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.”
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.”