Performing truth

The title of this blog entry could be yet another proposed synonym for mathematics, one that hints at an alternative to the sterile but persistent opposition between discovery and invention.  Or it could be an allusion to the practice of mathematicians by which what corresponds to our intuition is made to be true by a process of successive refinements and clarifications, a practice performed, for instance, by the characters designated by Greek letters in Lakatos’s Proofs and Refutations. The word “perform” is used in the sense of J. L. Austin’s performative utterances, by which states of affairs are brought about simply by pronouncing words.

In some cases we can make something the case by saying that it is. Alas, I cannot lose ten pounds by saying that I am doing so, nor can I persuade you of a proposition by saying that I am doing so.

That quotation from the Stanford Philosophy of Encyclopedia fails to do justice to the practice of a mathematician, which largely does consist in persuading colleagues of the truth of a proposition by pronouncing the right words in the right order.  I’m counting on the psychoanalysts following this blog to confirm (or disconfirm) my suspicion that psychoanalytic theory views speech as a source of pleasure insofar as it has the power to bring about changes in reality.  And this, I am tempted to argue (but I will resist the temptation), is a powerful source of pleasure in mathematics.

Having said that, I don’t doubt that some mathematicians find pure logical syntax pleasurable as well.

This time around I want to draw attention instead to the practice of making value judgments real simply by pronouncing them.  I have in mind the process by which, by publishing an article with the title John Horton Conway: the world’s most charismatic mathematician, Siobhan Roberts (or, more likely, her editor at the Guardian) has in fact made John Conway the world’s most charismatic mathematician, in the same way that James Brown has been the hardest working man in show business ever since he was introduced as such in 1963.  And while the numerous contenders for the  title of Mozart of mathematics can look forward to a rude struggle to claim the honor, Galois secured his position as Rimbaud of mathematics when the professional ice-hockey player François-Henri Désérable published last year’s best-seller Évariste.

Roberts also pronounced me, in a potentially performative tweet, a (the?) “poetic mathematician,” but there’s no chance that will stick; my prose is too obviously prosaic when read alongside the likes of Goethe (pp. 83, 172, 190, 208) or Leconte de Lisle (p. 163) or Rakim (p. 248) or Patti Smith (pp. 250-1) or Mos Def/Yasiin Bey (p. 252).  On the other hand, the very kind review by M. Schiff in Choice, by pronouncing that MWA is “part memoir” in a text primarily addressed to academic librarians, may well have turned it into a book that is part memoir — aided, indeed, by Amazon’s habit of ranking it among best-selling memoirs (today, most implausibly, it’s the 944th best-selling memoir in Canada’s Amazon site).  If so, I have no choice but to get used to it, even if I quoted Henry Lord Brougham as early as p. 14 to make the point that if the book is the memoir of anything it’s the memoir of an ideal-type, not of a “generally uninteresting and unvaried” individual like the one writing these lines.


9 thoughts on “Performing truth

    1. mathematicswithoutapologies Post author

      Is that what this guy would do?

      More seriously (?), I have always found it stimulating to read Pierce and some of the other pragmatists, including Rorty, but given my orientation it all comes back to me saying something like “human beings make their own history, but not in circumstances of their own choosing.” Plus the very enlightening discussions of signs in Pierce.

      This particular post would best be filed under “social realism,” in the sociological sense.


      1. Jon Awbrey

        From what I’ve seen, Peirce’s brand of pragmatism, as an application of the closure cum representation principle known as the pragmatic maxim and incorporating realism about generals, is a sturdier stage for mathematical performance than the derivative styles of neo-pragmatism that Gene Halton aptly described as “fragmatism”.


  1. Matt

    I’m always pleased to see this academic niche receiving free propaganda (in the case of Conway, not my particular subniche), so I’m not inclined to care so much about the veracity of the claims therein as much as I am about whom it attracts from physics, philosophy, or even those freshwater economists (who not very secretly want to be mathematicians anyways).


  2. Jon Awbrey

    On the relationship between ideal types, real personalities, and social realities we have this from The Man Without Qualities:

    The well-known capacity that thoughts have — as doctors have discovered — for dissolving and dispersing those hard lumps of deep, ingrowing, morbidly entangled conflict that arise out of gloomy regions of the self probably rests on nothing other than their social and worldly nature, which links the individual being with other people and things; but unfortunately what gives them their power of healing seems to be the same as what diminishes the quality of personal experience in them.

    Robert Musil


  3. Martin Krieger

    Eric Livingston did a book, The Ethnomethodolgical Foundations of Mathematics (not sure if this is the exact title), devoted to the performative character of work at the blackboard, when one is trying to explain a proof to another mathematician. It is fairly technical, since it draws on a particular way of thinking sociologically, but I believe its basic insights are to the point. A proof is actually an act of proving. He uses some simple examples in his later work, including an introduction to ethnomethodology. I suspect he is the most serious student of his advisor, Harold Garfinkel.



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