"I think therefore I am" is a much disputed "proof". As an argument, it presupposes many posits.
Being more cautious, one might make the claim, "I only know what I feel." Is this an ontologically closed statement?
'I think only what I feel' is the posit that Hume took. He took sense-impressions as basic and claimed we know of nothing else.
It is also at the root of the positivistic philosophy where 'I know only what I can measure'.
This had it successes. It was at the root of Ernst Machs philosophy of empiriocriticism which he had written about in his book on mechanics.
Poincare went from here to give an operational definition of simultaniety which Einstein used to come up with Special Relativity. It also guided Heisenberg in his own discoveries about QM.
Einstein himself was a famous adherent of the Machian philosophy. But this was as a young man. When he was in his forties, he repudiated it. At a physics colloquium given by Heisenberg at the University of Berlin in 1926, Einstein told the young Heisenberg who was then still a disciple of Ernst Mach:
Possibly I did use this reasoning ... but it is nonsense all the same ... on principle it is quite wrong to try founding a theory on observable quantities alone. In reality, the very opposite happens. It is the theory which decides what we can observe.
Thus, on Einsteins account, the positivistic philosophy in physics is not ontologically closed.
Likewise, Kant showed that in the human sciences that 'I know only what I can feel/know' was wrong, and the far more innocuous statement, 'I am therefore I can feel/know', a statement that most people would not give a second thought to, was truer.
notes: Shimon Malin, Nature Loves to Hide, Quantum Physics and Reality, A Western Perspective.
What do you mean by "know" and "feel"? I'm sure you've happily used the word " know" in places where you weren't talking about things you were feeling directly. Do you doubt that your friend's feet are sore after a marathon, just because you can't feel their pain?
It kind of sounds like the idea of sense-data to me that was popular around Russell's time. Like " I can't be sure that I am really looking at a football at the moment, but I can be sure that I am perceiving the sense data which looks like one" (like seeing these various colours in my visual field). Thus I should, to be correct, in future, say "I see the sense data of a car" instead of "I see a car". To me, it's just a useless change in notation, where the phrase " I see the sense data appearing to be X" will take on the role of " I see X".
I think, therefore I am is a valid expression within our rational subjectivity. I think suggests a process, and processes can only be performed by entities, therefore if a process exists, then a processor entity (which is me) exists: then, I exist.
But that is absolutely subjective, and even circular: if I exist and I process, ergo I think.
Nevertheless, it is a valid philosophical axiom: philosophy -and science- are based on rationally-subjective premises as this. Kant tried to make a line between the knowledge we come with, and the knowledge we build over the former one, but I personally think he contradicts himself on his books (and that means he was evolving, that's why he is a great lecture). For me, there is no a-priori knowledge, except our instincts.
For example, temperature is a feeling, and it is very difficult to define physically. The first law of thermodynamics is devoted only to have an objective agreement of what temperature is at a physical level. Temperature is not a property of atomic-level entities, but moreover a feeling on the skin. Nevertheless, it is a fundamental part of the current scientific set of thermodynamical knowledge. That is an example of how philosophy and science are highly dependent on our feelings, just like cogito ergo sum.
Your statement is similar, but personally I prefer it, due to it implies less things. Anyway, it keeps being rationally subjective.