I understand very well that the peano axioms for example are logical and not circular. My point was that I think your explanation relies on the experience on w

I understand very well that the peano axioms for example are logical and not circular. My point was that I think your explanation relies on the experience on what a number is, having used those equations before with the terms actually representing real numbers (such as 3 + 2 = 5 instead of a + x = b and sin(180) = 0 instead of sin(x) = 0). So as a definition of what a number is it's circular as you presume experience with numbers and what they mean.