Turing machines only model computation. Real life is interaction. Check the work of Peter Wegner. When interaction machines enter into the picture, AI can be embodied, situated and participate in adaptation processes. The emergent behaviour may bring AGI in a pragmatic perspective. But interaction is far more expressive than computation rendering theoretical analysis challenging.
Still an interesting take and will need to dive in more, but already if we assume the brain is doing information processing then the immediate question is how can the brain avoid this problem, as others are pointing out. Is biological computation/intelligence special?