When is an abstraction or description real (or useful, although I will use the term real exclusively here)? I would say that an abstraction or description is real if and only if the criterion for when to apply it depends on observable properties. It is also a corollary of this that a “real” abstraction or description can be said to capture causation as well.
Since that definition probably sounded pretty abstract itself allow me to give a concrete example. Consider the abstraction of “desk”. I say that desk is an abstraction because there is no one thing that is equivalent to a desk (as for example a photon is identifiable with a single kind of particle). Nor are there fundamental desk particles or fields that we can directly observe. However whether something is or is not a desk does depend on our observations, which (as argued earlier) do reflect what is real. Although the idea that the thing in front of me is a desk may be abstract, the arrangement of matter that gives me reason to decide that it is indeed a desk is not. It is also important to note that my criterion for what is a desk makes some things desks and some not, a criterion is meaningless if it says that everything is X or that nothing is. Moreover, the desk can said to be a real cause of events. Why does my computer stay off the ground? Because of the desk. There is no one thing that can be said to be keeping the computer aloft; it is only the desk that can be said to fill this role (the complex arrangement of matter in front of me that is what I have been identifying as an instance of “desk”). Obviously “desk” is an abstraction that corresponds very closely with the physical world, but all abstractions that are real can be identified in this manner. For example the decision to describe a system as capitalist is based on real monetary transactions, and the same can be said for any “real” abstraction (for example those I have described earlier here and here).
What kind of abstraction doesn’t count as real then? Almost all of our usual abstractions are real (that is why they are useful to us), so let us consider something made up, say the category “light-heavy”. I proceed then to describe several objects as “light-heavy”, but instead of basing my classification on some observed property of the objects I am mentally flipping a coin. This abstraction is not real; it does not depend on any real properties. It is hard to even say how it could be meaningful. Additionally it cannot possibly capture causation; there is no way in which the description of an object as “light-heavy” could be said to be the cause of anything. Since ultimately causation is dependant on observable properties, and “light-heavy” doesn’t capture any of these properties, the removal of the “light-heavy”-ness of an object wouldn’t affect a system in any way, and hence can’t be said to be a cause. (Once again see this account of causation.)
Now for the interesting consequences of this argument. From the above it follows that the gods of many ancient people were real. This is not to say however that there were beings with supernatural powers running around. Consider god in this sense: certain events are described as being embodiments of the god or the god’s will. The phenomena are observable, and there is a certain logic about which phenomena are associated with which god. Given the understanding of ancient people their abstractions can even be said to capture causality. For example consider a group of Vikings who think that the thunder is Thor’s anger. Thor’s anger passes the requirement for being real, because it is actual observations of lightning that are described as Thor’s anger, it is not arbitrary. Secondly Thor’s anger seems to have casual power, since without Thor’s anger (and thus its associated phenomena) trees wouldn’t be set on fire by storms, ect. Perhaps Thor as a big man with a hammer is a fiction, but the phenomena associated with him by ancient people with him were certainly real, and thus Thor as an abstraction of these (seemingly) mysterious events is real, and even useful (although ultimately not the best explanation when more accurate observations are made).