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 materialist or physicalist terms.

The presumptive barrier that prevents neurophysiological research answering this question, is that objective observations which can be made by a researcher — such as, electrical current moves through these 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 studied with 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 is a rational one—must be expressible in formal language.

(This claim may not be obvious. It's like claiming that some form of the Church-Turing thesis applies not only to mathematics and logic, but to rational discourse more widely, including empirical research.  I'm suggesting that any argument which is genuinely rational, can be expressed in a formal language. If some part of the argument can't be formalised then I think we will discover, on inspection, that it's because the argument isn't rational. Either it will be a non-sequitor, or it will be an appeal to emotion, or an ad hominem attack, or somesuch).

• 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 a sentence about oranges. I suggest that any formal language that does not satisfy this constraint is not a language we can use for rational discourse. It may still be fine for poetry; but not for being rational).

• I assert that any such attempted definition will, on inspection, turn out to be invalid.  That is, when we look at any such purported definition, we'll be able to see that it doesn't quite work and hence that the explanation which it supports will also fail. I do of course look forward to being proven wrong, but there aren't any attempts on the table so far.

I think any attempt to define 1st & 2nd  person words – I, you, me, we  – in 3rd person terms fails. Any definition using only 3rd person terms can only succeed in defining 3rd person 'things'.

The thought is somewhat similar to Chalmer's “Structure and functions” argument: anything you can define with structure and function will itself be structure and function. I think the grammatical argument is stronger, surprisingly (one doesn't expect arguing about grammar to prove anything!), because 1st and 2nd person speech and relationships is, and always has been, a core part of the reality of human experience.

Intuitively, throughout the modern era, people have always felt that a reductionist materialist account of humanity surely misses something. The grammar of every human language (at least, every one that I know of) embodies that fact.