Higher Variations of the Monty Hall Problem (3.0 and 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole's Footsteps, as Something the Brain Does

TL;DR

This paper explores advanced versions of the Monty Hall problem, analyzing their implications for understanding the mathematical nature of human cognition and decision-making, inspired by Boole's logical and probabilistic theories.

Contribution

It introduces higher variations of the Monty Hall problem and empirically investigates how these relate to the brain's mathematical processing, building on Boole's foundational ideas.

Findings

Higher variations of the Monty Hall problem demonstrate complex decision patterns.

Empirical evidence suggests the brain's approach to probability aligns with Boole's logical framework.

The study links mathematical cognition to specific probabilistic behaviors in decision-making.

Abstract

Generalizations of the Monty Hall problem are studied according to George Boole's (1853) "An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities"