From the Tao Te Ching to Chris Arnade's "Dignity" I really have found many reasons to become disillusioned with "intelligence" as a virtue.
He explores the idea that evolution and thought are the same phenomenon, and that what we call "mind" is ambient.
I asked my father the very thing I wrote above, and he answered that intelligence was the ability to reuse previously acquired knowledge in a given context. Which would seem fitting, if a bit stretching.
It's available on youtube here: https://www.youtube.com/watch?v=bQSUu2CRRBE
I only post this because it's a direct answer to the question, What is intelligence, and I find it to be a rather deep explanation compared to many others.
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.
Just to nitpick on that one, some wild animals seem to use fire to their advantage, such as birds of prey spreading wildfires. Some others were trained to be able to cook food, and light fire with tools. That said, to my knowledge, none are able to start fire with tools they crafted (I am not really either, to be fair). So this might be true for now, but I do not take it as a given.
I like your last paragraph, though, especially the ending. Nicely put :)
Interestingly, we're starting to find evidence for grammatical rules in other animal languages: https://www.newscientist.com/article/dn20615-first-evidence-...
This is a subjective interpretation. Human "intention" is informed by selective pressures as well, both those that have etched themselves into our genetics and those that have influenced mental development.
Trees are too slow to be technically intelligent. Although on a larger timescale what they are is indistinguishable from intelligence.
More specifically, there are two things that bother me with the way we usually look at intelligence: time scale, and individuality.
To assess intelligence, we often look at individuals, not at the group. And we tend to do it on our own time scales. But I wouldn't be surprised if the "individual" you have to assess is the ant colony, not the ants themselves. And who is to say that rocks aren't smart? Have you observed them over hundreds of millennia? (I'm just kidding about the last one, though the question is still theoretically valid).