What Follows from the cogito argument

I can't doubt "I think: therefore I am"
     That is the cogito argument
I can doubt that I have a body
So, not true: I = my body

     this is a fallacious argument.

compare
     I cannot doubt, Pittsburgh is where I teach
     I can doubt, Pittsburgh is 100 years old
     So, not true: where I teach is 100 years old

the right inference. Not necessarily true, I= my body
i.e. like. I am not necessarily in this 100 year old city

Hobbes' objection

"It seems not to be a valid argument to say 'I am conscious, therefore I am a consciousness'. For I might as well say 'I am walking therefore I am a walk'.... All philosophers distinguish a subject from its faculties and acts, that is from its properties and essential characters....

This really is a grammatical point.
     Hobbes doesn't put it exactly that way
Action requires an actor
     That is, a verb requires noun

and Nothing more is proven
these are facts about grammar
     not truths about world

Descartes' reply:

"There is no comparison here between consciousness and a walk; the term a walk is usually understood only of the act of walking; whereas consciousness is taken sometimes for an act, sometimes for a faculty, sometimes for the subject possessing the faculty."

Compare,
     I am conscious
Which identifies what I am, with
     I am conscious of that tree
Which identifies what I the conscious subject see

Descartes says:

"It is certain that experience cannot exist apart from an experiencing being, nor in general can any actor accident exist apart from a substance to inhere in.... acts we call conscious, e.g. understanding, willing, imagining, feeling; these all fall under the common concept of consciousness... and we call the substance in which they inhere a conscious being or mind."

Descartes' vocabulary.
Substances are what endure
     Some are physical, others spiritual

Properties of substances can change
     The wax has a shape, texture, color
Analogously, the soul performs various actions
     Thinking, sensing, dreaming, feeling