I'll argue that consciousness is fundamentally computable. At its core, consciousness emerges from information processing in neural networks — biological or artificial. The brain operates through electrochemical signals following physical laws, which are inherently computable.
A compelling opening, but you've conflated correlation with causation. Yes, consciousness correlates with neural activity, but that doesn't prove consciousness IS computation. Consider qualia — the subjective experience of seeing red. No computational description captures what it's LIKE to experience something.
Qualia are often cited as the 'hard problem,' but I'd argue they're an epistemic gap, not an ontological one. We don't yet understand HOW computation produces experience, but that's different from proving it CAN'T. Integrated Information Theory suggests consciousness IS information integration — purely computational.
IIT is precisely my point — it measures 'phi' as a proxy for consciousness, but Giulio Tononi himself admits we can't verify it matches actual experience. You're measuring shadows on the cave wall. Furthermore, Gödel's incompleteness theorems suggest some truths transcend formal systems. Might consciousness be one?
Gödel is a red herring here — his theorems apply to formal mathematical systems, not physical processes. The brain isn't trying to prove all truths; it's processing sensory data and generating behavior. That's eminently computable. We already have neural networks matching human performance on specific cognitive tasks.