I suspect you have bumped up against these in your wanderings through nature, at least cognitively. These are the concepts people actually entertain, as opposed to the concepts we suppose them to entertain according to whatever idealized theories of concepts we happen to believe are true.
Numbers are good examples.
If you study too much set theory, you may come away with the impression that everyone thinks about numbers the way von Neumann did or the way Russell did, as little sets of sets. But they don't, and you can establish this by doing experiments on real subjects. You can make predictions about certain properties numbers should have if they really were von Neumann numbers, e.g., and you can see if subjects are at all sensitive to properties like that. Most times, if you do the experiments properly, you will find that they are not sensitive to those properties. People, when they think about numbers cognitively, use rather different strategies from the ones used in axiomatic mathematics.