It is the purpose of this essay to examine both Descartes Cogito argument and his skepticism towards small and universal elements, as well as the implications these arguments have on each other. First, I willsummarize and explain the skepticism Descartes brings to bear on small and universal elements in his firstmeditation. Second, I will summarize and explain the Cogito argument, Descartes famous I think, therefore Iam (it should be noted that this famous implication is not actually something ever said or written by Descartes,but instead, an implication taken from his argument for his own existence). Third, I will critique the line ofreasoning underlying these arguments. Descartes attacks small and universal elements with the problem posedby the possibility of God being an omnipotent deceiver, but he seems to think his Cogito argument is immunefrom this type of criticism. Fourth, I will show how the Cogito is actually harder to establish than the existence ofsmall and universal elements. And, fifth, I will establish small and universal elements as an Archimedean point(i.e. a foundational claim). In Descartes first meditation, paragraphs 9-12, he arrives at the final and most devastating stage ofquestioning his beliefs. In his first two stages, he questions both small and distant objects and medium sizedobjects, and concludes that neither can be held as true with any certainty. He throws out the first because of thepossibility that the small and distant object is a mirage, and throws out the second because of the possibility thatwe are actually dreaming while perceiving medium sized objects. In his third and final stage of doubt, Descartesexamines small and universal elements. To this category belong things such as mathematics and the Law ofNon-contradiction, which deal with the most basic and elementary of concepts; such as that 2 + 2 = 4, and thatone cannot be both alive and dead at the same time. ...
