Science is also very comfortable with holding competing theories, whereas in conventional logic that would be "explosively" destructive.
Also, I do think that physics is pretty axiomatic right from it's roots. Newton's main inspiration for forming his theory is the work of Euclid, i.e. first formal system that was ever created.
And in terms of modern physics, I reiterate that there is no enthusiasm from either mathematicians or physicists to axiomatize physics.
And according to the first sentence of the summary the current formulation is axiomatic as well...
Science is comfortable with uncertainty, but not with things that are illogical. It has to be logical, and the scientists have to accept some sort of logic to give theories a better-worse hierarchy.
Except most of sciences take experiment as the criterion of truth rather than logical inference. Real-world science can almost always be expected to be inconsistent - simply because each scientific theory is a "local" approximation, and theories developed for different areas of the same science are not required to be mutually consistent in order to be useful. One (in)famous example is quantum mechanics and general relativity.
> This is it about axiom schemas and *rules of inference are almost the same thing except they allow us to actually distill the conclusion from the premises.