Interesting and insightful that Descartes leaves material as the last to be understood in his meditations.
Indeed, there is nothing a priori about experience. We have to go through it (experience it) to reach a conclusion about what thinking is or what does thinking. For Descartes he decided by the second meditation that it was the mind. I also had thought it was the mind. Jeffrey Kaplan thought we have inherited this belief from Descartes and have continued to run with it as common sense. But common sense it is not.
Some time later I have come to believe this is wrong, that I am not a mind, but a body with mind processes (thinking). The thinking thing is not the mind but the body.