Now when I say "you are conscious," I am talking about the similarity between the times when you are awake and the times when you are dreaming, in contrast with the times when you are asleep and not dreaming.
You don't have a separate word which means "Jiro's consciousness" and nothing else. You have a single word which is used both for mine and yours, which implies that they are the similar. What you've just described fails to imply that similarity, so it doesn't match the way you are using the word.
I deliberately failed to imply the similarity, since I said that we would define consciousness in that way even if I were not conscious.
However, you are quite right that I would not actually know about consciousness if I were not. And indeed, I notice the similarity between being awake and dreaming sleep, as opposed to dreamless sleep, in the same way that you do. So I quite rightly talk about consciousness being the same in you and in me.
(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!