if the body were not, the soul would not cease to be all that it now is
This is nothing other than the standard belief in the “soul” and its immortality as sweeped along through the reactionary idealism of religious ideology. This is certainly the most obvious concession to theological thought made in the section of the Discourse on Method surrounding the COGITO. Incidentally that whole section is included in Part Four of the text, titled itself: PROOFS OF THE EXISTENCE OF GOD AND OF THE HUMAN SOUL, what is not a good sign either! The guy had good reasons to have the jitters after all the materialist position he had already introduced.