The principal author of Logic or The Art of Thinking, famously known as the Port-Royal Logic, was Antoine Arnauld, although there is some indication that parts of it may have been written by Pierre Nicole (1625–1695) as well as by the Messieurs of Port Royal. Arnauld got his hands on the original manuscript of Descartes, Rules for the Direction of the Mind (also found in the remnant possessions of Leibniz) – long before it was published – through the good graces of one of Descartes' ardent supporters, Claude Clerselier. Consequently, when he came to compose Port-Royal Logic, Arnauld was heavily influenced by Descartes' work, which Arnauld duly and explicitly acknowledged. Incidentally, Port-Royal Logic was written for a young nobleman whose father, Duc du Luynes, had translated Descartes' Meditationes de Prima Philosophiae into French, a translation that Descartes had approved. It is surely, then, worth considering whether the authors of Port-Royal Logic would have construed the cogito as an argument or as an intuition. This will have to be a historical conjecture, since the Port-Royal Logic does not treat this issue explicitly.

In “Fourth Part of the Logic” of Port-Royal Logic, Chapter 6 begins with a Rule, thus: “Rules concerning axioms, that is, propositions which are clear and evident in themselves …” (AN, 246). There are two cardinal rules. First is the rule that no axioms require demonstration, that is, proof, although some axioms may require explanation.