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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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).
Citations of this work BETA
No citations found.
Similar books and articles
Russell's Logicist Definitions of Numbers, 1898–1913: Chronology and Significance.Francisco Rodríguez Consuegra - 1987 - History and Philosophy of Logic 8 (2):141-169.
Poincaré, Kant, and the Scope of Mathematical Intuition.Terry F. Godlove - 2009 - Review of Metaphysics 62 (4):779-801.
An Enhanced Argument for Innate Elementary Geometric Knowledge and its Philosophical Implications.Helen De Cruz - 2007 - In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific.
Axiomatizations of Hyperbolic Geometry: A Comparison Based on Language and Quantifier Type Complexity.Victor Pambuccian - 2002 - Synthese 133 (3):331 - 341.
Kant's "Argument From Geometry".Lisa Shabel - 2004 - Journal of the History of Philosophy 42 (2):195-215.
Edmund Husserl on the Applicability of Formal Geometry.René Jagnow - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 67-85.
Added to index2010-07-27
Total downloads21 ( #236,977 of 2,169,713 )
Recent downloads (6 months)1 ( #345,460 of 2,169,713 )
How can I increase my downloads?