Thanks for looking at the paper. The issue I was attempting to address is what is abstraction. I don't think we have a good answer. We all regard it as very important—especially in software and computational thinking. If you were going to define abstraction, what would you say? That's where I was going.So I guess that one of the important characteristics of concepts/abstractions is the ability to manipulate them mentally, to think with them, to use them to model the world. Apparently this is discussed in Rational Animals? by Susan Hurley and Matthew Nudds (Eds), including this paper by Ruth Garrett Millikan.
It wasn't where I was planning to go. (I'm not sure I knew where I was planning to go when I started.) But I kept getting pushed in the direction of attempting to understand what we mean by abstraction. I would up by saying that "abstraction" and "concept" are more or less the same. One contribution of the article (if there is one) is that "concept" depends on consciousness. Of course there is a very large philosophical literature on conceptualization. I can't claim to know much of it. (For example, the Stanford Encyclopedia of Philosophy has this article on concepts, which I haven't mastered.) But it does seem to me to be useful to say that a concept is a distinction that one is aware of making or being able to make--and hence depends on some level of self-awareness. So a concept is our way of making discrete chunks out of our experience.
It's not clear how widespread the ability to form concepts is. For example, dogs can recognize their masters. So they have a concept (an abstraction) of their master in some sense. (So even proper nouns are abstractions—of the thing named.) But do we know whether dogs can mentally refer to their masters? Can a dog think to itself something like, "I wish my master were home so she could take me out for a walk." Or is that too abstract? So perhaps some animals have the ability to form concepts but not to manipulate them mentally? Obviously I don't have all the answers.
A further thought. Consciousness is an emergent phenomenon. Emergent phenomena are epiphenomenal. But we experience consciousness as real. (The qualia problem.) Why is that?