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On the Relativity of Magnitudes: Delboeuf's forgotten contribution to the 19th Century problem of space

Fay, Jonathan (2023) On the Relativity of Magnitudes: Delboeuf's forgotten contribution to the 19th Century problem of space. [Preprint]

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Abstract

The argument for the Euclidean nature of space based on the relativity of magnitudes has been overlooked by contemporary
philosophers of physics and mathematics.In the present essay, we focus on the relevance of this argument to 19th Century philosophy of geometry. In this context, Delboeuf’s contribution has been unduly neglected. Delboeuf’s philosophy of geometry is more authentically neo-Kantian than that of Helmholtz, it is connected in curious ways to some of Leibniz’s unpublished writings and helps to resolve certain questions in the foundations of Poincare’s philosophy of mathematics. We refute a fallacious argument ´
against Delboeuf’s ideas, espoused by Russell, which seems to have gone unchecked since. We conclude with some comments concerning the relevance of the discussion to scientific methodology and present-day cosmology.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Fay, Jonathanhi20625@bristol.ac.uk
Keywords: Delboeuf Poincare Problem of space Relativity of magnitude Euclidean
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Physics > Cosmology
General Issues > History of Philosophy of Science
Specific Sciences > Mathematics
General Issues > Models and Idealization
Specific Sciences > Physics
Depositing User: Mr. Jonathan Fay
Date Deposited: 18 Sep 2023 16:42
Last Modified: 18 Sep 2023 16:42
Item ID: 22556
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Physics > Cosmology
General Issues > History of Philosophy of Science
Specific Sciences > Mathematics
General Issues > Models and Idealization
Specific Sciences > Physics
Date: 24 August 2023
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/22556

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