At 02:11 PM 9/24/2014, Benjamin wrote: [snip]
I'm just saying that if one regards mathematics mainly as a neural activity, then mathematics would seem absurdly effective in physics and other special sciences, as if an average child by doodling had invented a rocket ship.
HP: I do not see antipsychologism as a necessary stance if you understand neural activity as a product of evolution and learning. What do you mean by "mainly a neural activity"? If you think any mathematics, or any thinking, goes on elsewhere, then that thinking is still neural activity. What Kant says is absurd is thinking that your neural activity is not thinking about things-in-themselves.
Kant: ". . . though we cannot know these objects as things-in-themselves, we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears." Thinking about things-in-themselves is inescapable.
That's what Born meant by "everything is subjective, without exception," and what Hertz meant by, "we do not know, nor have we any means of knowing, whether our conception of things are in conformity with them" except by comparing the necessary behavior of our neural models (denknotwendigen) with the observed necessary behavior of nature (naturnotwendigen).
I emphasize that, so far, this is not psychologism, idealism, nominalism, solipsism, Cartesianism, Platonism, or any -ism. It is just evolution, observation (and a snippet of Kant). Anyway, thinking about a more detailed epistemology or ontology -- your own -ism -- would still be your own neural activity.
The scientific problem has always been to create neural models of things-in-themselves that generate predictions of observables that are as detached as possible from the states of individual brains.The first arithmetic rules and geometric proofs were invented to do just that. So was analytic geometry and calculus, but thinking about formal mathematical rules self-generated problems and new rules, and much of later mathematics became pure mathematics, freely imagined and not aimed at any application to physics. Its scientific success was at least fortuitous if not unreasonable.
BU: I see no reason to regard as a quirk or happenstance the world's alliance of bruteness of force and physical law together, and I can see that physical law involves bruteness in a way that mathematical rules do not, if that's what you're getting at.
HP: That is exactly what I was getting at. Note that the bruteness of laws execute in real time at an unalterable rate, whereas mathematical and logical rules may be executed at your leisure with no effect on the result. Laws do not exist by necessity of semiotic rules, nor do semiotic rules occur by necessity of laws. They are essential, irreducible, complementary categories.
Howard
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