Math and Reality

[Purple Rabbit]

"Pure mathematics consists entirely of such assertions as that, if such and such a
proposition is true of anything, then such and such another proposition is true of that
thing. It is essential not to discuss whether the first proposition is really true…. Thus
mathematics may be defined as the subject in which we never know what we are talking
about, nor whether what we are saying is true."
Betrand Russell

"How can it be that mathematics, being after all a product of human thought which is
independent of experience, is so admirably appropriate to the objects of reality? Is
human reason, then, without experience, merely by taking thought, able to fathom the
properties of real things?"
Albert Einstein

In the first part of Roger Penrose’s book The Road to Reality Penrose argues that mathematics has an objective reality. He points out that everybody who studies math comes to the same conclusions, and that seriously studying math has the feel of uncovering deeper and deeper truths.

It is undeniable that math is an investigation shared by the human race across time. However, this does not mean that math has an objective reality beyond its existence in humanity’s shared knowledge. Penrose belongs to a school of thought that is quite large in the world of math and that most attribute to Plato: the school that mathematical concepts have their own reality. A reality separate from nature that somehow dictates nature. IMO this borders on supernatural beliefs and as a naturalist I feel I should be able to disentangle the argument Penrose stipulated.

This is a subject on which I am in the phase of forming opinion. I might argue against it and then again I might argue in favor of it. Please join me on this quest for truth.