The Final Solutions of Monty Hall Problem and Three Prisoners Problem

TL;DR

This paper applies a novel quantum language framework to provide final solutions to the Monty Hall and Three Prisoners problems, emphasizing the importance of probability and dualism in understanding these classic puzzles.

Contribution

It introduces a quantum linguistic interpretation to solve the Monty Hall and Three Prisoners problems, offering a new philosophical perspective on probability and dualism.

Findings

Provides final solutions to the Monty Hall and Three Prisoners problems.

Highlights the role of probability and dualism in understanding these puzzles.

Proposes quantum language as a powerful tool for scientific description.

Abstract

Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory, or quantum language), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy).And we believe that this quantum language is the most powerful language to describe science. The purpose of this paper is to describe the Monty-Hall problem and the three prisoners problem in quantum language. We of course believe that our proposal is the final solutions of the two problems. Thus in this paper, we can answer the question: "Why have philosophers continued to stick to these problems?" And the readers will find that these problems are never elementary, and they can not be solved without the deep understanding of "probability" and "dualism". KEY WORDS: Philosophy of probability, Fisher Maximum Likelihood Method, Bayes' Method,The Principle of Equal (a priori) Probabilities