[Dylan16807]

There are an infinite number of fundamental logical truths out there, but we arbitrarily picked useful ones to make a system of math.

[dinkumthinkum]

I don't think you all are familiar with what "arbitrary" means. That is the error I am pointing out.

[LanceH]

Picking the useful ones is the opposite of arbitrary.

[Dylan16807]

There's an infinite number of potential 'useful' ones too, and we picked some, could have picked others.

[azinman2]

Exactly.

[Dewie]

But if you're unlucky, you pick a set of axioms that makes the whole system inconsistent, which means that you can prove anything, which means that the whole system is useless. To say that it is purely arbitrary is in a sense right, but it seems to undermine the care that you have to go through in order to be reasonably sure that the system is not set up to fail.