Contra Bellum: Bell's Theorem as a Confusion of Languages

Bell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k+1. We are inclined to think that k=0 corresponds to the classical world, while k=1 — to the quantum one. However, as the k=0 inequalities are violated by k=1 probabilities, the same relation holds between k=1 inequalities violated by k=2 probabilities, k=-1 inequalities violated by k=0 probabilities, and so forth. By accepting the logic of the Bell theorem, can we prove by induction that nothing exists?