I guess it would be more accurate to state Kants actual premises here as making the distinction between appearance and thing-in-itself rather than the deduction, but the deduction technique itself was fascinating when I first learned it so that's what I associate most with Kant lol.
I guess I have not thought critically why we couldn't use a Transcendental argument to support Descartes. I just treated it as a vague category error (to be fair I don't actually know Descartes philosophy that well, even less than I know Kants lol). Could be a fun exercise when I have time.
The previous section within the Transcendental Dialectic that focuses on the nature of the soul goes into a refutation of Descartes' statement. Kant basically finds "I think therefore I am" to be a tautology that only works by equivocating the "I" in each clause. "I think" pretends that the "I" there is an object in the world which it then compares to the "I am" which is an object in the world. Kant argues that "I think" does not actually demonstrate an "I" that is an object but rather a redundant qualification of thinking.
I am being a bit imprecise, so here is SEP's summary:
>For in each case, Kant thinks that a feature of self-consciousness (the essentially subjectival, unitary and identical nature of the “I” of apperception) gets transmuted into a metaphysics of a self (as an object) that is ostensibly “known” through reason alone to be substantial, simple, identical, etc. This slide from the “I” of apperception to the constitution of an object (the soul) has received considerable attention in the secondary literature, and has fueled a great deal of attention to the Kantian theory of mind and mental activity.
>The claim that the ‘I’ of apperception yields no object of knowledge (for it is not itself an object, but only the “vehicle” for any representation of objectivity as such) is fundamental to Kant’s critique of rational psychology.
[1] https://plato.stanford.edu/entries/kant-metaphysics/#SouRatP...