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

Jeremy Heis
University of California, Irvine
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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DOI 10.1080/00455091.2014.971689
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Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press.
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.
Lectures on Logic.Immanuel KANT - 1992 - Cambridge University Press.

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