Abstraction and Intuition in Peano's Axiomatizations of Geometry

History and Philosophy of Logic 30 (4):349-368 (2009)
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
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DOI 10.1080/01445340903250489
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References found in this work BETA
Mathematics as a Science of Patterns.D. Resnik Michael - 1997 - New York ;Oxford University Press.
Mathematical Thought and its Objects.Charles Parsons - 2008 - Cambridge University Press.
Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.

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