I've been toying around with the idea of discrete and objective categorizations of intelligence levels, and here's what I've come up with. The criteria for each level is essentially defined by a capability to comprehend various concepts. Let's jump in and you'll see what I mean.
Level 0: Unintelligent -- Just about everything falls into this category. Rocks, trees, fungi, stars, virii, and most animals. Unintelligent objects may be living or non-living, but are essentially bundles of blind natural processes that progress without any intentionality or agency.
Level 1: Self-aware -- A few animals seem to be self-aware, and many humans fit into this category. Self-aware objects are implicitly "alive" almost by definition: if a non-living object (e.g., a computer) were to exhibit self-awareness it would be considered to be "alive" by a significant proportion of undisputedly living beings. Self-aware beings understand the general nature of their own existence, consider themselves (and other intelligent beings) as distinct individuals set apart from the unintelligent objects that make up most of the universe, and are capable of intentional behavior and agency.
Level 2: Ignorance-aware -- Ignorance-aware beings are capable of comprehending the enormity of the gulf between their own intelligence and the level 3 intelligence of universe-aware beings. Although some humans are exclusively level 1 beings, most have rare "flashes of brilliance" and exhibit transient level 2 intelligence. Ignorance-aware beings understand how much about the universe remains unknown and unknowable to them regardless of the time and study they devote to the pursuit of knowledge.
Level 3: Universe-aware -- Universe-aware beings are capable of comprehending every aspect of the universe, given enough time and study. Implicitly then, a universe-aware intelligence is the most complex object in the universe, able to know and understand everything that exists (including itself). For the sake of the theory, let's set aside the question of whether it is possible for the universe to contain more than one level 3 intelligence (i.e., if there were two, could they understand each other?).
I've interjected my own opinion of how humans fit into these categories: generally level 1, with transience into level 2. Others would probably argue that humans are level 3 intelligences and capable of understanding everything, given enough time. A weaker form of this belief is that human civilization as a whole is a level 3 intelligence: even if no single human can understand everything, groups of humans working together can eventually comprehend the universe and ourselves. (Let's say, then, this weaker belief puts humans in a new category we shall call level 2.5.)
It's possible that the weaker belief is true and that humans are level 2.5; this is a classic halting problem that can never be satisfied. Who's to say that when we think we "know it all" that something new won't pop up in 1000 years? Or worse, what if we think we "know it all" but aren't even smart enough to recognize that there's still something about which we remain in ignorance? That would bump us all the way back down to level 1 without us even realizing it!
I see no reason to believe that the level of intelligence of the human brain is high enough to comprehend every aspect of the universe. Call the level of intelligence of a dog A, the level of intelligence of a human B, and the level 2.5 intelligence X. Few people would argue that A > X. Therefore, those who believe that B > X need to provide some explanation for why X just happens to fall between A and B:
B > X > A
Since we won't ever be able to prove or demonstrate that B > X, it would at least be nice to hear an argument for why anyone would believe such a thing. I personally believe that B < X, but I'm not sure why yet.