Contradiction, Quantum Mechanics, and the Square of Opposition

TL;DR

This paper examines whether quantum superpositions imply contradictions by analyzing the idea through classical logic, ultimately arguing that interpreting superpositions as contradictions faces significant conceptual and metaphysical challenges.

Contribution

It applies the traditional square of opposition to quantum superpositions to critically assess the claim that they involve contradictions.

Findings

Superpositions do not straightforwardly imply contradictions.

Logical and metaphysical analysis challenges the interpretation of superpositions as contradictory.

The square of opposition provides a useful framework for evaluating claims of contradiction in quantum mechanics.

Abstract

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schr\"odinger's cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist. We analyze that claim by employing the traditional square of opposition. We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them.