(October 16, 2018 at 1:46 am)vulcanlogician Wrote:(October 16, 2018 at 1:26 am)robvalue Wrote: We create maths. We discover ways in which particular maths has applications when applied to reality.
Remember that maths need not have any bearing on reality at all. To say that you "discover" a new mathematical system would be metaphorical only; it would be like exploring the platonic plane of abstract concepts.
Maths makes statements which are either true or false within their own framework. They are true, essentially, because we say they are true. They are a logical result of applying the rules which we say are true. Verifying they are true is a matter of making sure the rules have been correctly followed.
So (concerning right triangles) it is only true that the square of the hypotenuse is equal to the square of the sum of the other two sides because we say it's true. This is not a fact that we discovered about right triangles? Is this what you're saying?
We may at some point in time in the future discover a new way of categorizing values, but even if we find a new way, it doesn't take away from the truth of our current system. Such advancements wouldn't nullify our current understanding of numbers... it would only add a new dynamic to what we know.
