Ofc people that disagree on the axioms will disagree on the logical outcome.
There is plenty of room for criticism even without objective morality.
Because we are social beings who often reach broad consenus about what is right and wrong even if it's not entirely objective.
But why does it matter to come to consensus?
Because if most don't recognize it as their own moral code, it's meaningless since it will not get used in pratice.
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