Cogito, ergo sum : induction et déduction

The cartesian “cogito, ergo sum” appears for forty years as “an Inference and a Performance” (J. Hintikka). But what kind of inference are we talking about? This paper works towards two ends : first, to point out that the real question about the inference in the cartesian cogito does not concern the internal logical relation between cogito and sum, which is an intuition, but the external one between « cogito, ergo sum » and « quicquid cogitat, est ». Then, to show that this relation is both an induction and a deduction.