The blog As A Linguist makes the point that systems of communication are not automatically languages. Cats communicate--Shakespeare communicates with me on any number of things--but their communications are simple. (So far as we know.)
The fact is, many people think that animals can use and understand language when they really just mean to say that animals can communicate. All animals and even plants have their own way of communicating, but is that the same thing as human language? It is a matter of controversy, actually. Some claim that systems of communication amongst prairie dogs, dolphins, and chimpanzees have the same characteristics and level of complexity as human language does. Others, however, may concede the relative sophistication of certain communication systems, but argue that they still do not perform all the functions of a full human language.
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What about productivity? Animals certainly seem to be limited to certain chunks of informative utterances that aren’t generally productive. A cat may have something completely different in her mind, like “I’d really like a belly rub now”, but there are only so many variations on the meow theme that they have at their disposal, so we humans are left to guess what it might mean. Of course, body language can come in handy, but again – a fluffy tail will always mean “Holy crap!” and will never be used in novel ways to express something completely different.
Moreover, animal communication nearly always refers to the present time, which means there seems to be little or no capability for displacement. Sure, bees have been known to be able to communicate the way to a good pollen source, which is technically speaking, the past tense. But it’s the immediate past tense and never more than that. They can’t dance to communicate something like, “Dude, do you remember that great pollen we found last month? Yeah, that was great. They don’t make flowers like that anymore.”
Mrs. Parker will never be able to explain why she so loves the sleeve of a fleece robe. And finally, while some animals may have very sophisticated systems that can inform, express intention, and even convey emotion, they are still limited in what they can “say.” Meta-cognition, or meta-linguistics refers to our ability to think about thinking, or talk about talking. We are aware of the behavior itself and can discuss it. We don’t just have feelings; we lie on couches and pay good money to talk about those feelings, to analyze and process and understand those feelings. Who knows, maybe animals can do this too, but aren’t foolish enough to pay anyone to listen to them, but at this time, we don’t know if they can because they can’t tell us, at least not in a way we can understand.