>>11268800Allow me some corrections to your question.
Mathematics has no actual impredicativity. Mathematics works with perfect models. Even if you speak about probability theory I would argue that this is just caused by an incomplete model.
Physics however, (applied maths if you will) does support inpredictabilty:
https://en.wikipedia.org/wiki/Hidden-variable_theoryYou may find fractals interesting as they hint at the halting problem, kinda deals with inpredictability in computation:
https://en.wikipedia.org/wiki/Halting_problemThey also look at chaos theory (high sensitivity to initial conditions)
What did you have in mind with this question?
Maybe this:
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems 
