"Axioms are better thought of as universally accepted truths" Not really universally accepted. You just have to specify which set of axioms you are using. Diffe

"Axioms are better thought of as universally accepted truths" Not really universally accepted. You just have to specify which set of axioms you are using. Different problems may call for different axioms. Like if you want to prove theorems about the security of some computer system, you'll define a set of axioms that allow proving interesting results for that purpose. If you want to prove theorems about sets, you'll want to specify what set axioms you are using. You may even try to specify interesting minimal sets of axioms that make your theorem true. There is no reason to use the same axioms for everything, or to assume they are True in some teological sense.