Rethinking Wittgenstein's Tractatus through Statistics and Quantum language

For the last quarter century, I have been advocating quantum language (QL). QL should be regarded not only as a linguistic turn of quantum mechanics, but also as the ultimate formulation of epistemology in the sense of Descartes and Kant. Even more importantly, QL naturally and essentially includes statistics. Furthermore, Wittgenstein's dream — namely, a proof of why logic holds in our world, as pursued in his Tractatus Logico-Philosophicus (TLP) — can be realized within QL. In this paper, I propose to replace his picture theory with statistics, and to reinterpret statistics within the framework of quantum language.
In doing so, I demonstrate that Wittgenstein's dream can in fact be fulfilled within statistics itself, when properly described in the language of QL.

This version corrects two minor typos:  
(1) "\mathbb{P} \theta" was replaced by the correct form "\mathbb{P}_\theta", and  
(2) a missing percent sign was fixed by replacing "100%" with "100\%" in LaTeX notation.