News for hackers. Stuff that matters.

A comment on Roger Penrose – Is Mathematics Invented or Discovered? [video]. Parent comment

Re:Roger Penrose – Is Mathematics Invented or Discovered? [v... by danck on Friday April 17, 2020 @05:27AM (#22897498)
You can invent and pick axioms in many ways that (probably) won't lead to inconsistencies. But they won't all be powerful enough or relevant in the real world.
[ Parent | on HN ]
Re:Roger Penrose – Is Mathematics Invented or Discovered? [v... by vanderZwan on Friday April 17, 2020 @09:45AM (#22898910)
Well, then it sounds like your reasoning gets it backwards: the axioms that produce systems without significant consequences or connections outside of their own abstract realm end up being ignored.

Or in other words: the constraints on maths are imposed from outside of maths.

[ Parent | on HN ]
Re:Roger Penrose – Is Mathematics Invented or Discovered? [v... by gibspaulding on Friday April 17, 2020 @09:53AM (#22898973)
Doesn't this imply that, while you can invent all the axioms you like, you must discover which ones are consistent with each other and with experimental results.
[ Parent | on HN ]