The Circle, from Descartes’ Point of View

My project is to show that despite relentless criticism from the beginning, Descartes cannot be reasonably faulted in his attempt to relieve systematic doubt or as it is sometimes called, metaphysical doubt. By “cannot be reasonably faulted” I mean that Descartes is not open criticism either for having made assumptions that were unwarranted by standards of his own time or for having made errors in reasoning. The paper seeks to analyze Descartes’ struggle with metaphysical doubt and radical skepticism in relation to issues concerning provability and truth in arithmetic that are addressed by G?del-L?b provability logic.