Where do axioms come from and how are they tested?
Axioms are starting points of deductive systems. They are stipulations.
Axioms must avoid the traps of illogic, circularity, and infinite regress.
Axioms in scientific theories are assumptions derived either from induction as generalization from experience (data) or abduction in C. S. Peirce's sense as discovery through "educated guessing."
The objective of scientific inquiry is not to "prove" axioms, since axioms are the basis of proof in a logical system. Axioms function as criteria for syntactical or logical truth, also called "necessity."
Axioms in hypothetical-deductive systems provide the basis for the scientific method.
Assumptions of representational models stand or fall with the testing of models they are used to construct.
Scientific models are used to generate hypotheses that can be tested empirically by deriving hypotheses as theorems from the assumptions that serve as axioms for the system.
Failure of a hypothesis as a theorem of deductive system reveals semantic inconsistency or incompleteness and calls the system into question as a coherent explanation of the data.
This also calls the explanatory model into question as providing a causal explanation based on a representational model purporting to show causal transmission.
Correlation is not causation. Without a theory explicating transmission, there is no properly scientific explanation.
Lars P. Syll’s Blog
Why testing axioms is necessary in economics
Lars P. Syll | Professor, Malmo University
