Yet again, quantum indeterminacy is not worldly indecision

Abstract

It has been argued that non-relativistic quantum mechanics is the best hunting ground for genuine examples of metaphysical indeterminacy. Approaches to metaphysical indeterminacy can be divided into two families: meta-level and object-level accounts. It has been shown (Darby in Australasian Journal of Philosophy 88(2):27–245, 2010. 10.1080/00048400903097786; Skow in Philosophical Quarterly 60(241):851–858, 2010) that the most popular version of the meta-level accounts, namely the metaphysical supervaluationism proposed by Barnes and Williams (Oxford Studies in Metaphysics, Oxford University Press, Oxford, pp 103–148, 2011), fails to deal with quantum indeterminacy. Such a fact has been taken by many as a challenge to adapt supervaluationism to quantum cases. In this paper, I will focus on the very last of these attempts, i.e. the situation semantics account proposed by Darby and Pickup (Synthese 1–26, 2019). After having shown where quantum indeterminacy arises and having surveyed the assumptions endorsed by the participants of the debate, I turn to Darby and Pickup’s proposal. I argue that, despite the machinery introduced, their account still fails to account for quantum indeterminacy. After considering some possible counterarguments, I suggest in the conclusion that one can plausibly extend the argument to those meta-level approaches that treat quantum indeterminacy as worldly indecision.

Quantum metametaphysics

“…Quantum (sentential) logic is the logic obtained by interpreting a sentential language on quantum logical space, and identifying logical truth with truth in all quantum logical spaces. 13 One can now see that MI will arise in quantum logical space, for if |ψ @ is neither a member of S nor a member of its orthocomplement, then neither S nor − Q S obtains. For example, consider a one-electron system where S is the fact that the electron e is spin up along the z direction (i.e., S = {α| ↑ z e : α ∈ C}).…”

“…view by appealing to situation semantics; but see Corti [13] for a critique of the situationtheoretic approach.…”

Quantum Mechanics Without Indeterminacy

“…3 See Darby and Pickup (2019) for an attempt to resolve this challenge facing the metaphysical supervaluationist and Corti (2021) for criticism of their attempt.…”

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications

“…Beyond the physics community, many non-physicists are interested in the conceptual aspects of quantum mechanics [ 170 , 171 , 172 , 173 , 174 , 175 ]. These are of direct relevance to philosophy [ 3 ] (Section 6) [ 176 ] (p. 395) [ 177 , 178 , 179 , 180 , 181 , 182 , 183 , 184 ], although to date their influence on philosophy has been limited [ 185 , 186 ]. Less directly, these conceptual aspects of quantum mechanics can be relevant to wider society [ 29 ] (p. 607) [ 103 ] [ 187 ] (pp.…”