eodnhoj7: No, not all arguments are the same. In fact, it's completely false that we are even addressing an issue that can be decided by an axiom. There is a reason why the issue of whether numbers exist is not resolved by mathematicians themselves --- it's a philosophical question and not a mathematical one. Mathematicians can agree on the existence of a mathematical object by coming up with a definition for the object; however, the issue of whether such a defined object really exists or not is a matter of philosophy, which falls outside of mathematics. That's why it's completely irrelevant to discuss such things as how one can go about determining the sum of interior angles for planar objects by completing a circle of 360 degrees, and knowing a line is at a 180 degree angle. That has absolutely nothing to do with the issue of whether numbers exist.

The initial question reminds me of a Tom Sharpe novel.

"How often do you masturbate each day?
a. Twice
b. Three times
c. More often?"

1. All axioms are taken as self-evident, and as self-evident have a completely subjective nature where one person can see an axiom and see one thing, while another person can see another axiom and see another.

2. All axioms have an element of randomness to them where all axioms effectively mean nothing in themselves and are determined by the frameworks (equations, proofs, algorithms, number line, etc.) that determine them due to this subjective nature.

3. These frameworks, as axioms, are still subjective and in these respects contain an element of randomness in themselves based on point 1.

A question about masturbation is masturbation.