Famously Descartes said 'Cogito ergo sum'. I'm a bit puzzled by this. I do not need to think in order to assert/understand/intuit that I exist: when I wake up in the morning I immediately intuit that I exist. I see this understanding as a form of inner experience.
I can imagine myself as a bat, and as a bat, I do not have access to logic, formal or otherwise, but I would say (though as a bat I couldn't articulate this), that I would still feel I exist.
Descarte, as a human being, and as a philosopher, is in my opinion, privileging a quality peculiar to humans: thinking.
My feeling is, that Descarte is being seduced by the axiomatic method in mathematics to attempt a similar method in philosophy, that he's trying to conjure something out of nothing.
My preferred statement would be 'I am', or even more stripped down, 'am': I don't think a bat would conceive of itself as an 'I'.