One of the most attractive features of The Reasoner, www.thereasoner.org the montly zine out of Kent, is the interview this month with Hannes Leitgeb. One passage caught my attention:
"Hannes Leitgeib: Overall, and ultimately, mathematical methods are necessary for philosophical progress, yes. But of course there can be points in a philosophical argumentation at which there is no payoff applying such methods. And while I do not think that there is any area of philosophy that is ‘beyond mathematical methods’, in some areas they do not pay off as yet because these areas are not quite developed enough. Or that’s at least the diagnosis of a mathematical philosopher!"
Let's grant for the sake of argument that mathematical methods have a distinguished record of progress. (In the interview Leitgeib does not offer a historical argument for the claim, but surely we can point to the history of analytic philosophy with some satisfaction.) Let's also grant that all areas of philosophy can benefit from mathematical methods.
But what could the (mathematical???) argument be that mathematical methods are *necessary* for philosophical progress? What to make of un-mathematical philosophy; is all the progress achieved without mathematical methods merely apparent?
And...let's accept that philosophical progress by mathematical methods ought to be understood in terms of "clarity" (as Leitgeib seems to suggest in the interview). Ought we to accept that it is cost-free?
Here are some possible costs within philosophy (I created the list while thinking of the role of Bayesianism as an aid to understanding scientific practice in the fields I am familiar with):
1. Focus on tractable machinery and toy-examples (at expense of complexity)
2. Training in technical skill at expense of good judgment
3. Inflated expectations from technique rather than learning how to ask right questions (or the making of distinctions)
4. Focus on producing 'results' rather than insight
5. Focus on the model and not the messy world