A Defense of the Paraconsistent Approach to Quantum Superpositions (Answer to Arenhart and Krause)

TL;DR

This paper defends the paraconsistent approach to quantum superpositions, arguing it offers a valuable perspective distinct from traditional metaphysical stances and addressing criticisms by Arenhart and Krause.

Contribution

It introduces the Constructive Metaphysical Line of Research as an alternative to the Orthodox approach, supporting the viability of the paraconsistent interpretation of quantum mechanics.

Findings

Addresses and counters objections raised by Arenhart and Krause.

Proposes the CMLR as a new framework for interpreting quantum superpositions.

Clarifies the original perspective of the PAQS in response to criticisms.

Abstract

In (da Costa and de Ronde, 2014), Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause (2014) have raised several arguments against this approach. In the present paper we attempt to answer the main questions presented by Arenhart and Krause. We will argue, firstly, that the obstacles presented by them are based on a specific metaphysical stance, which we will characterize in terms of what we call the Orthodox Line of Research (OLR). Secondly, that this is not necessarily the only possible line, and that a different one, namely, a Constructive Metaphysical Line of Research (CMLR) provides a different perspective in which the Paraconsistent Approach to Quantum Superpositions (PAQS) can be regarded as a valuable prospect that could be used by different interpretations of quantum mechanics. Finally, we provide a set of specific answers to the main problems raised by Arenhart and Krause in order to clarify our line of research as well as the original perspective introduced by the PAQS.