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 $k\in\mathbb{Z}$, are violated by probabilities at level $k+1$. We are inclined to think that $k=0$ corresponds to the the classical world, while the quantum one is $k=1$. 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. Accepting the logic of the Bell theorem, can we prove by induction that nothing exists?