The Persuasive Value of Demonstration: Descartes’ Discourse
Abstract. The aim of this paper is to give an account of the possible doctrines of demonstration which could have served as a mode of exposition in Descartes’ Discourse and Essays. Assuming that Descartes needed to convince his readers that his method was a genuine procedure for advancing scientific knowledge, the presentation of the results in the Discourse should have a persuasive role. Granted that the reader would then believe Descartes’ method to be an endeavour worthy of attention, the Dioptrics and Meteorology should also have a demonstrative role. In the first sections, I sketch the early modern disciplines which could provide that, namely syllogism, dialectics and mathematical demonstrations. Next, I suggest that the most plausible source for Descartes’ mode of exposition is algebraic geometrical analysis. On this reading, the argumentative value of the suppositions resembles the hypothetical procedure of the analysis. Also, the kind of deduction implied by this procedure is not a formal one, as in the case of the demonstrative syllogism, but rather a relational geometrical one.
Keywords: Descartes, Discourse on the Method, demonstration, syllogism, dialectic, geometrical analysis, algebra.