Analytical Method in Descartes and the Cartesian Conception of Inference: Between Algebra and Platonic Dialectic

Abstract

In the following article, I intend to study Descartes' analytic method. I claim that Descartes' analysis must be understood in the light of his appropriation and use of algebra and his peculiar conception of inference. In this sense, I state that Descartes conceives of the analytic method as an algebraic manipulation of known and unknown terms, destined to expound their relations of interdependency and clarify the unknown terms. I assert that in this algebraic manipulation, the kind of inference that Descartes proposes plays a major role as an alternative to Aristotelian syllogistic inference and the inference associated with the traditional analytic-synthetic method. While Aristotelian syllogistic inference proceeds exclusively with propositions and is grounded in their grammatical forms, Cartesian inference is based on the content of ideas and proceeds by virtue of connections between ideas that, combined with algebraic manipulation, allow the conversion of the inferential sequence. This will show that Cartesian analysis and synthesis do not differentiate due to the inferential procedures they involve or the inferential direction they follow (traditional analytic and synthetic methods do differentiate due to these facets). While both Cartesian analysis and synthesis are grounded in algebraic manipulation and Cartesian inference, they differentiate from each other by the former aiming towards a clarification of unknown terms and the latter delivering conclusions from these solutions. Finally, I will also show that the algebraic interpretation of the Meditations is compatible with understanding the cartesian procedure as the deployment of platonic dialectics.