I am not a philosopher by any means, so maybe I am using some words incorrectly — i.e. I am not sure what the difference is between "conceptual" and "abstract". Please correct me if I am wrong.
I've been trying to prove a point that we think in abstractions — for example, when we think about a physical object, we abstract away a lot of its physical details. This goes even further when we deal with several objects of the same category — when I count pebbles, my brain needs to first put each pebble into the object category of "pebbles" before it becomes countable (enumerable?).
The question is, are object categories themselves abstract? Abstract is defined as existing in thought or as an idea but not having a physical or concrete existence. On one hand, real pebbles exist. On the other hand, "pebbles" as a category, does not have a physical existence.