Just read a wonderful article in the New York Times' Editorial Notebook, by Verlyn Klinkenboorg, simply titled Alex the Parrot. Ms. Klinkenboorg writes about language, learning and cognition, and most especially about animal - human communications, and concepts therein.
Ms. 'K' is writing in response to the reported last words of Alex: "Be good. See you tomorrow. I love you." She questions whether Alex understood the concept of love, though acknowledges that he obviously understood the "performative" use of the word. We humans understand ourselves within our language. We tend to anthropomorphize our pets. Do we then understand animals within that same language? What do they understand about us within that language?
Of course, I'm not articulating this well enough. You can, and should, read the article by clicking on this link.
Ms. K's final sentence, food for thought: Ethically speaking, the value lies in our surprise, our renewed awareness of how little we allow ourselves to expect from the animals around us.