I recently read Donald Davidson's "Rational Animals" (after re-reading Norman Malcolm's "Thoughtless Brutes"). Davidson's argument that possessing a single belief requires the possession of many beliefs, and that to be a thinking (rational) being requires language--being a "communicator" in the "full linguistic sense"--is rather impressive. I am not sure, however, what the "full linguistic sense" is, and Davidson's argument doesn't entail that (other) animals don't "think"--but that any thinking animals must be linguistic. (Do Wittgenstein's builder's think?)
Connecting thought to language is tempting. [Clarification: read that as taking thought to depend necessarily upon language.] But it strikes me that this really is a temptation. One reason to think so is that we have high-functioning autistic people like Temple Grandin who, to hear them tell it, insist that they think in non-propositional ways for the most part. And if animals that lack language still think in some sense, it is then not surprising that it would be more like what Grandin describes--and this would also enable us to make sense of why it is that her autism enables her to understand animals (or, see things as they do) better than most people.
Here's the main thing that strikes me about any Davidson-style argument: this whole way of approaching the issue privileges the proposition, and may even assume that all thinking--indeed all intentional states (all forms of thought)--are propositional. As I've seen others suggest, the temptation to think this may have to do with the tendency to begin analyses of intentional states by looking at belief, which seems inherently propositional (or incredibly easy to translate into Propositionalist language) as anything.
But as Alex Grzankowski argues in his forthcoming paper "Not All Attitudes are Propositional," Propositionalism runs into a great amount of trouble when confronted with the task of analyzing other intentional states (like fearing, liking, etc.) in terms of propositions. I'm not well-versed in this area of philosophy, but Grzankowski seems right, or on the right track. We like objects (or individuals), not propositions. (Well, we can like propositions, too, I guess, but the point is that in liking my wife, I like her, not some proposition or other.)
The next question I have (and here I have more reading to do) is how we might make sense of "animal belief" without appealing to propositions. I suspect this is related to why Malcolm talks about his dog "thinking" that the cat is up the tree, rather than of his dog believing it. In these cases it seems ok to say that our beliefs are about objects, but then we will also say that we believe certain propositions about those objects to be true. It might be that we could say that animals don't have beliefs (if we agree with Davidson that belief is inherently bound up with language), but that animals nevertheless make (and have?) observations. Malcolm's dog observes the cat go up the tree. And that observation, combined with a desire to eat the cat (the intentional state here can be non-propositional, the desire is for the cat, not for some relatable proposition), explain why the dog barks up the tree. Of course, we might ask: but is that thinking? Malcolm says, well, sure, my dog thinks the cat is up the tree. (That's why he's still barking, even though the cat isn't in that tree any more.) How do we get from observes the cat up the tree (or going up the tree) to thinks the cat is up the tree without attributing propositional content to the dog? Could we say that the dog continues to affirm a previously observed state of affairs while, not being a linguistic creature, cannot be understood as affirming the corresponding proposition? At any rate (since I'm in over my head here), could it not be that the dog thinks (believes) something about the world without believing any propositions (propositions are about the world, not part of it here)? If intentional states aren't all propositional, then must belief always take a propositional form? (Could that explain why we have thoughts that seem impossible to put correctly into words?)