Testing The Cogito Thesis As A Synthetic A Priori Judgement

“Je pense donc je suis”, translated as “I think therefore I am” is a critical thesis in philosophy.
I won’t bother with an introduction. Can the thesis be used as a demonstration of synthetic a priori judgments?
Well, we know that a priori judgments must come before experience, and that synthetic judgments are those in which the predicate is wholly separate from their subject.
What is meant by this, by my consideration, is not a strictly grammatical example of predicate, but rather that the action adds to, rather than clarifies, the subject. ‘This leaf is red’ is synthetic as being red is not a required characteristic of a leaf.
But of course, that is a posteriori, as the only way to confirm the truth of that statement is through seeing, i.e experiencing.
Back to the Cogito. Is it a priori? Well, it can be. If you change the statement from ‘I think therefore I am’ to ‘One who thinks, is’, the statement is indeed a priori.
Is this synthetic? No. If it were a matter of since I think, I exist, it would seem that the fact of one requires the other, and yet it is additive. But that illusion quickly fades away when you realize that existing is a prerequisite to the action of thinking, and therefore existing is simply a clarification of one of the facticities of any action. It is like saying that there are leaves therefore there is a plant. Yes, but this is only true because leaves, by definition, only exist through plants. In this same way, the Cogito is analytic as it is impossible to conceive of a thought as anything but the expression of existence. Moreover, the thinking can be replaced with any verb, and the statement would still be true. In reality, the statement is “I am, therefore I am”.
On that count, the statement fails. And yet, Kant thought that synthetic a priori judgements were required to know things practically, with certainty. It would seem that he is mistaken, as we can know, in noumenal terms, that we exist, through logical analysis, without the need for synthetic judgments.
