What Theoretical Equivalence Could Not Be

Philosophical Studies 178 (12):4119-4149 (2021)
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Abstract

Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead.

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Trevor Teitel
University of Toronto, St. George Campus

Citations of this work

How to Be a Spacetime Substantivalist.Trevor Teitel - 2022 - Journal of Philosophy 119 (5):233-278.
Theory (In-)Equivalence and conventionalism in f(R) gravity.Patrick M. Duerr - 2021 - Studies in History and Philosophy of Science Part A 88 (C):10-29.
What Are Symmetries?David John Baker - 2022 - Ergo: An Open Access Journal of Philosophy 9.

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How to define theoretical terms.David Lewis - 1970 - Journal of Philosophy 67 (13):427-446.

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