The notion that we can "observe our own states" does not stand up to genuinely deep insight about our phenomenology. Experienced practitioners in insight meditation have been able to shatter this illusion, and realize that we can only ever observe memories of some apparent "self" - that no real "self" observation of our observability 'in a recursive way' is going on (thus, pithily: "no self"). But of course, they're still conscious!
> we can only ever observe memories of some apparent "self"
To make a "self" we observe too many ideas, these experienced practitioners in insight meditation are simply removing those mental models and observing the simplest states. They are saving a memory of that, so when they stop meditating and go back to observing their "self" they remember they were conscious in a basic observation mode. That's all.
