History and Philosophy of Logic 30 (4):349-368 (2009)
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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References found in this work BETA
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford University Press.
A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.John P. Burgess & Gideon A. Rosen - 1997 - Oxford University Press.
Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
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