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Equivalence: an attempt at a history of the idea

Asghari, AH (2018) Equivalence: an attempt at a history of the idea. Synthese: an international journal for epistemology, methodology and philosophy of science, 196. pp. 4657-4677. ISSN 0039-7857

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Open Access URL: https://link.springer.com/article/10.1007/s11229-0... (Published version)

Abstract

This paper proposes a reading of the history of equivalence in mathematics. The paper has two main parts. The first part focuses on a relatively short historical period when the notion of equivalence is about to be decontextualized, but yet, has no commonly agreed-upon name. The method for this part is rather straightforward: following the clues left by the others for the ‘first’ modern use of equivalence. The second part focuses on a relatively long historical period when equivalence is experienced in context. The method for this part is to strip the ideas from their set-theoretic formulations and methodically examine the variations in the ways equivalence appears in some prominent historical texts. The paper reveals several critical differences in the conceptions of equivalence at different points in history that are at variance with the standard account of the mathematical notion of equivalence encompassing the concepts of equivalence relation and equivalence class.

Item Type: Article
Uncontrolled Keywords: 2203 Philosophy, 2202 History and Philosophy of Specific Fields, 0801 Artificial Intelligence and Image Processing
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
L Education > L Education (General)
Divisions: Applied Mathematics
Publisher: Springer Verlag
Date Deposited: 24 Feb 2020 10:31
Last Modified: 24 Feb 2020 10:53
DOI or Identification number: 10.1007/s11229-018-1674-2
URI: http://researchonline.ljmu.ac.uk/id/eprint/12301

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