(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.
