Abstraction and intuition in Peano's axiomatizations of geometry

Rizza, Davide ORCID: https://orcid.org/0000-0002-1375-371X (2009) Abstraction and intuition in Peano's axiomatizations of geometry. History and Philosophy of Logic, 30 (4). pp. 349-368. ISSN 1464-5149

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Abstract

Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it into a particular form.

Item Type:	Article
Faculty \ School:	Faculty of Arts and Humanities > School of Philosophy (former - to 2014)
UEA Research Groups:	Faculty of Arts and Humanities > Research Groups > Philosophy Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	EPrints Services
Date Deposited:	01 Oct 2010 13:58
Last Modified:	11 Nov 2024 09:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/10017
DOI:	10.1080/01445340903250489

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