What you say has been "known since Aristotle" appears to be wrong. There is really no evidence that this ability, or any cognitive ability, is "unique to humans". Yes, humans have more of this ability to "recognize abstractions and make generalizations" than pretty much any other species on this planet, but it is not unique to humans. In the contrary, there is lots of evidence that generalization and some amount of abstraction are fundamental to all forms of problem-solving (and "all life is problem-solving") and that the fundamental neural mechanisms that lead to these capacities are no different in quality between different species, just in quantity. This is being demonstrated in objective research again and again... there is no cognitive capacity we humans have that you can point to and say "this is totally different, no other animal has anything like this." Yes, your linguist abilities are orders of magnitude more sophisticated than those of most other animals, but even there it is only a matter of degree, not of a fundamental kind.
For a very good treatment of this subject by a highly respected primatologist, see Frans de Waal's recent books. But he isn't alone... until fairly recently it was taboo to say that animals are "intelligent" or "conscious" or "sentient", but this is thankfully beginning to change, and among the current generation of biologists, ethologists and animal cognitive psychologists many consider the notion that animals aren't sentient to be outmoded, or as Frans de Waal puts it, "anthropodenial".
But there is one thing that makes us truly different from all other animals and it's only indirectly related to cognition: for better or for worse we are the only animal that uses and controls fire. It's fire that really defines humans, not our big brains (and fire probably came first; cooking made our calorically expensive large brains possible). And it is fire that may be the end of us, as well.