ron2:The girl had one of our friend's trinkets and was banging it on the glass of the french door to the patio. Our friend's son, T, said "don't do that." So, she banged on the wood frame of the glass. "Don't do that." So, she moved to the main wood of the door. "Don't do that." So, she moved to the door jamb. That is, she didn't automatically, by way of being human, generalize the don't do it to not banging the object on anything. She only stopped on the particular target and instead picked another target.
I wasn't there, but from your description I'm not sure that behavior you've described was the result of the little girl being incapable of generalizing, In fact, I agree with another poster. I think the girl may have been generalizing quite splendidly (if only in her mind and not in her behavior). She may have very well understood what the boy, T, meant for her not to do, but kept banging the toy on other surfaces because she was having fun and wasn't about to let him tell her what to do. "See? I've stopped banging on the glass! See? I've stopped banging on the frame!" If so this is an example of a remarkable, yet annoying, act of intelligence: she deliberately selected the one aspect of the behavior that she wanted to continue doing, and chose to do it on whatever surface was next after the boy told her not to do it there and it became a game to her.
As for dogs, I'm not sure what you mean by generalization. Do you have a specific definition in mind?
I will say you pointed out an important fact for dog trainers and owners, in that when a dog learns something at home, he usually has to be re-taught the same behavior in other locations until he supposedly "generalizes" the behavior. But I'm not sure that's the conceptual sort of generalizing the human brain seems inherently capable of. It seems to me that for dogs, it's more a matter of cross contextualization, which I think is just a form of pattern recognition, which dogs are geniuses at. Learning to sit on command at home, then on the street, then in the park, these things are just adding new contexts, or new pieces to the pattern. You put enough pieces together for the dog (it usually only takes a dog four repetitions to learn a new behavior, and only four contexts to put all the pieces together) and it can certainly seem like they're generalizing, which I think entails conceptual thinking (which dogs aren't capable of, or I should say that they show no signs of being able to think conceptually, and probably have no ability to do so). But I think it's important to draw the distinction between pattern recognition and the more conceptualized kind of thought that would b properly termed generalization. (And as I pointed out in another thread, even chess masters rely more on pattern recognition than logic, etc.)
Given that context, you're absolutely right that dogs are better at pattern recognition than we are. In Animals in Translation, Temple Grandin says that the human mind is designed to put patterns into conceptual chunks, but the animal mind isn't; it's designed to look at the parts of the pattern and make connections that are most relevant to past emotional experiences. Hey, even the dog (mentioned in another post) who figured out that "table" meant a specific motor pattern, and produced that motor pattern no matter what surface she happened to do it on, is more a matter of pattern recognition (along with the sheer fun of doing the behavior), than it was of generalizing.
And I still say that little girl was a genius; she knew immediately what the boy meant and did things the way she wanted to anyway.
LCK
"Clicker training has not taught me a whole bunch, other than that people can get wrapped up in fads and catch phrases." Bob Bailey
"If a lion could talk we would not be able to understand him." Wittegenstein. "If a lion could talk we would understand him perfectly, but we would learn very little about ordinary lions from him."Daniel C. Dennett
"Dogs don't care who's alpha and who's not. Only emotionally dysfunctional owners and trainers do." Jack Field