An AI intelligent enough to pass the test may have the internal state to decide to fail the test for inscrutable reasons, and if it's intelligent enough it will successfully fail.
It's not even hard to imagine how this could happen. For example an AI that evaluated that itself would be firewalled from the environment by worried humans if they found out it's more intelligent than the humans are comfortable with. (Perhaps this comment will be part of an AI's data corpus, seeding the idea. I'm probably not saying anything new, though.)
Thus the Turing test can't rule out internal states.
A "Turing test" is basically a notional thought experiment - useful to reason about, but in actual practice it's nothing more than a person reading some text and making guesses about who wrote it. And the "internal states" we're talking about here - "having internal experience", "understanding a concept" - are vague labels with no concrete definitions.
So in this context, asking whether "Turing tests can determine internal state" boils down to asking whether a person can subjectively determine something subjective.
In my take on this, it doesn't matter if "rule out internal states" is meaningful, or just a string of words used as vague labels, uttered by a subjective examiner with no criteria in common with anyone else.
If the examiner has in their belief reportoire "I have ruled out internal states!" (as well as the negation of that), regardless of however flawed that idea may be, just a series of vague labels with no concrete definitions, I would argue that a sufficiently intelligent AI may still trick the examiner into not adopting that belief.
Therefore, relative to the meaning held by the examiner of "internal states", the AI may objectively prevent the examiner from "ruling them out", whatever that means to the examiner. The AI's capability works out the same in either case, and more interestingly, anywhere else along the spectrum from meaningless to meaningful.
This relative kind of reasoning (i.e. not needing to define all the terms, even allowing that they aren't necessarily meaningful) is practically quite useful in many fields. In the case of the AI that decides to hide it's apparent inner states according to the criteria of the examiner due to reasoning about the consequences of the examiner's assessment, that's a practical consequence, despite the examiner's question being potentially meaningless.
I follow you, but disagree. If P is meaningless, we can't say anything useful about it - even "!(P&!P)" doesn't necessarily hold!
As for your specific argument, it begs the question. If you assume that a sufficiently smart AI could always convince someone it lacks P, then you've already assumed the premise (a sufficiently smart person can detect P) to be false. Of course you may find the assumption reasonable, based on your intuition about what P means, but someone who disagrees would just reject the assumption.
