BTS: No, but if it did, it would not change the immense usefullness of science (assuming it is quite rare or interact very little with ordinary matter, which it must be, at least in our neck of the woods). What i argue is that such assumptions are not required as foundation of science, because they could be violated tomorrow - allbeit in a mild sence - and science would tick along just happily, just as it would if we found God or something.
If i was to give an axiomatic definition in 5 minutes, it would perhaps be something like this:
0) Mathematics exist.
1) It is possible to communicate.
2) It is possible to make at least one statement about the universe which is either true or false which can be communicated. Call all statements A
3) Humans can reason in a plausible way
4) At least one system of plausible reasoning can be applied to a large subset of the statements in A.
5) Use the system of plausible reasoning which offer the most predictive power on the statements in A.
And, well, it would kind of work i think. 0, 1 and 2 are trivially true (for 2 consider: "The sun set tomorrow"). 3 is also self-evident; its essentially to extend logic to cover "common sence" which has even been formalized using mathematics (note the formalization is not strictly required). 4 is an observation, and 5 is to remove degenerate systems of reasoning - "all statements are false" - and get the word "predictive" in, which i just figure have to be there.
The laws of physics would fall out when one reason on the true-false statements. Perhaps one need a axiom 6: Expand the set A to cover as much as possible 7) make the plausible reasoning as easily communicateable as possible (that is, make laws of physics).
But i digress. I dont think that is a very good definition. I think that it would be better to put it in words, like:
"We can define what is meant by plausible reasoning (long exposition). Science is to use that to describe the world in all its beauty, and aided with the imagination of humans and carefully crafted experiments to expand our knowledge beyond what we have previously thought possible, and thereby aid the living standard of humanity".
because then it does not sound totally booring and meaningless, and i dont think anything important essential is lost, really.
I cant remember which poster suggested it a couple of pages ago, but perhaps philosophy is the land of "wild and crazy" ideas, and science from time to time gobble up some of those ideas, expand, formalize and experiment on them, and turn whatever they then become into "science". Many 20th century developments in mathematics seem to follow this outline.