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Cognition Without Construction: Kant, Maimon, And The Transcendental Philosophy Of Mathematics, Nicholas A. J. Birmingham
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 …
Epistemology Of The Cartesian Image, Mikhail Pozdniakov
Epistemology Of The Cartesian Image, Mikhail Pozdniakov
Electronic Thesis and Dissertation Repository
This study is an examination of the epistemological history of the image. Its first strands are to be found in the Christian concept of profanity, in the difference of the world to the divine. The highest form of intelligibility profanity could have, second only to theology, was mathematics. Derived from the problems surrounding this concept are the techniques of inquiry that eventually resulted in the development of analytic geometry by Descartes. The latter marked a new sensibility regarding the physical universe and its constitution, one that is coterminous with the development of exact procedures in science. Being that exactitude regards …