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Science can't be logically inconsistent. If a system is logically inconsistent then you can prove anything from it, so there would be nothing for science to explain - everything would follow from the inconsistency.

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.

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> then you can prove anything from it

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.

It's not "experiment rather than logical inference" it's experiment and logical inference.

There seems to be a markdown error (and a grammatical error) in:

> 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.

Science doesn't even have axiomatic foundations. The consequence of two competing scientific theories is not logical explosion...

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