We axiomatize a theory when there are evident truths from which we can derive other truths by a previously defined set of rules of inference. Since Frege, though, a lot have changed and mathematics is not the only object of formal logic, and the reasoning style changes completely.
Is there a way to know if a conceptual system, i.e. a body of knowledge, is ready for axiomatization? Are there indicators of whether such an axiomatization would be fruitful?
I thought of some criteria, such as complete description of phenomena with few basic concepts.