Tom Siegfried has his doubts:
[T]he consciousness problem is inherently similar to another famous problem that actually has been proved unsolvable: finding a self-consistent set of axioms for deducing all of mathematics. As the Austrian logician Kurt Gödel proved eight decades ago, no such axiomatic system is possible; any system as complicated as arithmetic contains true statements that cannot be proved within the system.
Gödel’s proof emerged from deep insights into the self-referential nature of mathematical statements. He showed how a system referring to itself creates paradoxes that cannot be logically resolved — and so certain questions cannot in principle be answered. Consciousness, in a way, is in the same logical boat. At its core, consciousness is self-referential awareness, the self’s sense of its own existence. It is consciousness itself that is trying to explain consciousness.