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Cognition Without Construction: Kant, Maimon, And The Transcendental Philosophy Of Mathematics, Nicholas A. J. Birmingham

Electronic Thesis and Dissertation Repository

In the Critique of Pure Reason, Immanuel Kant takes the ostensive constructions characteristic of Euclidean-style demonstrations to be the paradigm of both mathematical proofs and synthetic a priori cognition in general. However, the development of calculus included a number of techniques for representing infinite series of sums or differences, which could not be represented with the direct geometrical demonstrations of the past. Salomon Maimon’s Essay on Transcendental Philosophy addresses precisely this disparity. Maimon, owing much to G. W. Leibniz, proposes that differentials of sensation achieve what Kantian constructions could not. More importantly, Maimon develops a kind of symbolic cognition that …