Axioms have a lot to do with truth, and little to do with meaning.
Would that make the Euclidean axioms just “false” according to you, instead of meaningfully defining the concept of a Euclidean space that turned out not to be completely corresponding to reality, but is still both quite useful and certainly meaningful as a concept?
I first read the concept of axioms as means of logical pinpointing in this and it struck me as brilliant insight which may dissolve a lot of confusions.
Axioms have a lot to do with truth, and little to do with meaning.
Would that make the Euclidean axioms just “false” according to you, instead of meaningfully defining the concept of a Euclidean space that turned out not to be completely corresponding to reality, but is still both quite useful and certainly meaningful as a concept?
I first read the concept of axioms as means of logical pinpointing in this and it struck me as brilliant insight which may dissolve a lot of confusions.
Corresponding to reality is physical truth, not mathematical truth.