Ginkgo wrote:As you say, there may well be a 'true triangle'. If there is we can only establish its truth by doing metaphysics. Once we have established our metaphysical truth in relation to triangles we then attempt to show how this truth about triangles applies to the real world. As Hume would say, this is when we run into big trouble. My above post also points out the difficulties.
Another problem is we cannot seem to overcome the problems inherent in language and mathematics. Kant was very much aware of this problem. He wanted to try and discover of there is any metaphysical knowledge that is necessary and universal that was neither mathematical nor empirical. His success or other wise is subject to volumes of debate. Whatever we do we cannot shake off the bonds of language when it comes to understanding. Kant himself acknowledges this in a indirect way. Kant would assert that knowledge of propositions and hence truth value can be found only by considering the definitions of the terms involved.
A good example of this would be when we consider a priori propositions. The truth or falsity of the claim, "All green apples are green" is based on the relation of the subject to its to predicate. It is a logical relationship as we look at it; so to speak.
Any true triangle is only thus because we choose to identify it as such. The triangle does not think it is one. It says very little about fundamentals of the universe except that at some molecular level in the gene sequence a set of atoms build on one another in a mathematical sequence no different from a child's building blocks have to assemble in a particular way. So when we look at piece of Romanesque Broccoli we think we have discovered something fundamental about the universe, or that we have seen the hand of God, when what we really see is the simple consequence of building blocks falling in a sequence determined by their structure. This is not evidence that the universe is written in the language of mathematics, but still further evidence that maths is a useful means of modelling that universe; and that sometimes the chaos shows a little apparent order; and that the material universe is determined by material forces.

This is not God applying the Mandelbrot Set; this is a broccoli demonstrating that it is determined by a physical sequence , that a bloke called Mandelbrot modelled.