The argument that everyone remembers Rene Descartes for is "I think therefore I am." I know that he made other contributions to western thought, the point of this is not to critique his work in general, just to critique this one argument. The argument goes something like "You must believe that you exist because if you did not exist you would not be able to think that you do not exist."
It sounds convincing at first, but the problem is characters in fiction do, in a fashion, think things and hold beliefs. For example, the gas station owner in The Great Gatsby believed that Jay Gatsby ran over his wife. I know you could argue that fictional characters don't actually exist or think or that even if they only exist in a story they would still need to exist in that story in order to think in that story, but the point is that you still need to prove that in order to think you must exist for Cogito Ergo Sum to be valid.
It sounds convincing at first, but the problem is characters in fiction do, in a fashion, think things and hold beliefs. For example, the gas station owner in The Great Gatsby believed that Jay Gatsby ran over his wife. I know you could argue that fictional characters don't actually exist or think or that even if they only exist in a story they would still need to exist in that story in order to think in that story, but the point is that you still need to prove that in order to think you must exist for Cogito Ergo Sum to be valid.