Miller, Michael (2016) Mathematical Structure and Empirical Content. [Preprint]

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Abstract

Approaches to the interpretation of physical theories provide accounts of how physical meaning accrues to the mathematical structure of a theory. According to many standard approaches to interpretation, meaning relations are captured by maps from the mathematical structure of the theory to statements expressing its empirical content. In this paper I argue that while such accounts adequately address meaning relations when exact models are available or perturbation theory converges, they do not fare as well for models that give rise to divergent perturbative expansions. Since truncations of divergent perturbative expansions often play a critical role in establishing the empirical adequacy of a theory, this is a serious deficiency. I show how to augment state-space semantics, a view developed by Beth and van Fraassen, to capture perturbatively evaluated observables even in cases where perturbation theory is divergent. This new semantics establishes a sense in which the calculations that underwrite the empirical adequacy of a theory are both meaningful and true, but requires departure from the assumption that physical meaning is captured entirely by the exact models of a theory.

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Item Type:	Preprint
Creators:	Creators Email ORCID Miller, Michael michael.earl.miller@gmail.com
Keywords:	Structure of theories, quantum field theory, quantum mechanics, classical mechanics, perturbation theory
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories General Issues > Theory/Observation
Depositing User:	Mr. Michael E. Miller
Date Deposited:	07 Dec 2016 15:54
Last Modified:	07 Dec 2016 15:54
Item ID:	12678
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories General Issues > Theory/Observation
Date:	7 December 2016
URI:	https://philsci-archive.pitt.edu/id/eprint/12678

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