Quantum mechanics and the interpretation of the orthomodular square of opposition

TL;DR

This paper explores the logical structure of quantum mechanics through the lens of the orthomodular square of opposition, highlighting fundamental differences between classical and quantum notions of possibility.

Contribution

It extends the Aristotelian Square of Opposition to orthomodular structures with a monadic quantifier, revealing distinct behaviors of classical and quantum possibilities.

Findings

Classical and quantum possibilities behave differently in the orthomodular framework

The orthomodular square of opposition can be enriched with a monadic quantifier

Quantum possibility exhibits radically different formal properties from classical possibility

Abstract

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.