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Kant (vs. Leibniz, Wolff and Lambert) on real definitions in geometry

Published online by Cambridge University Press:  01 January 2020

Jeremy Heis
Jeremy Heis*
Affiliation:
Department of Logic and Philosophy of Science, University of California, Irvine, CA, USA
*
*Email: jheis@uci.edu
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Abstract

This paper gives a contextualized reading of Kant’s theory of real definitions in geometry. Though Leibniz, Wolff, Lambert and Kant all believe that definitions in geometry must be ‘real’, they disagree about what a real definition is. These disagreements are made vivid by looking at two of Euclid’s definitions. I argue that Kant accepted Euclid’s definition of circle and rejected his definition of parallel lines because his conception of mathematics placed uniquely stringent requirements on real definitions in geometry. Leibniz, Wolff and Lambert thus accept definitions that Kant rejects because they assign weaker roles to real definitions.

Keywords

KantLambertLeibnizWolffEuclidgeometrydefinition
Type
Research Article
Information
Canadian Journal of Philosophy , Volume 44 , Issue 5-6: Special Issue: Mathematics in Kant’s Critical Philosophy , December 2014 , pp. 605 - 630
Copyright
Copyright © Canadian Journal of Philosophy 2014

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