racist phrase.

A screengrab if the bottommatter of the first page of Gandy's paper. Received July 24, 1955. 1 Indeed A. M. Turing once told me that he had done this, and that the proof was fairly difficult. I have found among his manuscripts two versions of the proof: one is rather short and contains a fallacy which could not, I think, easily be put right; the other (perhaps a second draft) is unfinished and only a beginning. He may therefore have discovered and surmounted the fallacy. On the other hand, he always spoke of the axiom of extensionality as being 'the nigger in the woodpile', which suggests that he did not think his consistency was transcendental enough to accord with Gödel's theorem; but, by the results of this paper, it would have to be just that.
[Turing] always spoke of the axiom of extensionality as being ‘the nigger in the woodpile’, which suggests that he did not think his consistency proof was transcendental enough to accord Gödel’s theorem.

Yikes. Those unfamiliar with this particular racist phrase will be disappointed to learn that it’s still current enough in the UK to be used “totally unintentional[ly]”… whatever that means.

Gandy’s paper isn’t the first time I’ve been pulled out of my mathematical/logical/philosophical reverie by racist bullshit. When I was reading Ronald Clark’s The Life of Bertrand Russell, I posted a thread on Twitter of Russell’s many racist utterances, with a selection of three racist Bertrand Russell quotes; two anti-racist quotes repudiate his earlier statements, offering some modest redemption.

I found these episodes of casual, by-the-way racism jarring: they pulled me out of my investment with the material and my ability or even desire to identify with the author.

What’s galling is that Turing “always” spoke of the axiom of extensionality this way; Gandy thought the phrase worth repeating verbatim; the reviewers and editors and publishers thought the phrase acceptable; and those who cite the paper don’t seem to find this footnote worth remarking on. Gandy’s paper is important and widely cited—a foundational resource on extensionality in general, and functional extensionality in particular—but if I refer someone to it, I’m going to let them know to expect a disappointingly racist quote from Turing.

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