For anyone who read MWA it’s obvious that its author would never be mistaken for, nor would want to be mistaken for, a philosopher.  Still, three referees for the journal Synthèse were kind enough to put to rest any lingering doubts on that score (there were none) in their reviews of the article I have just posted on arXiv under the title Virtues of Priority.

In the fall of 2018 I received a message inviting me to contribute to “a special issue of the philosophy journal Synthèse on virtues and mathematics.”  The prospective guest editors wrote, “We would be delighted to be able to list you as a prospective contributor. This would, of course, be in no way binding on either party.”  This looked like the perfect excuse to write on a topic that had been much on my mind ever since the controversy broke out among number theorists on the correct attribution of the conjecture on modularity of elliptic curves.  From the very beginning this controversy was marked by the contrast between the acrimony with which certain colleagues addressed one another and the superficiality of the analysis with which they justified their positions.  Even while Wiles labored in secret in his attic, I was already wishing for a philosophical umpire to require the warring parties to base their arguments on general principles rather than on raw chronology and personal affinities.

The story is interesting, well written and the conjecture as well as the main actors play important roles in 20th century mathematics. In that sense the paper was a good read, but a good read is not enough to make a good philosophical paper.… The paper does not connect to the current debates on value ethics in mathematics at all; in fact, none of the papers on the reference list belongs to the philosophy of mathematics, and the most recent reference is from 2001. The paper should be situated more firmly in the recent literature on mathematical values … Along the same line, the paper does not make a clear and substantial contribution to current philosophical debates on virtues in mathematics. The paper does not contain a clear problem statement, and the virtues encountered in the historical case are only commented on en passant, but the paper does not provide a structured discussion or a collected conclusion. … The paper lacks methodological reflections. Why is the case in question a good case to explore the philosophical questions at hand and why are the chosen sources the right sources to explore the case? It should be made crystal clear why a dispute over priority of a conjecture is a good case to explore the nature of mathematical values.

A second referee was more encouraging:

This submission represents an excellent idea for an article and a solid initial effort at fulfilling that idea, not yet suitable for publication in Synthese.

but this indulgence can be dismissed because the referee is someone I know.  And, as this referee accurately perceived,

the virtue ethics aspect currently reads as something tacked on to a stimulating but not philosophy-journal-ready fireside/blackboard-side chat about a curious and gossip-ready extract of the history of the theory of elliptic curves.

The third referee’s objections came under three headings:  “The philosophical upshot of the paper is thin,” “The paper neglects other work on priority disputes,” and most tellingly, “The search for a functional significance of the dispute may be overstated”:

Merton observes that, in some instances, battles over priority have no functional significance (i.e., the authors fight over the priority of a finding even if the discoveries are independent and epistemically equivalent). This is due in part to the reward system of science. Moreover, along the same lines, there is a psychological explanation in terms of ego-protective biases. The paper should examine this possibility more closely.

This last objection is silly.  Referee number 3 may never have met anyone as ego-protective as several of the protagonists of the controversy, but the point of my essay was to ask whether the controversy might not shed some light on the value system driving contemporary mathematics — and “functional significance” is not the point either.

In nearly all other respects all three referees were absolutely right about the article.  It did not connect to current philosophical debates, it did not engage in methodological reflections, it neglects the literature on priority disputes, and it was not written in the style of a philosophical paper.  But this is not what I thought the editors had in mind when they asked a mathematician for a contribution.

I accepted the invitation to contribute to the special issue in good faith, on the assumption that the issue’s editors had good reason to believe that the thoughts of a professional mathematician on the roots of an unusually bitter controversy in the field would have a place in the journal, and could provide useful raw material for analysis by philosophers who are curious about the value systems that actually guide the practice of professional mathematicians, even though the mathematician in question has never claimed to be a philosopher.    Had the editors of this special issue made it clear to me that my submission would be judged on the basis of familiarity with “the current debates on value ethics in mathematics,” as these are pursued by philosophers who “have been taught mathematics at university level,” or by its author’s efforts to situate the submission in relation to “relevant secondary scholarship,” I would have replied that I have neither the time nor the inclination to undertake a project on that basis.  That the editors of Synthèse and the referees find it helpful to erect artificial barriers* to dialogue between professional scientists and those philosophers who claim to be interested in the values of such scientists is not my concern.   But I consider it unprofessional as well as irresponsible on the part of the issue’s editors to have failed at any time to explain to me the unfamiliar standards that would be applied to my article.

This was my response to the rejection letter from Synthèse, which concluded:

I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every success in finding an alternative place of publication.

Finding a place of publication on arXiv was easy and is a perfectly satisfactory alternative, but philosophers may not think to look there for raw material.  I consulted with the philosopher David Corfield — who first convinced me of the relevance of Alasdair MacIntyre’s virtue ethics to mathematical practice in the article he published in Circles Disturbed — and he offered to help draw out the philosophical material through a dialogue on the n-Category Café.  His first comment on the arXiv publication is already online.

*In view of the events of the last few weeks, I am now ready to acknowledge that fears of disciplinary cross-contamination may be justified in some circumstances.