Consciousness is often discussed as if it were a binary quality--you either have it or you don't. Humans, of course, are assumed to have "it". Viruses and bacteria are often not discussed in terms of consciousness; we usually assume that they don't have "it". Some think they don't even have life. The occasional philosopher or five-year-old will wonder about dogs and cats and gorillas--do they have a soul? Are they conscious? These types of questions are usually applied to mammals, because they are cute and fuzzy and we like them because they are similar to us. We rarely ask about ants or tapeworms or cockroaches.
We also rarely acknowledge the experience that we have all had at some point or another--the desperate attempt to understand a big idea, and idea that someone has just given you or that you have just read or glimpsed somewhere in your head. We are familiar, though, with the burst of awareness that accompanied calculus or Kafka, or subtraction, or reading the first new word. That feeling can be described as a raising of consciousness: we are taking our existing consciousness and making it better, higher, more conscious. Another word for what we are doing is "learning".
We are not the only animals capable of learning--indeed, there are none I can think of that are not capable. Is it not possible, then, that "lower" animals can experience this same raising of consciousness? Indeed, in saying that we are just playing semantic games with an accepted truth ("all animals can learn"). Consciousness, then, is more properly thought of as a continuum.
This makes sense--our kingdom can also be read as a continuum (albeit a branched one) of traits. So consciousness is a trait animals possess in varying degrees, not in an absolute, binary sense (we'll leave the other kingdoms out of this for now, mostly because I'm most familiar with the behavior of animals and not, say, fungi). It seems logical to me, at this point, to define consciousness as a property of the nervous system, and say that when we speak of degree of consciousness we are speaking of the degree of complexity of the nervous system.
If there's one thing that a technical discussion of the nervous system has taught me, it is to not underestimate the complexity that can arise from simple things. The statement "the brain is behavior" seems to imply that by understanding the brain, behavior is understandable. But there are only twenty-six letters in the English alphabet, and nobody will claim that a six-year-old who has mastered them has mastered English and all of its possibilities. How much more is possible with even 26,000 neurons, much less 26 to the 12th?
At least two distinct issues worth further discussion. Your last, the combinatorial one, entirely appropriate: yes, of course, saying what creates the possibilities is far from having enumerated all possible states. "Understanding behavior" has an even greater problem though, which also derives from the "brain = behavior" presumption. It is the brain doing the understanding, which means that it is changing, which means that what one is attempting to understand is changing, which means ...
As for a continuum of consciousness, I certainly think that will turn out to be a necessary improvement on the having it or not having it dichotomy. But for a somewhat different reason. Yes, all animals learn. I'm not sure though that all animals experience the "raising of consciousness" you describe. For that one needs not only to learn but also ... ? PG