Umm, no. Look at Godel's Incompleteness Theorem. You can prove that you will always be able to make a paradox in any formalized system of logic; at least, under our current understanding of logic. Expanding that (Godel, Escher, Bach by Hoffseader goes into it well) you then can say that any theory of the universe must have holes in it and any machine or system that attempts to formalize the observations will always come up with paradoxes. You are right, you can formalize everything (maybe, jury is still out on that, but I think so), but at the risk of then making paradoxes in the system.
I'm aware of this theorem and it has nothing to do with scientific method, it only gives us an idea of possible results of research and it does not tell us that you cannot formalize life sciences or chemistry. Indeed, there are theories that cannot be proven, but they are itself subject to formalization and research.
