A blog dedicated to mathematical philosophy.
I would like to second the plea for tolerance and pluralism Branden has made elsewhere. I think spending time calling each other names in public forums is not wise, productive, or good for the profession (especially given the current climate).
I should add that both Branden and Hannes are excellent examples of philosophers that practice "formal" philosophy to address question that are relevant to a broader philosophical audience!In fact I would argue that the one between formal and non-formal philosophy is ultimately a false dichotomy, but perhaps this is not the best place to defend this view :-)
Gabriele, many thanks for your comments!May I ask you what you have in mind about the "false dichotomy"? Just to be sure: I do not take 'mathematical philosophy' or 'formal philosophy' to denote a particular philosophical field, such as, say, epistemology or ethics, but rather a manner or style of doing philosophy (applying to whatever area of philosophy).
That is an excellent and often neglected point, Hannes. Putting aside its more controversial themes, the following passage from Clark's statement make a similar point regarding the kind of things that can be found in the formal philosopher's toolbox: "One might think this work, and much else like it, that realizes Friedman’s vision in various ways, would be an inspiration to philosophers. Not so. It is largely regarded as marginal or idiosyncratic, “not philosophy.” Philosophy, while it can be combined with empirical work, is an a priori effort, and the tools of the a priori are opinion, logic, mathematics and the theory and practice of computation. To use them, Friedman’s vision requires as well a knowledge of the sciences. Learning logic and mathematics, learning to prove and to program, or at least how to write a decent algorithm, requires some sustained effort that philosophers have largely foresworn not only for themselves but also in the instruction they give to their graduate students. The run of philosophers use, and even acknowledge as philosophical tools, only the first, called “intuition.” (I am reminded of a remark by a philosopher, Laurie Paul in fact, who complained when I used a bit of elementary Boolean algebra in a lecture that philosophers should not be expected to know such things. In one sense of “expected” she was, alas, right.) I do not think philosophical work based only on intuition is always worthless, but it is a little bit like refusing to learn to walk on perfectly good legs and instead walking on your fingertips. It is obtuse."
Hannes,May I ask you what you have in mind about the "false dichotomy"?Setting aside the issue that "formal" covers a wide variety of disparate tools and methods (ranging from e.g. quantified modal logic to game theory and from Bayes nets to set theory), what I had in mind is that most analytic philosophy is to some extent formal and that the distinction between formal and non-formal philosophy is not an absolute distinction but rather better seen as a continuum in which formal tools play an increasingly important role until they become indispensable to the argument being made. Even close to the non-formal end of the spectrum, analytic philosophers tend to use bits and pieces on formalism (e.g. basic logical notation or even, I would argue, 'S knows that p'). Of course, we wouldn't regard that as formal philosophy but the distinction seems to be one of degree not of kind. The more the formal notation and tools become indispensable to the argument, the more we tend to regard the philosophy being done as "formal."Also I think that this is a false dichotomy because there is nothing intrinsically good or bad about doing philosophy using more "formal" tools and so there should be no reason to glorify or denigrate "formal" (or "non-formal", for that matter) philosophy in and of itself. The question in each case is whether the specific tools that is being used helps to shed any light on the problem under consideration and how much, on the other hand, they contribute to obfuscating the philosophical assumptions that being made. I am truly a pluralist in these matters and I think that a lot of good philosophy is done by using formal tools and a lot of good philosophy done without using almost any formal tools. I simply don't find that distinction very useful. I think people like Clark are actually doing a disservice to people who work in formal philosophy by turning this into some sort of culture war within philosophy. I'm very happy to see that there is no such tendency at MCMP!!! (Btw, I don't know if I've mentioned this to you already but it's a great initiative to post podcasts of the colloquium series!)
Gabriele,thanks! About your points:(1) The distinction 'formal' vs. 'non-formal' is vague, and there is a continuum from non-formal to formal philosophy.Absolutely, I agree. But a vague distinction is still a distinction; to say the obvious: if we eliminated all vague concepts because they are vague, we would not be left with a lot of concepts.(2) There is nothing intrinsically good about using formal tools in philosophy. There is no reason to glorify 'formal'.Again, I agree completely. Tools are just as sensible as the people who apply them; they can be applied incorrectly, or without necessity, merely in order to show off, or in order to hide some deficits, or… But I don't know a colleague who works in the more mathematical corners in philosophy who would think otherwise anyway. (I am sure, Clark Glymour does not think otherwise either.) Certainly, at the MCMP, no one is glorifying approaching philosophical questions and problems by mathematical means.And I am also a pluralist: that's why I said at the end of my post at 'Leiter reports' that I regard the 'mathematical way' as just one way of doing philosophy. But for many questions and problems it can be a very useful way; and one needs a label for it in order to talk about its methodological virtues and vices: hence 'formal philosophy', or, as I prefer personally, 'mathematical philosophy'.(Many thanks for what you say about our podcast series -- this is all due to Roland Pöllinger, http://logic.rforge.com/, one of our fellows.)
Thanks, Gabriele. I just want to echo all of Hannes's remarks. We are in complete agreement.
I think we agree, Hannes. I still feel that Clark's "manifesto" is (to say the least) a bad piece of PR for "formal" philosophers (and, sadly, an excellent reading for a critical thinking class on fallacies).I think it would be good if more "formal" philosophers publicly distanced themselves from it (as Branden did at NewAPPS and you did at Leiter's) instead of trying to defend it as it's happening at NewAPPS.
I'm late in the day here, as this discussion was taking place while I was on holiday, and somehow it seems to have escaped my attention.I just want to say that I agree with Gabriele's assessment that the Glymour manifesto does a bit of a disservice to formal/mathematical philosophy. By emphasizing a polarization between formal vs. non-formal philosophy, it mostly has the effect of alienating those non-formal philosophers who might in fact be sympathetic to the whole approach.As said before here, formal/mathematical philosophy is a methodological approach, not a thematic sub-area of philosophy. It is a particular way of treating philosophical topics, which can in principle come from any sub-area of philosophy.As for the extent to which analytic philosophy in general is 'formal': as I suggested in a post on the origins of analytic philosophy a while back, one of the issues seems to be that analytic philosophy developed as a strange confluence of Russellian logical analysis and Moorean 'common sense philosophy'. So there is this tension at the heart of the enterprise between formal methods and intuition-based methods.
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