Half-baked Philosophy (Part 3)

I'm growing increasingly powerful in my ignorance. It has become my universal acid. For example, about two weeks ago I reached a point in my immersion in philosophy where I honestly had no idea what "explanation" was. The week after, it was "levels of analysis" which were utterly opaque. (What is this metaphor doing here, at the heart of things?)

Anyway, if you recall the last post about Steiner's book, I've reached that point of ignorance with him. Having read his book (well, I skimmed the last third since I don't speak math, so I trust him to have uttered only truths in regard to the eigenvalues and Hamiltonians and complex lie algebras and SU(3) symmetries and what have you), I have no idea what motivated him to write it. This is the fulcrum. His main argument seems to be that mathematics is anthropocentric since its development relies on human considerations such as beauty and convenience. OK. That's fine. And then he says this is trouble for "naturalism" which he defines as merely anti-anthropocentrism. He then uses these troubles of naturalism to take aim at science, somehow. The problem here, it seems to me, is that the anthropocentrism he defends, and on which the traction of his argument rests, is trivial. Math is anthropocentric, at least covertly, because humans do it. So of course it will advert to human characteristics at some point. Everything does. That's the weakest possible form of anthropocentrism, and there's no way to get around it.

So either Steiner is tilting at straw windmills (I know it's a mixed metaphor--bite me), or scientists are so naive that it's not even childish. Knowing a few scientists, I'm gonna go with Steiner having taken a wrong turn. I suspect he thinks that the naturalism he's opposing bleeds into the Quinean type of naturalism, which views philosophy as an extension, and based in, science. How that's related to anti-anthropocentrism is a complex story. To be sure, anti-anthropocentrism is a guiding principle in many fields of scientific endeavor, but that does not generalize to everything.

For my part, I do think that math is anthropocentric in Steiner's sense. I think I gestured in the last post about how it's a field of endeavor that progressively abstracts and sharpens the Kantian-type "categories" our minds come furnished with. So it's a great way of thinking straight, or kind of straight, when physicists/chemists/biologists/etc. co-opt it.

So. What the hell is abstraction? And what are these categories?

I'm incredibly powerful in my ignorance.

Consider: "Only laughter can blow a colossal humbug to rags and atoms at a blast. Against the assault of laughter nothing can stand."