What is an abstraction?

This question occurred to me as I was reading a little more about the supposed platonism revival mentioned in the previous post, and alluded to by Steve Esser in a couple of recent posts. Platonism makes what I think to be the "classic" (so to speak) mistake of reifying at least certain kinds of abstractions (mathematical and geometric, principally, but also possibly property-like) -- that is, it makes "things" out of abstractions, and then, having done that, it has the problem of determining the ontological status of the things, including where they exist, etc. Without going any deeper into platonism itself at this point, I'll just say that I don't think abstractions as such, of any kind, are things at all, and so have no ontological status, special realm, etc., to worry about. Apart, that is, from their existence as concepts, or psychological/cultural constructs, in which sense they are part of each individual's cultural imprint and exist as physical states in each individual's brain. Thinking about that, however, made me wonder about how such concepts are formed in the first place, and what that might say about the nature of abstraction itself?

For example, consider what happens when a child is learning to speak (or, for that matter, when an anthropologist is learning a language in another culture) -- someone points to something and utters a word, "dog" say. The pointing is an action that directs or focuses attention, but there's no indication from that alone what the utterance is supposed to "mean" -- within the field of attention, it might refer to a particular object (a proper name), a type of object, a property of an object, or a behavior or a process. In the early stages of language-learning, in fact, these distinctions themselves would be meaningless, and the very notion of an "object" might be unclear (though this might also be hard-wired in some fashion, giving rise to "natural objects", e.g., mama and dada). But after repeated pointing-acts accompanied by the same utterance, it's noticed that there is something in common in the phenomenal field to which attention is directed, and a generalization is made and tested -- the child herself does the pointing action and utters the sound whenever a dog-like object presents itself, and then looks for confirmation. But this "noticing" can't be a simple observation, it has to involve some kind of structuring -- that is, the repeated uttering of a sound in different circumstances generates, in a sense, a commonality to those circumstances. This is because the elicited structure will almost certainly be wrong initially ("wrong" as defined by the ones doing the pointing) -- "dog" will need to be distinguished from "cat", for example, or "squirrel" (or maybe "pillow"), "red" from "orange" or "pink" (or "ball"). So it isn't that the sound simply links to, or labels, a pre-existing structure, it's more like the pointing-and-uttering behavior as a whole has forced experience to take on a structure. And then, in an iterative and essentially social process of generalization and distinction, the structures will be aligned -- the "meaning" of the utterance will be brought into semantic harmony with everyone else (a process that continues all through life, though not with such major adjustments).

After some initial concepts have been formed in this way, more sophisticated abstractions of abstractions can be formed, so that "animal" can be used for both dog and squirrel (but not pillow), or "color" for both red and orange (but not ball), etc. And at some point after that, it starts to become possible to use words themselves to shape experience -- generalizations and distinctions can be made into verbal rules, and both communication and thought can come into being. But initially, and essentially, an abstraction is just a named common feature, element, or aspect of experience -- experience that may include other, already-formed abstractions. This sort of ability to create a semantic structure out of experience is also a linguistic capability just as syntax is, and its potential must be as built-in or hard-wired.