Abstraction and Intuition in Peano's Axiomatizations of Geometry

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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.
Original languageEnglish
Pages (from-to)349-368
Number of pages20
JournalHistory and Philosophy of Logic
Volume30
Issue number4
DOIs
Publication statusPublished - Nov 2009

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