[Archaea]

In fairness, this question requires more familiarity than most retain from the initial philosophy class. I have forgotten Descartes arguments on the matter, but I remember the arguments of Peirce, more through James and a little bit through Dewey than I do Descartes.

Perice argued for a scientific explanation of philosophy, he argued in favor of a method of inquiry, and was made famous through the two followers.

SEIQ can explain it better as he framed the question, but Descartes saw doubt as a tool, and in fact proof of his own separate existence. Now it's strange to me that he would argue it can be feigned instead of natural, but I no longer remember the arguments, so help us out SEIQ. (Yes I'm not that dumb, cogito ergo sum).

In a nutshell, one might simplify the inquiry, as Descartes arguing you must throw everything into question, and CS Peirce requiring you to accept and justify everything, weeding out what cannot be used or shown through systematic inquiry. That is how I'm interpreting the question but perhaps I err. SEIQ can clean up my mess, but that's what one far removed from school can remember.