From the op: "there is still no complete and unambiguous explanation for what concepts are". Well, there's your problem.<p>If you pick any related concept which you are clearer about, the problem vanishes. e.g. let's use sorts, or kinds, instead. As in "a cat is a kind of a mammal." Take a look at your visual field. :-) Is there anything there which doesn't fit into some category as in being some kind of thing or another?<p>E.g. right now I see my computer screen, letters, web pages, etc etc. Anything I see shows up as being one kind of thing or another. I can give you examples of more things of that same kind, and I can state the relationship of that kind to other kinds.<p>And most importantly, if I want to describe what is in my visual field to you, or if we want to compare visual fields, we can do that fast and fluently, because we share the same system of kinds.<p>Even if you look at something that you don't exactly know what it is, you see it as a physical object, or as an optical illusion, or even as a blurry visual field, i.e. as being of one kind of thing or another.