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Is It Possible to Nominalize Quantum Mechanics?

Published online by Cambridge University Press:  01 January 2022

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.

Type
Interpretations of Quantum Mechanics
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

I wish to thank Jody Azzouni, Mark Colyvan, Steven French, and Joseph Melia for extremely helpful discussions.

References

Armstrong, David (1989), A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Balaguer, Mark (1998), Platonism and Anti-Platonism in Mathematics. New York: Oxford University Press.Google Scholar
Field, Hartry (1980), Science without Numbers. Princeton: Princeton University Press.Google Scholar
Field, Hartry (1989), Realism, Mathematics, and Modality. Oxford: Basil Blackwell.Google Scholar
Hilbert, David (1971), Foundations of Geometry. La Salle: Open Court.Google Scholar
Lewis, David (1986), On the Plurality of Worlds. Oxford: Blackwell.Google Scholar
Malament, David (1982), “Review of Field 1980”, Review of Field 1980 79:523534.Google Scholar
van Fraassen, Bas (1980), The Scientific Image. Oxford: Clarendon Press.CrossRefGoogle Scholar
van Fraassen, Bas (1989), Laws and Symmetry. Oxford: Clarendon Press.CrossRefGoogle Scholar
van Fraassen, Bas (1991), Quantum Mechanics: An Empiricist View. Oxford: Clarendon Press.CrossRefGoogle Scholar
von Neumann, John (1932), Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press.Google Scholar
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