One of the key points of I Am a Strange Loop is how the “I” develops into consciousness. The constant reinforcement (and self-enforcing) of the “I” gives rise to perception, symbols, meaning, and reality. On the other hand, the key point of mindfulness (at least to me) is recognizing the illusory self.
If the self is an illusion then it must not be real. The “I” is merely an abstraction over consciousness that disappears upon closer inspection (in meditation, this is the “look for the one who is looking” idiom). However, abstractions themselves are real.
Does the “I” give rise to consciousness to begin with or is it the other way around? Does the failure to inspect the strange loop in consciousness make it an illusion?
Maybe both are true. Everything arises in consciousness and the “I” is inseparable from reality.