Feintzeig, Benjamin H. (2017) Deduction and Definability in Infinite Statistical Systems. [Preprint]

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Abstract

Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from a theory describing only finite systems? In this paper, I change the subject in order to consider the motivations behind the definability and deducibility requirements. The classical accounts of intertheoretic reduction are appealing because when the definability and deducibility requirements are satisfied there is a sense in which the reduced theory is forced upon us by the reducing theory and the reduced theory contains no more information or structure than the reducing theory. I will show that, likewise, there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the properties of finite systems, and the properties of infinite systems contain no information beyond the properties of finite systems.

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Item Type:	Preprint
Creators:	Creators Email ORCID Feintzeig, Benjamin H. bfeintze@uw.edu
Keywords:	algebraic quantum theory, C*-algebras, category theory, reduction
Subjects:	General Issues > Models and Idealization Specific Sciences > Physics > Quantum Field Theory General Issues > Reductionism/Holism Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User:	Benjamin Feintzeig
Date Deposited:	12 Jul 2017 14:35
Last Modified:	12 Jul 2017 14:35
Item ID:	13197
Subjects:	General Issues > Models and Idealization Specific Sciences > Physics > Quantum Field Theory General Issues > Reductionism/Holism Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date:	11 July 2017
URI:	https://philsci-archive.pitt.edu/id/eprint/13197

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