Sometimes at bedtime my cat will go to the door and scream nonstop. I don't know why he does it. Maybe it is for food or attention. But the only way I have found to get him to stop is to pick him up, put him on his special pillow, squish him, and have my partner join me in telling him "we are going to bed, it's bedtime".

I'd say about 80% of the time he listens. So he is capable of understanding what we want him to do, and capable of supressing his own personal desires in order to maintain harmony in our group. Funny enough, he won't go to bed unless both me and my partner tell him it is bedtime, so maybe he is only obeying because there is some majority consensus?

Because of this, I find it easy to believe that a cat or dog could be taught something as abstract as "self" if they can understand commands and intent and group dynamics. It's just difficult to tell what is "understood" and what is just conditioned behavior. Hell, I can't even answer that question for myself as a human.