Chop, Chop, Chop

At any given time, that which is highly respectable  is already dead, work on the advancing fronts of a field is mixed (thus the soaring observer in the sky discerns some merit in it) and that which is below the salt and off the reservation is the future. The last category might be described more mildly, as is done by Aaron Preston in an article on Analytic Philosophy concerning metaphysical system builders. That activity is not countenanced by today’s philosophers, he says; not, he adds, “as a respected professional activity” (link).

My own honored mentors on the nature of culture insisted that absolutely everything is saturated with the feelings of the time. But they hoped to teach that cultures change; they were satisfied if only that was understood; therefore they did not carefully describe the coexistence of ossification, transformation, and emergence.

In a field like mathematics which is inaccessible until its extreme abstraction is penetrated enough to reveal some of its meaning (or lack thereof), the cultural influence is difficult to discern. But sure enough it’s there. I only briefly ventured into analytic philosophy in the first place in order to confirm my impression, prompted by the fact that at least three big names in math had played roles there (Friedrich Frege, Bertrand Russell, and Willard Quine). Thus I once more had to enter that unfortunate slaughterhouse where all your hear is chop, chop, chop. Life is stopped at the door and isn’t permitted in; inside blood and guts and shanks of meat. It pleased me to discover that this form of philosophy, while evidently absolutely dominant in the English-speaking world, and spreading to other parts, is already showing advanced decay—and is dominant because of that. Here is a field that attempted to materialize meaning, thus to make it fit for scientific study. This was achieved by turning philosophy into linguistics, semantics, and grammar and forcing its statements to be expressed in formal reductive logic. In the process it caused meaning to vanish, which is the life of that cattle, retaining only its grammar: cattle made meat.

I find this fascinating. Mathematics emerged as a distinct language by means of which additional layers of meaning in reality could once be made accessible. And like any other language—ordinary, philosophical, poetic—so also math retained ambiguities and marvels. But when it had been reduced to its pure grammar by analytic chop, chop, chop it ended up with a vast immensity of tiny marbles in fixed categories the endless rearrangement of which into meaningless patterns is now the only “respected professional activity” in the realms of higher math. Or so at least Morris Klein observes in his worthy exposition of math—although he does so with a certain amount of nostalgia. (Speaking of language, the right word here is really the German Wehmut.)