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Platonic ideas?

April 16th, 2015 · 4 Comments

http://darwiniana.com/2015/04/07/magee-on-kant-to-schopenhauer/comment-page-1/#comment-738949
The issue of mathematics often fails to see the cases where math fails: we cited one yesterday: differentials in economics (marginalism).
But the question of mathematics even since Plato has been haunted by the Platonic Ideas, and Schopenhauer actually refers to them directly.

1 NK // Apr 16, 2015 at 11:47 am

I find it odd that contemporary scientists (in this case, Smolin and Woit) seem unaware of the Kantian perspective which transcends and subsumes both of their viewpoints:

“On the third hypothesis, about the nature of mathematics and its relationship to physics, I just fundamentally and radically disagree. For a shorter version of Smolin’s argument, see this essay, which he has recently submitted to the FQXI essay contest. I’ve been writing something about how I see the topic, will blog about it here very soon. What I’m writing isn’t a response to Smolin’s arguments, but a positive argument for the unity of math and physics at the deepest level.”

http://www.math.columbia.edu/~woit/wordpress/?p=7552

2 NK // Apr 16, 2015 at 11:50 am

More on Woit’s viewpoint:

“As for the question on the PBS site:

Is math a human invention or the discovery of the language of the universe?

the answer is the latter.”

http://www.math.columbia.edu/~woit/wordpress/

Tags: General

4 responses so far ↓

  • 1 NK // Apr 23, 2015 at 11:17 am

    https://scientiasalon.wordpress.com/2015/04/21/smolin-on-mathematics/

  • 2 NK // Apr 23, 2015 at 11:19 am

    But Smolin’s positive argument doesn’t end there. He recognizes that he has to come up with an alternative account for what has been called the “unreasonable effectiveness of mathematics” [5], or with an answer to the closely related “no miracles” argument for mathematical realism put forth by Quine and Putnam [6]. It does so by a dual, in my mind compelling, strategy: he wants to show that the effectiveness of mathematics in physics is actually somewhat overrated, and then proceeds to propose a multiple-stage account of the development of mathematics as a discipline.

    In terms of the first point, Smolin observes that mathematical objects are actually seldom, if ever, a perfect match with objects in the real world, which is to be expected if one thinks of mathematics as dealing in part with abstractions from the real world. Also, mathematical models are grossly underdetermined by physical systems, in the sense that most mathematical laws do not actually have a physical counterpart, or do not uniquely model the physical systems they are intended to account for [7].

  • 3 nemo // Apr 24, 2015 at 12:25 pm

    I need to study up some more here. Mathmatics is not helping economics at this point, as I have tried to point out.
    I am dealing with the claims by some physicists that string theory (math) is misleading…

  • 4 nemo // Apr 24, 2015 at 3:06 pm

    I will get to this tomorrow

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