Taking it slowly, #2

The new Hans Rausing Professor of HPS here, Hasok Chang, is planning to run seminars in the mode of Peter Lipton’s much admired institution — and the plan for the first term, is to look at the collection of essays Scientific Pluralism, edited by Stephen Kellert et al. I’ve been having a quick browse, to see if I will want to go along. Well, I think not. The book seems a lightning tour ranging over far too much: I don’t find that kind of enterprise likely to be of much value.

I’m sad to say that this seems particularly the case with the essay by Geoffrey Hellman and John L. Bell on ‘Pluralism and the Foundations of Mathematics’ (complete in the Google Books excerpt linked above). I much admire both authors, but this is really ill-judged.

The essay divides into two parts. After a preamble, there are four pages — yes, just four pages — arguing to the conclusion that the “classicism-constructivism duality in mathematics” illustrates the need for a “pluralistic approach”. This is feeble stuff indeed. There is a bit of Dummett bashing that assumes that he just has a verificationist theory of meaning (as if e.g. Crispin Wright had never written). There’s the bald claim that “it is clear that classical reasoning is especially useful in scientific contexts” (so much for Neil Tennant’s defence in depth of the claim that good science only needs intuitionistic logic). There’s a long quote of David Lewis’s now too-familiar passage “I’m moved to laughter at the thought of how presumptious it would be to reject mathematics for philosophical reasons. Etc. Etc.” which, as a number have by now remarked, is dangerously near point missing (see for example Alexander Paseau’s essay in BJPS 2005). Fictionalists, predicativists, constructivists have their philosophical reasons for making philosophical claims, perhaps discriminating between different metaphysical statuses for different parts of classical practice: and sure, most mathematicians aren’t interested in reflecting on those discriminations. But so what? I’m afraid that Hellman and Bell’s breathless pages wouldn’t pass muster as part of a final year undergrad. dissertation.

The second part of their paper is mostly about topos theory as an alternative to set theory as a foundational framework. But again, as you’d expect from the fact that it is only seven-and-a-bit sides, this is far too fast and allusive to be of use to anyone who doesn’t already know a lot about this stuff (and even if you do, it is pretty unclear what the take-home message is).

Isn’t this kind of thing becoming more and more common? — pieces written for Yet Another Collection, maybe generated by Yet Another Conference, which don’t have to get past an anonymous refereeing process, and which just go too fast. I think it behoves philosophers, of all people, to take things slowly. Or am I just getting old?

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