Quantum metaphysical indeterminacy and worldly incompleteness
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Quantum metaphysical indeterminacy and worldly incompleteness Alessandro Torza1
Received: 28 November 2016 / Accepted: 23 September 2017 © Springer Science+Business Media B.V. 2017
Abstract An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically indeterminate whether p just in case it is neither true nor false that p, and no terms in ‘ p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent. Keywords Ersatz world · Ersatzism · Superposition · Quantum mechanics · Quantum physics · Nonclassical logic · Compositionality · Bivalence · Semantic completeness · Supervaluationism · Metaphysical indeterminacy · Possible worlds · Impossible worlds
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Alessandro Torza [email protected] Instituto de Investigaciones Filosóficas, UNAM, Circuito Mario de la Cueva, Ciudad Universitaria, Del. Coyoacán, 04510 Mexico, D.F., Mexico
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Synthese
1 Precisificational possibilities The idea that indeterminacy may be not only semantic (originating in language1 ), but also metaphysical (originating in the nonrepresentational world), has been a fringe view until not long ago, mostly due to a combination of two factors: an influential argument of Evans (1978) against vague objects,2 as well as a lack of theories that could capture metaphysical indeterminacy in a clear and rigorous fashion. The tide turned with a number of recent papers which have brought the notion of metaphysical indeterminacy out of disrepute. I will focus on the most discussed proposal, developed by Elizabeth Barnes and Robert Williams (henceforth, BW).3 The BW account models metaphysical indeterminacy in terms of precisifications: roughly, the world is indeterminate just in case there are multiple ways it can be made precise. The idea is spelled out by way of the standard distinction between a world, a concrete object made up of things and properties, and an ersatz world, an abstract representation of a world. For our present purpose, we can assume linguistic ersatzism, the view that what does the representing are maximally consistent sets of sentences defined in a semantically nondefective world-making language—although nothing essential hinges on the linguistic construal of ersatz worlds. That the
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