Jreige, Rami (2025) Relational Abstraction in the History of Mathematics. [Preprint]

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Abstract

The philosophical literature on mathematical structuralism and its history has focused on the emergence of structuralism in the 19th century. Yet modern abstractionist accounts cannot provide an historical account for the abstraction process. This paper will examine the role of relations in the history of mathematics, focusing on three main epochs where relational abstraction is most prominent: ancient Greek, 17th and 19th centuries, to provide a philosophical account for the abstraction of structures. Though these structures emerged in the 19th century with definitional axioms, the need for such axioms in the abstraction process comes about, as this paper will show, after a series of relational abstractions without a suitable basis.

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Item Type:	Preprint
Creators:	Creators Email ORCID Jreige, Rami rami.jreige@gmail.com 0009-0001-8584-9366
Keywords:	Philosophy of Mathematics, History of Mathematics, Metaphysics of Relations, Mathematical Abstraction
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Practice
Depositing User:	Rami Jreige
Date Deposited:	12 Feb 2025 19:38
Last Modified:	12 Feb 2025 19:38
Item ID:	24736
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Practice
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/24736

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