Volume 16, 2008
The Unity of the Cartesian Method in the Rules
1) Gaukroger estimates that there exist two irreconcilable theses in the Cartesian method in the Rules. The first thesis concerns the problem of the cognitive grasp of inference, the other the problem of the method of discovery. Descartes, by integrating deduction as a simple object of intuition, rejects the psychological
interpretation of inference, and elevates deduction to the status of a necessary condition of knowledge. On the other hand, the problem of the method of discovery requires that inference produces a new truth as its conclusion. Descartes takes the algebraic solution of equations as the model of this method. But this orientation leads Descartes to deny all cognitive function operating in the inference of synthetic form. Thus, according to Gaukroger, these two theses tend
to be opposed, calling into question the unity of the method. 2) We admit the cognitive analysis of Gaukroger on the Cartesian inference. However, Gaukroger does not see the importance of “the natural power of the mind” in the Rules. Indeed, the cognitive role of inference is always understood by Descartes, in light of this natural power. Thus, the main role of the method is to teach ways of increasing this power. Descartes tries to pose, by the algebraic treatment of questions, an analogy between the mathematical order and the order of the operations of the mind, enabling him to discover pure schemes of these operations. And, It is by theses schemes that the mind exercise itself in order to increase its natural power. For this reason, we must reconsider Gaukroger’s thesis that Descartes
assimilates literally the method of discovery and algebraic solution, as well as his thesis of the inconsistency of the Cartesian method.