I really think people overstate the value of causality in Science. F = ma has nothing to do with causality. It merely states that the time-derivative of velocity is equal to the sum of the forces at the objects location at that particular point in time divided by the mass of the object. (Techncially that's a = F/m, but never mind that.) You can interpret this formula as saying that the force "causes" the object to move, but that's not neccesary to use the theory, and I think that in some ways this interpretation is misleading.
Similarly, most theories do not actually
require causality, although causality does make things a lot easier to understand.
1. Metaphysical Naturalism: The material Universe is what exists, or if there is a more fundamental level of reality, it cannot be determined by observation.
I was under the impression that the observable world and the material world were by defintion the same. But if not, I don't see why science requires that the universe be made out of "matter." Anything that can be observed can have the scientific method applied to it. If there are observable patterns, then science should in principle be able to find them.
And frankly, I have trouble imagining a completely patternless phenomenon. Even if it was completely random, "completely random" seems to be a testable claim. So if you can observe it, you can apply science to it.
And of course, the Scientific Realism interpretation of science (which I think is silly) implies that there
is a more fundamental level of reality, the numbers underlying the physical phenomenon.
2. The Principle of Uniformity: The Universe follows laws that apply uniformly and universally.
The way I see it, science isn't about truth, it's about "seeming to work." It is not thus not neccesary that a law apply universally. It is merely neccesary to have a theory which has fit all the data so far. (And which isn't just the result of just rigging up the formula to fit the data.)
And in my opinion, "seeming to work" is the very highest degree to which we can support
any belief about the nature of the external world as true.