Not much gap between instinct and intention. You could say instincts are default intentions selected by evolution.

> Cats aren't Turing complete because they don't have intentionality. Everything it was doing was a result of instinct.

Well, first, cats most likely do have intentionality. But mostly, why do you think intentionality is a requirement for Turing Completeness ?

You might argue that animals don't have intentions (especially if you never observed one closely). However, it seems difficult indeed to believe that a cat has less intentionality than an abstract Turing machine -- or your desktop computer for that matter.