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Equivalence: An Attempt at a History of the Idea

Asghari, Amir (2018) Equivalence: An Attempt at a History of the Idea. [Preprint]

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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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Asghari, Amirasghari.amir@gmail.com0000-0001-9658-2137
Additional Information: Dedicated to David Fowler and his “lost” unpublished manuscript ‘Equivalence relations and classes: an attempt at a history of these ideas’.
Keywords: Dedekind; Equivalence; Equivalence class; Equivalence relation; Euclid; Russell; Variations
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Depositing User: Dr Amir Asghari
Date Deposited: 06 Jan 2018 22:44
Last Modified: 06 Jan 2018 22:44
Item ID: 14261
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Date: 3 January 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14261

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