Jalloh, Mahmoud (2023) The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. [Preprint]

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Abstract

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary.

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Item Type:	Preprint
Creators:	Creators Email ORCID Jalloh, Mahmoud mahmoudtimbojalloh@gmail.com 0000-0001-8511-9294
Additional Information:	Forthcoming in Oxford Studies in Metaphysics.
Keywords:	quantity, symmetry, dimensional analysis
Subjects:	General Issues > Scientific Metaphysics General Issues > Laws of Nature Specific Sciences > Physics Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Mahmoud Jalloh
Date Deposited:	12 Jan 2023 17:39
Last Modified:	12 Jan 2023 17:39
Item ID:	21643
Subjects:	General Issues > Scientific Metaphysics General Issues > Laws of Nature Specific Sciences > Physics Specific Sciences > Physics > Symmetries/Invariances
Date:	January 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/21643

Available Versions of this Item

• The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. (deposited 22 Jul 2022 22:31)
  • The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. (deposited 24 Sep 2022 13:11)
    • The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. (deposited 12 Jan 2023 17:39) [Currently Displayed]
      • The Π-Theorem as a Guide to Quantity Symmetries and the Argument Against Absolutism. (deposited 07 May 2023 18:54)

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