Isn't it ironic that in a whole being the subjective eventually has to recognize the objective and the objective eventually has to look at the subjective?
That the observer is obviously both, or tat tvam asi? That the subject and object are the same
Don't think this is obviously true. As Gangesa points out in opposition to the Advaitin and Prabhakara positions, when we perceive the world, we don't do it in propositional attitudes of "I am aware of this chair", but in the bare propositional form "this chair exists", and that self-reflexive cognition would be 1.) superfluous and 2.) would be of the form x.f(x&f(x...)) which would not only be infinitely recursive, but also require the cognition to posit as its content itself without the relation of the sense-organ to it, meaning that it would require the cognition to step out of itself to cognize itself as a mental content, which is epistemically impossible.
The upshot, I feel, is a pretty strong argument against the very possibility of the Advaitin position of pure being positing conventional objects with itself as ground and then comprehending itself as conventional objects in the same cognitive act.