From George Boole To John Bell — The Origins of Bell’s Inequality

Abstract

We consider a combinatorial problem which was enunciated by George Boole (1854) and explore its identity with fundamental puzzles in a diverse range of fields such as statistical theory, propositional logic, the theory of computational complexity , the Einstein-Podolsky-Rosen paradox in quantum mechanics, the theory of neural networks, and the Ising spin model. Introduction. Understanding a theorem consists in more than merely following its proof. Since mathematicians are human, they prefer proofs which provide more than a syntactic link between the axioms and the proposition. They prefer explanatory demonstrations, those which indicate why the proposition is true(l). But what is it that makes certain proofs transparent and others to appear as "tricks"? It seems to me that part of the answer can be traced to the "holistic" nature of mathematical knowledge. Often, theorems which appear enigmatic when taken in isolation become transparent when associated with other, seemingly unrelated mathematical results.