Shorter explication of Peter Carruthers: On Being Simple Minded

My explication of Carruthers' critique of a Davidson argument that animals have no thoughts is rather long. That's ok, but I feel like it needn't be so long. It gets a bit tangled at the end, too. So here's a terse explication.

Carruthers argues that requiring thoughts to be expressible (by the thinker) as that-clauses requires that someone else be able to express that very thought as a that-clause. To express a thought one must be able to think that thought. However, there are thoughts of very smart people (like Einstein) which no one else could think (or, at least, there could be such thoughts). Such thoughts would not be co-thinkable, thus they would not be thoughts. But they are thoughts, so co-thinkabilty (and thus expressibility as a that-clause) is not a necessary condition of thoughthood. Thus, animals cannot be said to lack thoughts merely on this ground.

My problem with this is that I do not see where actual co-thinking is required by the Davidson argument. Surely, it is enough that someone can express the content, or, more to the point, that someone with the requisite limits lifted could express (and think) it. The point is to be hooked up to language in general, not to any particular language user.