The cogito appears first in the Discourse on the Method, in French, as je pense, donc je suis. "I am thinking, therefore I exist." The Meditations presents it differently. Descartes writes, "this proposition, I am, I exist, is necessarily true whenever it is put forward by me."
I don't think Descartes overcame Cartesian skepticism with this, because Descartes concedes that he could be misled about simple mathematical truths.
From the Discourse on the Method: "since there are men who make mistakes in reasoning, committing logical fallacies concerning the simplest questions in geometry, and because I judged that I was as prone to error as anyone else, I rejected as unsound all the arguments I had previously taken as demonstrative proofs."
From the Meditations: "since I sometimes consider that others go astray in cases where they have the most perfect knowledge, may I not similarly go wrong every time I add two and three or count the sides of a square, or in some even simpler manner, if that is conceivable?"
If you can be wrong about 2+3=5, you can be wrong about the cogito too. Descartes' skepticism is too severe to be rationally addressed, once its appropriateness is granted.
I don't think Descartes overcame Cartesian skepticism with this, because Descartes concedes that he could be misled about simple mathematical truths.
From the Discourse on the Method: "since there are men who make mistakes in reasoning, committing logical fallacies concerning the simplest questions in geometry, and because I judged that I was as prone to error as anyone else, I rejected as unsound all the arguments I had previously taken as demonstrative proofs."
From the Meditations: "since I sometimes consider that others go astray in cases where they have the most perfect knowledge, may I not similarly go wrong every time I add two and three or count the sides of a square, or in some even simpler manner, if that is conceivable?"
If you can be wrong about 2+3=5, you can be wrong about the cogito too. Descartes' skepticism is too severe to be rationally addressed, once its appropriateness is granted.