How Simplicity Helps You Find the Truth without Pointing at it [chapter]

Kevin T. Kelly
2007 Induction, Algorithmic Learning Theory, and Philosophy  
It seems that a fixed bias toward simplicity should help one find the truth, since scientific theorizing is guided by such a bias. But it also seems that a fixed bias toward simplicity cannot indicate or point at the truth, since an indicator has to be sensitive to what it indicates. I argue that both views are correct. It is demonstrated, for a broad range of cases, that the Ockham strategy of favoring the simplest hypothesis, together with the strategy of never dropping the simplest
more » ... until it is no longer simplest, uniquely minimizes reversals of opinion and the times at which the reversals occur prior to convergence to the truth. Thus, simplicity guides one down the straightest path to the truth, even though that path may involve twists and turns along the way. The proof does not appeal to prior probabilities biased toward simplicity. Instead, it is based upon minimization of worst-case cost bounds over complexity classes of possibilities. ical force of simplicity arguments, but wonder why they should be so compelling. 1 Presumably, epistemic justification is supposed to direct one toward the truth and away from error. But how could simplicity do any such thing? If you already know that the truth is simple or probably simple, then Ockham's razor is unnecessary, and if you don't already know that the truth is simple or probably simple, then how could a fixed bias toward simplicity steer you toward the true theory? For a fixed bias can no more indicate the truth than a compass whose needle is stuck can indicate direction. There are answers in the literature, but only irrelevant or circular ones. The most familiar and intuitive argument for realism is that it would be a "miracle" if a complex, disunified theory with many free parameters were true when a unified theory accounts for the same data. But the alleged miracle is only a miracle with respect to one's personal, prior probabilities. At the level of theories, one is urged to be even-handed, so that both the simple theory and its complex competitor carry non-zero prior probability. Then since the complex theory has more free parameters to tweak than the simple theory has, each particular setting of its parameters has lower prior probability than does each of the parameter settings of the simple theory. So the miracle argument amounts to an a priori bias in favor of simple parameter settings over complex parameter settings. But that is just how a Bayesian agent implements Ockham's razor; the question under consideration is why one should implement it, so far as finding the true theory is concerned (cf. Kelly and Glymour 2004) . Another standard argument is that simple explanations are "better" and that one is entitled, somehow, to infer the "best" explanation (Harman 1965). But even assuming that the simplest explanation is best, that sounds like wishful thinking (Van Fraassen 1981), for one may like strong explanations, but that doesn't make them true. The same objection applies to the view that simplicity is just one virtue among many (Kuhn 1970 ). An apparently more promising idea is that simple or unified theories compatible with the data are more severely tested or probed by the data and, hence, are better "corroborated" (Popper 1968) or "confirmed" (Glymour 1980) . But if the truth isn't simple, then the truth is less testable than falsehood, so why should one presume that the truth is simple? Either considerations like testability and explanatory power are irrelevant to the question at hand or one must assume, circularly, that the world is simple in order to explain why one is entitled to prefer more testable theories. Another idea (Sklar 1977) is that if a simple theory is false, future data will lead to its retraction, so that a simplicity-biased, rational agent will converge to the truth in the limit of inquiry. But the question at hand is not merely how to overcome one's simplicity bias. If Ockham's razor is truly helpful, as opposed to merely being a defeasible impediment, it should facilitate truth-finding better than competing biases. But since other biases would also be over-ruled by experience eventually, mere convergence 1 Van Fraassen focuses on the problem of theories that are not distinguished even by all the evidence that might ever be collected. There is no question of simplicity guiding you to the truth in such cases, since no method based only on observations possibly could. On the other hand, it is almost always the case that simple and complex theories that disagree about some future observations are compatible with the current data and the simpler one is preferred (e.g., in routine curve-fitting). I focus exclusively on this ubiquitous, local problem of simplicity rather than on the hopelessly global one.
doi:10.1007/978-1-4020-6127-1_4 dblp:series/leus/Kelly07 fatcat:5n6larmyovd7nmxodg25a2sacy