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Synthese

Modelling deep indeterminacy

George Darby, Martin Pickup

Published Feb 28, 2019• 25 citations
Publisher

Abstract

Abstract This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen–Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (Oxf Stud Metaphys 6:103–148, 2011). We construct a variant of Barnes and Williams’s theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We evaluate the resulting theory and contrast it with similar alternatives, concluding that our model successfully captures deep indeterminacy.

DOI
10.1007/s11229-019-02158-0

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Abstract This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen–Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (Oxf Stud Metaphys 6:103–148, 2011). We construct a variant of Barnes and Williams’s theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We evaluate the resulting theory and contrast it with similar alternatives, concluding that our model successfully captures deep indeterminacy.
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We use the framework of determinable and determinate properties to provide a novel account of the constraints imposed by the Kochen-Specker theorem. Specifically, we show that the result may be understood as a prohibition on the possibility of providing an account of quantum properties, as they are usually represented using Hilbert space operators, according to which quantum systems are fully determinate. That is, the Kochen-Specker theorem entails that any account of quantum properties compatible with the predictions of quantum mechanics must exhibit determinable-based metaphysical indeterminacy.
Abstract Many features of quantum mechanics (QM) suggest that, at the microscopic level, objects sometimes fail to determinately instantiate their properties. In recent years, many have argued that this phenomenon indicates the existence of an ontological kind of indeterminacy, often called metaphysical indeterminacy , which is supposed to affect the ontology of QM. As insisted by Glick ('Against Quantum Indeterminacy, 2017, Thought), however, once we look at the major realist approaches to QM we learn that the indeterminacy disappears from the description of the world at its most fundamental level. This absence might be taken as a good reason for adopting some form of eliminativism towards quantum mechanical indeterminacy. The aim of this paper is to distinguish three ways of defending eliminativism, and to argue that none of them eventually succeeds. The upshot is that QM does in fact suggest the existence of metaphysical indeterminacy, although only as an emergent phenomenon.
Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen-Specker Theorem. Although we disagree with this last statement, the models play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality --with an emphasis on operational definitions-- and argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.