This is doable… Let d be the length of the diameter of some circle, and c be the circumference of the same circle. Then if you have an integer number (m) of sticks of length d in a straight line, and an integer number (n) of sticks of length c in a different straight line, then the two lines will be of different lengths, no matter how you choose your circle, or how you choose the two integers m and n.
In general, if the axioms that prove a theorem are demonstrable in a concrete and substantive way, then any theorems proved by them should be similarly demonstrable, by deconstructing it into its component axioms. But I could be missing something.
There are sets of axioms that aren’t really demonstrable in the physical universe, that mathematicians use, and there are different sets of axioms where different truths hold, ones that are not in line with the way the universe works. Non-euclidean geometry, for example, in which two parallel lines can cross. Any theorem is true only in terms of the axioms that prove it, and the only reason why we attribute certain axioms to this universe is because we can test them and the universe always works the way the axiom predicts.
For morality, you can determine right and wrong from a societal/cultural context, with a set of “axioms” for a given society. But I have no idea how you’d test the universe to see if those cultural “axioms” are “true”, like you can for mathematical ones. I don’t see any reason why the universe should have such axioms.
This is doable… Let d be the length of the diameter of some circle, and c be the circumference of the same circle. Then if you have an integer number (m) of sticks of length d in a straight line, and an integer number (n) of sticks of length c in a different straight line, then the two lines will be of different lengths, no matter how you choose your circle, or how you choose the two integers m and n.
In general, if the axioms that prove a theorem are demonstrable in a concrete and substantive way, then any theorems proved by them should be similarly demonstrable, by deconstructing it into its component axioms. But I could be missing something.
There are sets of axioms that aren’t really demonstrable in the physical universe, that mathematicians use, and there are different sets of axioms where different truths hold, ones that are not in line with the way the universe works. Non-euclidean geometry, for example, in which two parallel lines can cross. Any theorem is true only in terms of the axioms that prove it, and the only reason why we attribute certain axioms to this universe is because we can test them and the universe always works the way the axiom predicts.
For morality, you can determine right and wrong from a societal/cultural context, with a set of “axioms” for a given society. But I have no idea how you’d test the universe to see if those cultural “axioms” are “true”, like you can for mathematical ones. I don’t see any reason why the universe should have such axioms.
This is not doable concretely because you can only measure down to some precision.