Is it possible to nominalize quantum mechanics?

Philosophy of Science 70 (5):1424-1436 (2003)
Abstract
Hartry Field (1980) has developed an interesting nominalization strategy for Newtonian gravitation theory—a strategy that reformulates the theory without quantification over abstract entities. According to David Malament (1982), Field's strategy cannot be extended to quantum mechanics (QM), and so it only has a limited scope. In a recent work, Mark Balaguer has responded to Malament's challenge by indicating how QM can be nominalized, and by “doing much of the work needed to provide the nominalization” (Balaguer 1998, 114). In this paper, I critically assess Balaguer's proposal, and argue that it ultimately fails. Balaguer's strategy is incompatible with a number of interpretations of QM, in particular with Bas van Fraassen's version of the modal interpretation. And given that Balaguer's strategy invokes physically real propensities, it is unclear whether it is even compatible with nominalism. I conclude that the nominalization of QM remains a major problem for the nominalist.
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DOI 10.1086/377419
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Fictionalism, Theft, and the Story of Mathematics.Mark Balaguer - 2008 - Philosophia Mathematica 17 (2):131-162.
Fictionalism in Metaphysics.Frederick Kroon - 2011 - Philosophy Compass 6 (11):786-803.
Can the Constructive Empiricist Be a Nominalist? Quasi-Truth, Commitment and Consistency.P. Dicken - 2006 - Studies in History and Philosophy of Science Part A 37 (2):191-209.
Can the Constructive Empiricist Be a Nominalist? Quasi-Truth, Commitment and Consistency.Paul Dicken - 2006 - Studies in History and Philosophy of Science Part A 37 (2):191-209.

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