As Roger Ariew shows, one of the most fascinating challenges for the authors trying to create a Cartesian complete course on philosophy was coming up with a Cartesian Logic based on the existing texts of the master (Ariew 2014). Were the few simple rules from the Discourse on Method the “logic” of Descartes? Were the Rules for the Direction of the Mind “logic”? How can we even have a logic without syllogism? When looking at the authors studied by Ariew one finds that the best that they could come up was adding some Cartesian elements on what remains basically a traditional Aristotelian Logic. It seems that there was no Cartesian Logic after all.
I want to show here that Cartesian Logic is something else, not exactly “Logic” in the way that was taught in the first year of college, but something meant to replace Aristotelian Logic once we have...