The Applicability of Mathematics to Physical Modality

Synthese 194 (9):3361-3377 (2017)
Authors
Nora Berenstain
University of Tennessee, Knoxville
Abstract
This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of the physical world. The no-miracles argument is the primary motivation for scientific realism. It is a presupposition of this argument that unobservable entities are explanatory only when they determine the empirical phenomena they explain. I argue that mathematical entities should also be seen as explanatory only when they determine the empirical facts they explain, namely, the modal structure of the physical world. Thus, scientific realism commits us to a metaphysical determination relation between mathematics and physical modality that has not been previously recognized. The requirement to account for the metaphysical dependence of modal physical structure on mathematics limits the class of acceptable solutions to the applicability problem that are available to the scientific realist.
Keywords modality  scientific realism  applicability problem  indispensability argument  novel prediction  scientific explanation  mathematical structure  no-miracles argument  grounding  instantiation
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Reprint years 2017
DOI 10.1007/s11229-016-1067-3
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References found in this work BETA

No Work for a Theory of Grounding.Jessica Wilson - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535–579.
Grounding in the Image of Causation.Jonathan Schaffer - 2016 - Philosophical Studies 173 (1):49-100.
There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.

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