(June 13, 2020 at 8:23 am)Belacqua Wrote:(June 13, 2020 at 12:29 am)Grandizer Wrote: Example, if there's symmetry involved in the real world, then the maths that makes use of symmetry will naturally be applicable to the real world.
I don't think anyone doubts that math has applicability to the material world. We could barely get through a day without it.
The controversy starts up when people say that math is always and only a description of the material. The metaphor that math is only a language to talk about the material appears to break down at some point.
And it's not only Platonists who say that numbers have a kind of independent existence, in a non-language kind of way. The number 2 exists in a way that the word "cat" doesn't, for example. That's what Popper, Penrose, and many others say is the case.
In the end it's a metaphysical question, not a scientific one. People who are fully committed to a material-only kind of metaphysics will deny that there is anything else. Since I don't know the answer, and I take Popper and Penrose et.al. seriously, I have to keep an open mind on this.
Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er.
One difference is that math is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.
And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.
In exactly what sense do numbers have an 'independent existence'? From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.
