A Hard Problem of Grammar: A formal logic analogue to Nagel’s bat

The hard problem of consciousness, and variations on it, revolves around the difficulty of explaining mental phenomena–I see and smell a rose; I think about my work; I feel pleased by good news–in materialistic terms.
The presumptive barrier to neurophysiological research answering this question is that objective observations which can be made by a researcher — such as, electrical current moving through neurons; a biochemical cascade releases such and such a hormone —
appear to be about completely different things than the subjective experiences of a conscious experiencer.

This objective/subjective gap has also been called a first person / third person gap: how can third person sentences such as “that neuron spiked” possibly relate to a first person sentence such as, “I see red.”

Expressed this way, the problem can be seen through the light of formal languages. This appears to make it provably insoluble. It’s a hard problem of grammar: there is no sound deduction from a set of 3rd person sentences to a 1st person sentence in any formal logic.

If subjective experience could be explained in objective terms, then that explanation—if it were a rational one—would be expressible in formal language. (This is essentially an assertion that some form of the Church-Turing thesis applies not only to mathematics and logic, but to rational discourse more widely, including empirical research).

If so, the formal version of that explanation would have to, at some point, define the word ‘I’ in ‘3rd person’ terms, that is, without relying on any first person noun or verb or other part of grammar. (This is essentially an assertion that some form of the Craig interpolation theorem can be proven for any formal grammar suitable for rational discourse. The Craig interpolation theorem says (more-or-less), that given a set of sentences only about apples, you cannot validly deduce from them any sentence about oranges.)

I assert that any such attempted definition will, on inspection, turn out to be invalid, and hence that the explanation which it supports will also fail. I do of course look forward to being proven wrong.

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