REFINED INDUCTIVE ARGUMENT
contains simple theories (simple in one or more respects) that were at least temporarily empirically successful. 'lhe other contains temporarily successful theories that are complex or at least not particularly simple.
Immediately, we are confronted with the Laudan “pessimistic induction” problem: historically, if judged by today's evidence, most proposed theories, simple or not, temporarily successful or not, have turned out to be empirically unsuccessful, given today's evidence, to the degree that many are regarded as just plain false.[77] Even so, perhaps the simple ones have a better success rate than the complex ones. To be very generous, suppose that historically 20% of the simple theories that were temporarily empirically successful remain so now, and that 80% do not. And suppose that only 10% of complex theories that were temporarily empirically successful remain so now, while 90% do not. (Lacking a measure of “success,” these assumptions are admittedly vague, but perhaps clear enough to formulate the argument.) Finally, let us also suppose that we are concerned only with theories in which other potentially epistemic qualities are pretty much equal.Using these historical data as the basis for an inductive conclusion, we might say that the probability that a simple theory that is temporarily empirically successful will remain empirically successful is twice that of a temporarily empirically successful complex theory (20% vs. 10%). So, indeed, we might conclude that, other things being equal, a temporarily successful simple theory has twice the chance of being empirically adequate, or perhaps even true, that a temporarily successful complex one has. (“Empirical adequacy” is to be understood as going well beyond “temporary empirical success.”)
We need a stronger conclusion than this to defend the Epistemological Claim.
We need to argue that the simplicity of a theory compatible with the data is a good epistemic reason for believing that the theory is true or empirically adequate. But if 80% of the simple, temporarily empirically successful theories have turned out to be empirically unsuccessful, given our present data, then although simplicity increases the chance of empirical adequacy and doubles the chance of empirical adequacy over complexity, it is not a very good historical reason for believing in the empirical adequacy or the truth of simple theories generally. Inductions here, as Laudan says, are “pessimistic.” Using this sort of induction, simplicity will be a poor indicator of truth or empirical adequacy.Even worse, what frequently happens to a simple theory is that it gets more complex as it becomes more fully developed. Its simplicity at the outset is often achieved by neglecting certain factors whose inclusion would make the theory more empirically successful at the price of more complexity. The ideal gas law is simple, but it neglects intermo- lecular forces, and as a result its empirical success is limited. If we introduce a virial equation, we get broader empirical success but more complexity. Newton's theory of gravity is simple if we use it to explain the orbit of a planet as a two- body problem, neglecting the forces of other planets. But then we lose some empirical accuracy. If we introduce other forces acting, we get more empirical success, but also more complexity (indeed, too much for computational purposes). There are several equations giving the energy density of an oscillator at a given temperature: the Rayleigh-Jeans equation, the Wien equation, and the Planck equation. The first fails in the high-frequency region of black body radiation, the second at low frequencies. The Planck equation gives better results for all frequencies, but it is a good deal more complex than the other two.
An even more important reason why a theory that started out simple gets more complex over time is that new experimental results force such a change.
Think of the history of the atomic theory from the mid-nineteenth century to the present. At first, simple atoms without structure are postulated subject to laws of classical mechanics. This yields fairly good results in explaining and predicting certain properties of gases and liquids. Then, as a result of experiments, such as those of J. J. Thomson on cathode rays, electrons are discovered, and are claimed by Thomson to be the sole constituents of atoms (the “plum pudding” model). Then other constituents of atoms are discovered, and the laws governing these constituents are no longer conceived to be classical ones, but quantum ones, making the atomic picture much more complex. Indeed, on the basis of an induction, one might conclude that the probability is very high that, as new phenomena are discovered, a simple theory with some temporary empirical success will turn into, or be replaced by, a more complex one with much more (at least) temporary empirical success. If this happens more frequently than a simple theory's remaining simple over time, then an inductive defense of the epi- stemic claim for simplicity becomes very dubious. So does an inductive defense of the ontological claim that nature itself is simple.7.