The metaphysics of mixed quantities. - Turner, Jason (Nous (0029-4624), 2026)
This article focuses on the metaphysics of physical quantities, particularly mixed quantities—those expressed as products or quotients of basic quantities like mass, length, and time—and their role in explaining nomic constants such as the gravitational constant. It develops a representationalist framework called Rational Reductionism, which extends standard representationalism by defining mixed quantities as relations (products and quotients) among basic quantities, thereby providing a number-free, intrinsic account of what numerical values of constants represent. The article addresses a challenge known as the Pandora problem, which arises for comparativist views that treat quantities as nonfundamental, by showing that incorporating fundamental relations tied to mixed quantities can preserve determinism and distinguish physically distinct worlds. It also compares Rational Reductionism with an alternative view, Algebraic Realism, which treats mixed quantities as fundamental entities related by additional algebraic operations, discussing their respective advantages and challenges without endorsing one conclusively. The work aims to clarify how physical laws involving mixed units can be understood metaphysically without reliance on arbitrary numerical assignments or extraneous mathematical objects.