I see your point. My view is different. I do not think that, since the world is finite, there is only a limited finite number of all possible states.

But... suppose we accept your model. What kind of numbers would you use to ensure finiteness? Is there such a model? Say, we consider all numbers as being module 2^270. No, it won't work. NSA? There is a finite number of elements, but there is no limit. Any ideas?