Excellent argument, Zanzoken. Context allows us to make sense of an otherwise perplexing statement. Considering there are several schools of philosophical thought, one should really read some of Descartes' works so one can determine where he's coming from, what premises he starts with and what he's trying to prove.
The following link may help understand more about the background of "cogito ergo sum";
Quote:
Famously, Descartes puts forward a very simple candidate as the “first item of knowledge.” The candidate is suggested by methodic doubt—by the very effort at thinking all my thoughts might be mistaken. Early in the Second Meditation, Descartes has his meditator observe:
I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. (Med. 2, AT 7:25)
As the canonical formulation has it, I think therefore I am (Latin: cogito ergo sum; French: je pense, donc je suis)—a formulation which does not expressly arise in the Meditations.
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Descartes' Epistemology (Stanford Encyclopedia of Philosophy)