The relation between the Kochen-Specker theorem and bivalence

TL;DR

This paper explores how the Kochen-Specker theorem implies that certain quantum propositions cannot be assigned definite true or false values simultaneously, challenging classical bivalence.

Contribution

It demonstrates that the Kochen-Specker theorem necessitates non-bivalent truth assignments for some quantum propositions, highlighting fundamental logical constraints in quantum theory.

Findings

Certain quantum propositions lack bivalent truth values

The theorem implies limitations on classical truth assignments

Quantum logic must accommodate non-bivalent truth values

Abstract

In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment function imposed on such a set cannot be total. This means that at least one proposition associated with the said set must be neither true nor false.