Geometric Exposition

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Abstract

In the Second Set of Objections to the Meditations, Descartes is asked to “set out the entire argument in geometrical fashion, starting from a number of definitions, postulates and axioms” (see Objections and Replies). The objectors then add, “You are highly experienced in employing this method, and it would enable you to fill the mind of each reader so that he could see everything as it were at a single glance, and be permeated with awareness of the divine power” (AT VII 128, CSM II 92). Mersenne and his fellow objectors, in effect, are asking Descartes to do for his metaphysics what Euclid had done for geometry. Euclid in The Elements systematizes geometry by using what came to be known as the geometrical method. That is, by using a small set of stipulated definitions, axioms, which are taken to be self-evident, along with postulates, which are sometimes understood to be assumptions that are not self-evident (Heath 1926, 1:123–24), together with the rules of deduction, various theorems can then be demonstrated.
Original languageEnglish GB
Title of host publicationThe Cambridge Descartes Lexicon
EditorsLarry Nolan
PublisherCambridge University Press
Pages319-321
DOIs
StatePublished - 2016

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