I know this question had been asked many times before but maybe not in this form. So I really need the exact axiomatization of Physics. I have been looking for it for a long time. Precise logical axioms written in a first order (or maybe higher order) language. So not just a couple of differential equations but the pure skeleton of Physical theory itself. I need the axioms from which important theorems of chemistry and Physics and maybe Biology etc. can be derived logically. I really think that formalizing problems can lead us to much better understanding and I am hungry for that kind of knowledge. Can you link ANYTHING that answers my question? Is there anybody (Physicist, mathematician, philosopher, logician or any kind of scientist) whos professional field is similar to that?
I'm adding some concrete notes and questions(to unlock the topic):
I have started to learn some physics just for fun and I found that lots of proofs use infinitesimals. Those proofs are heuristic and I think they can be made more precise and exact by using infinitesimal analysis (that is in fact part of logic). Does anyone know any books with this approach?
I am just looking for the axioms really, like Newton's axioms etc. Because I find it fascinating that from a couple of axioms we can get so many things. Are there books or papers which emphasize this kind of logical structure of Physics? (Like they write the axioms and theorems they use from Geometry and then put some Physical axioms next to it.)
Any books on the "meta" side of Physics, like problems of determinism or locality (I have read a few about that in wikipedia but still know next t nothing about it) and their formalization? Thank you!