ABSTRACT

Idealization is ubiquitous in science, being a feature of both the formulation of laws and theories and of their application to the world. There are many examples of the former kind of idealization: Newton’s first law (the principle of inertia) refers to what happens to a body that is subject to no external forces, but there are probably no such bodies; the famous ideal gas laws do indeed idealize the behavior of real gases (which violate them in various ways, sometimes significantly); and economics refers to perfectly rational agents. Theory application is largely about idealization. Philosophers of science often focus their attention on scientific theories as expressed by a relatively small set of fundamental axioms, laws, and principles: for example, the laws of Newtonian mechanics plus the principle of the conservation of energy in the case of classical mechanics, or some variant of von Neumann’s axioms in the case of quantum mechanics. However, if real science were restricted to making use of such resources, then it would be much less empirically and technologically successful than it is. The reason is that often the systems being studied are not amenable to a complete analytical treatment in the terms of fundamental theories. This may be because of the sheer complexity and size of systems in which scientists are interested; for example, it is not possible to use Newtonian mechanics to describe the individual motions and collisions of particles in a gas because there are so many of them. Another factor is that some mathematical problems cannot be solved exactly, as is the case, for example, with the famous three-body problem of classical mechanics. Scientific knowledge is at least as much about how to overcome these problems with idealization as it is about fundamental theory. This may mean abstracting the problem by leaving out certain features of the real situation, or approximating the real situation by using values for variables that are close enough for practical purposes, but strictly speaking wrong, and/or using approximating mathematical techniques. So, for example, in physics, large bodies such as planets are often treated as if they are spherically symmetrical; in chemistry, crystals are often treated as if they were free of impurities and deformities; and, in biology, populations of reproducing individuals are often treated as if their fitness is independent of how many of them there are in the population.