Distribution can be Dropped: Reply to Rumfitt

TL;DR

This paper argues that adopting quantum logic is both possible and rationally justifiable, countering claims that it is unnecessary or impossible due to rule-circularity or unsoundness, by providing a new semantics and modifications to quantum mechanics.

Contribution

The paper demonstrates that rule-circularity issues in quantum logic can be resolved with an appropriate semantics and that slight modifications to quantum mechanics restore soundness, making quantum logic adoptable.

Findings

Rule-circularity in quantum logic can be eliminated with suitable semantics

Soundness of quantum logic is recoverable through minor modifications to quantum mechanics

Quantum logic can be rationally adopted over classical logic in quantum reasoning

Abstract

Most believe that there are no empirical grounds that make the adoption of quantum logic necessary. Ian Rumfitt has further argued that this adoption is not possible, either, for the proof that distribution fails in quantum mechanics is rule-circular or unsound. I respond to Rumfitt, by showing that neither is the case: rule-circularity disappears when an appropriate semantics is considered, and soundness is restored by slightly modifying standard quantum mechanics. Thus, albeit this is indeed not necessary, it is however possible for a quantum logician to rationally adjudicate against classical logic.