Quantum metaphysical indeterminacy and worldly incompleteness
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.
KeywordsErsatz world Ersatzism Superposition Quantum mechanics Quantum physics Nonclassical logic Compositionality Bivalence Semantic completeness Supervaluationism Metaphysical indeterminacy Possible worlds Impossible worlds
I would like to express my gratitude to Axel Barceló, Aldo Filomeno, Eduardo García-Ramírez, John Horden, Ricardo Mena, Elias Okon and Jessica Wilson for helpful and constructive feedback on previous versions of this paper. I also would like to thank the audience of the workshops Logical Space. Logical and metaphysical issues and Philosophical Aspects of Modality, which took place at the Instituto de Investigaciones Filosóficas, UNAM, in September 2016. This work was supported by the PAPIIT Grant IA400316.
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