Cogito Ergo Sum is usually translated as I think therefore I am. This in itself may be misleading. We can see this if we deconstruct it:
(i) think... therefore ...(i) am
"i" possess the quality/activity "thoughts"... therefore ..."i" am a stateable bearer of properties
It should be obvious that if we accept the condition "'i' think" then the conclusion "'i' am" follows; no further logic is necessary to extract this from the conditional. If it is true that 'i think' then we know immediately that 'i am'. The second half is in fact the hidden axiom upon which the conditional first half is based. In order to 'think', I must 'be'. If it is true that 'i think' then clearly (without any more logical steps), i must be. I cannot think if I am not.
Of course, one needs to understand: if there are thoughts (which we know there are) then the existence of thoughts is apparent. If Descartes is wholly identifying 'i' and 'thoughts' then his logic is secure. Could it be that all he intended to say in the first step was that, these thoughts, these phenomena which are all that I am, exist. Existence is apparent and this I can give the handy label 'i'.
In Descartes' reply to Mersenne, he establishes that existence is not found from thought by any logical proces or manipulation: existence is already present within the axiom of "i think". 'i think' being a self-evident assertion (notwithstanding the separation of 'i' and 'think' into separate ontologies via grammatical obfuscation), 'i' (that is, existence) is already apparent - it has already been stated and does not need to be deduced.
Thus, the cogito ergo sum (much clearer in Latin) is merely an articulation of identity, of A=A.
Thus, I believe that Descartes is not setting out to prove the existence of a mental, cohesive, self...but to establish a criterion of truth. Cogito ergo sum makes it clear that there is, despite scepticism, ascertainable, definite, knowable and self-evident truth. That this truth is contentless is not the issue. The fact is, that truth can be established where there is no room for doubt. This is Descartes' gift: the grounding of solidity and the establishment of a basic epistemological principle. "is". There are thoughts. If there are thoughts, and those thoughts are me, then i am.¹ A=A is not effaceable. If "there are thoughts", then "there is a definite criterion of truth". The conditional statement at the beginning of the formula, "if 'i think'..." leads immediately, without application of logic or any other data, to "then there is such a thing as existence, for existence need not be any (cannot be any) more established than the fact we already know "i think". Perhaps a better translation would be:
thoughts? -> existence
¹Although the cogito can in this way be expressed as a syllogism, we must still understand that its conclusion is not really an extrapolation: it is already present in the first condition.
Post-Script. Since first posting this it has been brought to my attention that Descartes originally formulated the cogito in French, and it does in fact contain the personal pronoun. Perhaps then I am confounding my own intention with Descartes. My point in general however, still stands.