Laraudogoitia, Jon Perez (2025) ON A PUZZLE ABOUT SUMS. Oxford University Press.

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Abstract

While the problem of the philosophical significance of Riemann's theorem on conditionally convergent series has been discussed in detail for some time, specific versions of it have appeared in the literature very recently, over which there have been widespread disagreements. I argue that such discrepancies can be clarified by introducing a rather conventional type of composition rule for the treatment of some infinite systems (as well as supertasks) while analysing and clarifying the role of the concept of continuity by stripping it of the excesses that its application by the Leibnizian tradition has led to. The conclusion reached is that the indeterminacy associated with conditional convergence has a clear philosophical significance, but no fundamental ontological significance.

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Item Type:	Other
Creators:	Creators Email ORCID Laraudogoitia, Jon Perez jon.perez@ehu.es 0000-0002-9003-4946
Additional Information:	Forthcoming in Analysis
Keywords:	Conditional Convergence; Continuity; Expansionist Analysis; Balance Principle; Ross Paradox
Subjects:	General Issues > Scientific Metaphysics General Issues > Philosophers of Science
Depositing User:	Dr. Jon Perez Laraudogoitia
Date Deposited:	14 Apr 2025 13:17
Last Modified:	14 Apr 2025 13:17
Item ID:	25051
Journal or Publication Title:	Analysis
Publisher:	Oxford University Press
Subjects:	General Issues > Scientific Metaphysics General Issues > Philosophers of Science
Date:	12 April 2025
ISSN:	0003-2638
URI:	https://philsci-archive.pitt.edu/id/eprint/25051

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