Earlier quoted context omitted.
Axioms are only arbitrary in terms of the logical system they are involved in. If they conflict with other axioms, one of them has to go. So the choice of axioms isn't totally arbitrary, even at the level of logic. When it's time to take an idealized theory and use it to make predictions about the real world, we first have to check that the axioms match our sense data. If they don't, it's not an applicable theory. Th…
You're assuming a logical system, but these "axioms" aren't like math, trying to find a contradiction is itself a moral judgement. So you're just arguing in circles. None of the grounding in reality is actually connected to moral judgements in the sense of proving them wrong or right.
Here: https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...