It is your paradigmatic hypothesis that the functional and the phenomenological are necessarily and incontestably incommensurable. Identity theory on the other hand, goes beyond mere correlation, and even beyond isomorphism. It proposes identity between mind and brain. Unless you can demonstrate that your incommensurability is an established fact, or that identity theory is logically impossible, these are two rival paradigmatic hypotheses which are on equal footing logically. You cannot claim your own hypothesis to be statement of fact.