It seems you are no longer ruling out a science of other minds
No, by "mind" I just mean any sort of information processing machine. I would have said "brain", but you used a more general "entity", so I went with "mind". The question of what is and isn't a mind is not very interesting to me.
I've already told you what it would mean
Where exactly?
Is the first half of the conversation meaningful and the second half meaningless?
First of all, the meaningfulness of words depends on the observer. "Robot pain" is perfectly meaningful to people with precise definitions of "pain". So, in the worst case, the "thing" remains meaningless to the people discussing it, and it remains meaningful to the scientist (because you can't make a detector if you don't already know what exactly you're trying to detect). We could then simply say that that the people and the scientist are using the same word for different things.
It's also possible that the "thing" was meaningful to everyone to begin with. I don't know what "dubious detectability" is. My bar for meaningfulness isn't as high as you may think, though. "Robot pain" has to fail very hard so as not to pass it.
The idea that with models of physics, it might sometimes be hard to tell which features are detectable and which are just mathematical machinery, is in general a good one. Problem is that it requires good understanding of the model, which neither of us has. And I don't expect this sort of poking to cause problems that I couldn't patch, even in the worst case.
(This post grew out of an old conversation with Wei Dai.)
Imagine a person sitting in a room, communicating with the outside world through a terminal. Further imagine that the person knows some secret fact (e.g. that the Moon landings were a hoax), but is absolutely committed to never revealing their knowledge of it in any way.
Can you, by observing the input-output behavior of the system, distinguish it from a person who doesn't know the secret, or knows some other secret instead?
Clearly the only reasonable answer is "no, not in general".
Now imagine a person in the same situation, claiming to possess some mental skill that's hard for you to verify (e.g. visualizing four-dimensional objects in their mind's eye). Can you, by observing the input-output behavior, distinguish it from someone who is lying about having the skill, but has a good grasp of four-dimensional math otherwise?
Again, clearly, the only reasonable answer is "not in general".
Now imagine a sealed box that behaves exactly like a human, dutifully saying things like "I'm conscious", "I experience red" and so on. Moreover, you know from trustworthy sources that the box was built by scanning a human brain, and then optimizing the resulting program to use less CPU and memory (preserving the same input-output behavior). Would you be willing to trust that the box is in fact conscious, and has the same internal experiences as the human brain it was created from?
A philosopher believing in computationalism would emphatically say yes. But considering the examples above, I would say I'm not sure! Not at all!