Carson, E. (1997): Kant on intuition and geometry

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@article{carson1997,
    Author = {Carson, Emily},
    Journal = {Canadian Journal of Philosophy},
    Month = {December},
    Number = {4},
    Pages = {489--512},
    Title = {Kant on Intuition and Geometry},
    Volume = {27},
    Year = {1997}}

Overview

This paper further develops the ‘anti-formalist’ and ‘phenomenological’ reading of Kant’s philosophy of mathematics, as developed by Parsons, Brittan, and Beck. Carson mostly develops the view as against Friedman’s formalist reading. She argues that (i) Friedman is wrong to interpret Kant as arguing that the role of intuition in geometrical knowledge is purely logical, in that it allows Kant to transcend the limitations of his monadic logic; (ii) construction in pure intuition “exhibits the objective reality of geometrical concepts by showing the possibility of an object corresponding to the concept” (502). Along the way Carson argues that mathematical concepts must be given real definition via appeal to construction in intuition in order for mathematical knowledge to be possible (504, 507-8).