A strict external audit against the axiomatic method in math
This is a strict external audit against the axiomatic method in math and how it is a problem for physics
You can not distinguish dogma from non dogma if your system is a closed axiomatic system because utility and consistency can still work and be found inside of a false axiom
You can not distinguish dogma from non dogma without the ability to test your claim against reality, and if it has no external justification because utility and consistency can still work and be found inside of a false axiom.
Viewed strictly from outside the system the axiomatic method is a closed system.
You can not test a math axiom itself against reality by definition and it has no external justification because utility and consistency can still work and be found inside of a false axiom.
Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics
Viewed strictly from outside the system, the axiomatic method in math smuggles in epistemic empirical claims and limits about reality systematically. By definition the axiomatic method limits and restricts what you can even ask, and logically validate within its system
applied physics and science can not systematically ignore the axiomatic method in math past addition of physical matter externally, because if you adopt a formal system, you systematically automatically inherit every foundational rule that makes that system work. Just because physics can “ignore” an axiom doesn’t mean they actually ignored it.. it just means they broke down a wall in the closed maze to make physics work.. they are still operating inside the closed axiomatic system past addition of physical matter
(This is a strict cut throat external audit against the axiomatic method in math itself. There is no external justification for it and thats the least of your worries)
This post is mostly for the philosophers of math here not math academia. Math can not defend this without retreating to solipsism and denying reality to be used as the baseline