I have absolutely nothing to add in the cats vs. dogs debate, however, if I might draw a couple of literary device parallels, albeit both more contemporary references (don't read if you don't wish to be spoiled for "Harry Potter and the Half Blood Prince" or "His Dark Materials", please don't read them!):
1. Parallel (possibly conscious, certainly subconscious) with
Horcruxes from
Harry Potter, the fixing of part of one's "soul" within a thing or person by use of magic. The destruction of a Horcrux results in the loss of that part of the soul fixed inside it. The One Ring might have been a predecessor/inspirational model for this, as part of Sauron is fixed inside the Ring, and to destroy it is to destroy him.
2. Parallel with the fantastic application of
quantum entanglement from
His Dark Materials. This theory, which I haven't really looked into has something to do with imprinting materials with certain identical "quantum states," which cause them to be intertwined and thus, one particle feels the effect of a force inflicted upon the other particle, even if they are separated by a great distance. The way it is used in "His Dark Materials" reeks of witchcraft, really, and who would have thought the fields of Modern Physics and Magic could be brought so close together! But in a way, this is the relationship of Sauron to his Ring. He feels it, if only faintly at a distance, but since it can only be destroyed in the Fires of Orodruin, we get the sense that it has to be in proximity to him. If there had been a dragon extant, perhaps the Ring could have been consumed in that way and some sort of "quantum entanglement" proven, but of course, we all know the dragon would just sit on it, hoarding it like all its other treasure!
I guess I'm not trying to prove anything with this post, especially not whether the Ring is canine or feline in nature, just that this "entanglement" idea is pervasive and thus in my mind, a feature of its applicability.
Cheers!
Lyta