One of the most important of all concepts philosophers need to understand when trying to apply causal reasoning to explain phenomena is that of Levels of Abstraction. At its simplest, the idea is simply that there is an appropriate system level for each type of phenomena. Causal rules can be identified within a level, which explains the behavior of phenomena discussed on that level. It is generally an error to assume the objects and causes on one level are constructed from, implied by, or reduce to, the objects and causes on a lower or higher level, although sometimes such an idea is not without some validity.

There are a number of metaphysical problems involved in the idea of levels of abstraction (”levels”). One of the first is, how “real” is a level? Since levels are about how we think of a group of related objects and phenomena, one might be justified in supposing that levels don’t really exist, that they’re just metaphors useful to limited minds that can’t deal with the complexity of the actual world, so we clump it in various ways to make it easier to think about it.

I don’t think such a way of thinking about levels is justified. After all, it would not be useful to contruct a theory of some level if it didn’t have some explanatory force, which implies there is something about that theory that is observable.

One sort of level theory is the theory of Electronics. Objects on the level of electronics include, units of force called voltage, volume, called current, and individual elements called resistances, capacitances, inductances, switches (or “gates”), power sources, conduits of conduction (”wires” and “connections”), etc. A casual acquaintance with fundamental physics knows resistors, capacitors, and conductors, are not elementary objects; each is a composite structure made with complex materials consisting of billions of atoms and having aggregate properties which only make sense in relation to these objects. The causal laws of electronics are expressed in terms of these composite abstract objects, such as Ohm’s law (E=IR).

In the case of electronics theory, there is every reason to believe the abstract objects, forces, and relations are reducible to or wholly explainable by the more fundamental objects and forces of particle physics and quantum theory. Nevertheless, no one would seriously suggest deleting electronics theory from our sphere of knowledge, because it describes objects which can be measured and phenomena which can be observed. You might say the electronics level is a “summary” of physical laws at lower levels, which is abstracted in order to focus on a relevant subset of general natural phenomena.

Mundane life contains many examples of highly complex abstract objects which nonetheless appears to be reducible to more elementary objects and forces. Chairs, tables, cars, diamond rings — a host of objects and their concomitant relations are familiar examples. A chair is just an assemblage of atoms, with the peculiar property that the sort of atoms assembled is irrelevant to the nature of the object as chair; it’s only the structure and function of the object as “chair” that matters, and it can be made out of wood, steel, plastic, composite carbon fiber, or cotton candy.

Not all levels of abstraction are as easily reduced, though. Consider economics. Economics consists of objects like dollars and euro’s, and jobs, markets, businesses and corporations. There is nothing physical about a unit of currency. Indeed, more currency is represented by plastic and implemented by computer financial systems than exists as copper and paper. It isn’t the physical material or structural design of the currency that makes it money (what has happened to the paper francs of the pre-euro economy?) Try to analyze “jobs” into physical elements, and remember, it isn’t the employee who defines the “job.”

Even more complex abstract levels exist. What is a society made of? Is it the people who comprise it? The land they occupy? The buildings and cities they construct? The monuments and artifacts they pass on to the archaeologists of the future? Their customs and traditions? Their language? And yet, despite its airy foundation, societies definitely exist, and understanding them is something we have to do.

In the case of the Mind itself, trying to find the decomposition of minds and mental phenomena to the physical world of quarks and photons is probably not completely possible, nor even particularly useful. Here, it becomes important to realize the arbitrary nature of a level theory. A railroad, for example, is not explainable by physics. A pair of tracks are laid from point to point, and locomotives and cars are built of steel and other materials to ride on the tracks, but the level of “trains” includes many more elements. A schedule is a structure in time and isn’t made of steel or paper. Consider that, given tracks from city A to city B, it remains undefined whether the train on those tracks moves west (B -> A) or east (A -> B); it can in fact move either way, and sometimes will run east, and sometimes will run west. The odd thing about building the tracks and a device that can move on them is that a new freedom of action emerges: movement east and movement west. The schedule encompasses this, whereas the tracks do not. (The tracks themselves are static, and lie there connecting the two points in exactly the same manner, no matter what the train does on them.)

Another simple example is the game of chess. The rules of chess are not derived from the nature of the wooden pieces and the board. Chess can be played with those objects, but the idea of chess is in addition to those materials, which serve merely as representations of the ideas of chess. This is exactly the same relationship as the theory of economics has to the pieces with which it is played.

And the ultimate point of this degree of independence that exists between layers, where new possibilities and alternatives arise in the behavior of new objects, is that Free Will, such as it is, consisting of the highly abstract objects of Purposes and Intentions, Choice, and Consequences, is not fully explained by any lower levels of objects and relations that represent these things. Physical causality is no more the explanation of mental behavior than it is an explanation of a train schedule.

Levels of abstraction, in other words, are the vehicles through which “emergent properties” arise (see Wikipedia, Systems Theory).