Oh, brother.

There is no "problem of induction" because induction doesn't do the things that argument requires it to do.

There's doubly no "problem of induction" because there's no contrast between deduction and induction. Deduction is a subset of induction. The former can do nothing that the latter cannot.

Frankly, I don't believe you really grasp what a "world of chaos" would look like.

This is just silly.

No, it's simply a truth you haven't developed enough to grasp yet. The beginning of wisdom is recognizing that you know nothing, in the sense that people often use 'know'.