Friday, June 29, 2012

The Real Analytic/Continental Divide: Fashion

We wrap up Turing Week with one of my favorite all-time posts:

There is a civil war in philosophy. On one side you have the continental philosophers -- think cigarette-smoking, angst-ridden souls who try to impress you by randomly lapsing into French, German, and Greek -- and on the other you have analytic philosophers -- think science-worshipping logic techno-geeks. Aspazia, a few days ago, set out the distinction in terms of the respective rhetorical bad habits of each side. I've always thought the real difference is that the continentals got dates.

Then I realized the real dividing Walk into a meeting of the American Philosophical Association and without saying a word to anyone, you could easily partition the crowd into continental and analytic classes by just looking at the clothes. (The third group of philosophers -- Americanists -- can also be easily spotted: they're the ones in front of the hall with big pleading eyes and signs that say, "Will talk about Dewey for food.") Analytics and continentals dress differently...and that's putting it nicely. Continentals dress themselves to the nines whereas it is hard to find nine analytics who can dress themselves. So, being a science-worshipping logic techno-geek, I started to think about what accounted for this difference...and I believe I have an answer:

The nature of fashion is predicated upon the satisfaction of the "goes with" relation, G. An outfit meets the conditions of fashion acceptability only if it is comprised of a bottom covering, b, and a top covering, t, such that it is true that Gtb.

While the satisfaction of the "goes with" relation for top and bottom coverings is a necessary condition for an outfit to be categorized as "sharp," it is not sufficient for sharpness as the if-clause requires accessorization.

Initially, it was thought that accessories would require the "goes with" relation to be expanded from a binary to an arbitrary n-ary relation, but it was shown possible to group accessorization constants into a single variable which have been determined to satisfy the relation themselves. That is, one can show that shoes and a belt go together independent of the outfit and that if a given bottom covering, say a particular pair of pants P, and given top covering, say a given shirt S, have been demonstrated to go together, that is for which GPS has already been demonstrated, then for a pair of shoes, h, to be fashion acceptable they must satisfy the "goes with" relation G(PS)h. Such iterations must be repeated until a complete outfit has been assembled.

The reason why analytic philosophers (and similarly mathematicians and cognitive scientists) have a difficult time dressing themselves or dress poorly is that the satisfaction of any sentence involving the "goes with" relation is not finitely decidable. There is no algorithm by which one can in a finite amount of time, much less in the morning before you are too late for class, decide with deductive certainty whether an outfit is sharp and properly accessorized. Now, there are rules which by which we can rule out entire classes of ordered pairs, e.g., let x be a member of the class of checked clothing and y be a member of the class of striped clothing, it is fairly trivial to show that for all such x and all such y, Gxy must be false (I leave it as an exercise to the reader to provide a proof). But for the general case there is no finitely executable decision procedure such that for any two arbitrary articles of clothing one may determine the satisfaction of G.

There were, of course, hopes in the 40s and 50s for such a breakthrough. But the dream of a "Cou-turing machine" faded with the suicide of Alan Turing. "Not only did he have the greatest mind in history for devising formal solutions to problems like this, but as a snazzy dressing gay man himself, he was the only one who could bring all the elements together -- the Carson Kressley of the post-war computation theory set. Bloody MI-5, with their homophobic poppycock," a former colleague was reported to have said, "They doomed all of us geeks to a series of lonely Saturday nights."

While that explains the lack of fashion sense on the analytic side of the aisle, the continental fashion phenomenon is also easily saved because we are dealing only with an infinitely more simple limiting case. For continental philosophers, the "goes with" relationship is trivially true because it can be shown as a direct result of a basic lemma (the Klein theorem -- that's Calvin, not Felix) that for all pieces of apparel x and y which are proper subsets of the class B of black clothing, the sentence Gxy must be true.

So, what is to be done with this initial working through of fashion logic? My suggestion is that work be directed at developing theorems which hold for non-black clothing. The place to start would be with a possible generalization of the simplest lemmas which are known in the field as the "Garanimal postulates." Unfortunately, little work has been done finding a material instantiation since the initial work in the mid-70's with various forms of corduroy, but with new techniques there is hope that the work could be revived in a new, more mature form. If anyone out there is looking for a dissertation topic...