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September 21, 2006

The Why and Wherefore of History

Posted by David Corfield

Here are some notes for my talk at the Berlin workshop. Fortunately I was upgraded to a 45-minute talk. Even so, I didn’t manage to reach the last part where I discuss David Carr’s ideas.

I would be interested in a discussion here about practitioners’ histories. A couple of examples we might consider are Baez and Lauda’s draft History of n-categorical physics and Ronald Solomon’s A Brief History of the Classification of Finite Simple Groups, BAMS 38(3) 315-382.

I ran across another passage of MacIntyre yesterday that I’d like to share:

Let me cast the point I am trying to make about Galileo in a way which, at first sight, is perhaps paradoxical. We are apt to suppose that because Galileo was a peculiarly great scientist, therefore he has his own peculiar place in the history of science. I am suggesting instead that it is because of his peculiarly important place in the history of science that he is accounted a peculiarly great scientist. The criterion of a successful theory is that it enables us to understand its predecessors in a newly intelligible way. It, at one and the same time, enables us to understand why its predecessors have to be rejected or modified and also why, without and before its illumination, past theory could have remained credible. It introduces new standards for evaluating the past. It recasts the narrative which constitutes the continuous reconstruction of the scientific tradition. (The Tasks of Philosophy, p. 11)

I take it that MacIntyre’s saying there’s nothing beyond being a great scientist than what would be captured by a proper history of the field. Of course, we could write a bad history of the natural sciences and omit to mention Galileo. It would be bad because it was unjust, and because it would fail to serve its readers well, by omitting to tell them of an important stage on the path to the best present understanding. MacIntyre’s claim presumably also means that there can be no great scientist who makes endless discoveries in his laboratory but never shares them with the community, unless we’re allowed to write histories which say “Had X’s discoveries been known…”. This bears on the point of a practitioner’s responsibility to contribute to the ongoing dramatic narrative which their practice represents.

Posted at September 21, 2006 9:11 AM UTC

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5 Comments & 1 Trackback

Re: The Why and Wherefore of History

I cannot not resist from paraphrasing Marx’s
11th Thesis on Feuerbach:

The historians of mathematics have only written the history of mathematics, in various ways; the point is to make it.

Posted by: Alexandre Borovik on September 21, 2006 10:56 AM | Permalink | Reply to this

Re: The Why and Wherefore of History

The reference to Marx is extremely apt. Others of the theses, such as the 9th, could be similarly paraphrased to make a point about philosophy of mathematics.

Something we discussed in Berlin was the point of both history and philosophy of mathematics. Who are we writing for, and why? As for myself, if I thought that my writings had and would make no difference to mathematicians, I would give up. Learning from mathematics as a flawed yet excellent example of a tradition of intellectual enquiry, I want to develop a conception of the rationality of such a tradition. And this to recommend changes to mathematics, and to other less excellent practices. Just to give a couple of examples of recommendations: mathematical exposition at all levels should be actively promoted and rewarded; there should be a greater willingness to expose research programmes to dialectical criticism. I have mentioned this before, but that Pierre Cartier should have to think twice before writing A Mad Day’s Work (he told me that he wouldn’t have written it had it not be commissioned, as he doubted a journal would accept it), is a mark of rank irrationality in the discipline. Another such mark is that one has to dig about to find a response by Connes to Cartier’s proposed unification of his conception of space with Grothendieck’s.

I know that you, Sasha, are concerned about the state of mathematics education, and that you see mathematics as an exemplary discipline. I thoroughly agree with you.

Posted by: David Corfield on September 21, 2006 11:55 AM | Permalink | Reply to this

Re: The Why and Wherefore of History

I agree with David: mathematics, as a cultural system and a professional community, badly needs some rational discourse about itself.

Posted by: Alexandre Borovik on September 21, 2006 4:40 PM | Permalink | Reply to this

Re: The Why and Wherefore of History

Can you give a reference to Connes’ response to Cartier?

Posted by: James on September 21, 2006 12:53 PM | Permalink | Reply to this

Re: The Why and Wherefore of History

I give a reference here.

Posted by: David Corfield on September 21, 2006 1:03 PM | Permalink | Reply to this
Read the post MacIntyre on Rational Judgment
Weblog: The n-Category Café
Excerpt: How explicit must rational reasoning be?
Tracked: November 16, 2006 10:36 AM

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