Kant on real definitions in geometry

Canadian Journal of Philosophy 44 (5-6):605-630 (2014)
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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

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Jeremy Heis
University of California, Irvine

Citations of this work

Kant on Method.Karl Schafer - forthcoming - In Andrew Stephenson & Anil Gomes (eds.), The Oxford Handbook of Kant. Oxford: Oxford University Press.
Dedekind and Wolffian Deductive Method.José Ferreirós & Abel Lassalle-Casanave - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie:1-21.

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References found in this work

Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press.
Critique of Pure Reason.Immanuel Kant - 1781/1998 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Kant and the Exact Sciences.Michael Friedman - 1990 - Harvard University Press.
Critique of Pure Reason.Wolfgang Schwarz - 1966 - Philosophy and Phenomenological Research 26 (3):449-451.

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