"without any reason of the kind we are currently thinking about."
What sort of reasons are we currently talking about though? I want to hear reasons based on the properties of the objects being classified. You seem to accept whatever reasons you can come up with.
a coffee table is not merely something that has a certain shape, but something that was made for a certain intended use, even if you personally use it for sitting.
Here'e an example of weird reasons. How can shape not determine the difference? If IKEA made two identical objects and labeled one "chair" and another "table", would they then actually be different objects? IKEA can have whatever intentions they want, but http://www.ikea.com/us/en/catalog/products/20299829/ is a stool. Are you seriously telling me that it isn't? Now, one could say that a stool can be both a chair and a table, and I think that's what IKEA does, but then you've already claimed this to be impossible.
In the case of the robot, we do not know what the robot's feeling is like, or even if it has any. So we cannot compare it to our feeling of pain.
That's assuming that "feeling" is a meaningful category. If you didn't start from that assumption, and instead identified your experiences with brain states, you could go one step further and ask "are the states of the robot's processor/memory similar to my brain states", but then you hit the obvious classification problem. There are some similarities and there are some differences, and you have to choose which of those are the most important to you, and there is no one right way to do it. Lack of knowledge isn't the main problem here.
What sort of reasons are we currently talking about though? I want to hear reasons based on the properties of the objects being classified. You seem to accept whatever reasons you can come up with.
"Properties of the objects being classified" are much more extensive than you realize. For example, it is property of pain that it is subjective and only perceived by the one suffering it. Likewise, it is a property of a chair that someone made it for a certain purpose.
...If IKEA made two identical objects and labeled one "chair" and another
(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!