Re:Brouwer–Hilbert controversy
by protonfish on Thursday November 08, 2018 @10:36AM
(#18406969)
I guess I just don't see any mystery. We've used a language of symbols to communicate and think about the world around us since language first evolved. That fact that it works well should come as no surprise to anyone. Especially since we use a language of symbols to discuss the language of symbols so things that don't fit neatly into that system are inherently undiscussable.
It's not just the medium _can_ be used to create accurate representations, by a skilled master. It's that mathematical concepts created with no regard for the natural world but purely on their formal elegance, turn out, years later, to be an elegant way to describe and predict natural phenomena.
I don't think it "proves" anything, it's just... mysterious. The mystery doesn't go away if we insist that math is just an arbitrary human invented formal system. There's no a priori reason it should work to describe and predict the natural world at all, is there?
We could invent other arbitrary formal systems based on completely different axioms and rules that _weren't_ useful to describe and predict the natural world at all, could't we? I think?