A BAYESIAN REPLY: EVIDENCE

A Bayesian who accepts the concept of B-evidence given in chapter 1 will reply that if simplicity raises the probability of truth or empirical adequacy at all, then, no matter what the absolute probability is, the fact that simpler theories have been more successful than more complex ones counts as evi­dence for the truth or empirical adequacy of a simple theory.

First, the defender of B-evidence needs to be reminded that the inductive argument presented is entirely hypothet­ical. It is based on a speculative assumption for which no ev­idence has been offered, viz. that simpler theories have had a sustained empirical success rate that is better than that of complex ones. 'lhe most that the Bayesian can say is that if this is so, it is evidence for the continued empirical success of simple theories. But this is a big “if,” especially in view of the fact that in order to retain empirical success, many simple theories have to be modified or replaced by more complex assumptions

Second, as noted in chapter 1, I reject this Bayesian B- concept in favor of my A-concepts because, among other reasons, the former is much too weak to capture a basic idea that I regard as important for evidence, viz. the idea of pro­viding a good reason to believe. Increasing the probability of a hypothesis need not provide any reason to believe a hypoth­esis. If I play golf, the probability of my being killed by lightning increases. But this by itself is not evidence that I will be—it is not a good reason to believe this—since the probability is so tiny. (According to the New York Times Magazine, June 18, 1995, in 1993, 24.5 million golfers played nearly 500 million rounds; one golfer died via lightning.) This is important be­cause the Epistemological Claim for simplicity says that the simplicity of a theory compatible with the available evidence is a good reason to believe the theory is true or empirically adequate.

Third, on my A-concepts of evidence, as well as on the (much-improved) concept of explanatory B-evidence of chapter 1, section 10, for e to be evidence that h, there must be a high probability of an explanatory connection between h and e, given e. But that is not satisfied by appeals to histor­ical facts about the success of simple theories. Consider, as an example, J. J. Thomson's hypothesis in 1897:

(h) Cathode rays are negatively charged particles.

For the sake of argument, let us accept the idea that

(e) h is a simple theory about cathode rays, and simple theories have had a good success rate.

On my concept of (potential) evidence, as well as that of ex­planatory B-evidence, it is not the case that e is evidence that

h. It is not at all probable that, given e, there is an explanatory connection between h and e. It is not probable, given e, that cathode rays are negatively charged particles because this is a simple theory about cathode rays and simple theories have had a good success rate; or that h is a simple theory and simple theories have had a good success rate because cathode rays are negatively charged particles; or that some fact explains both h and e. What does count as evidence for (h), or did for Thomson, was the fact that

(e') Cathode rays are deflected toward a positively charged plate.^[78]

Given e', which was demonstrated in '1 homson’s experiments, and given other background information known at the time, the probability is high that there is an explanatory connec­tion between h and e' (the probability is high that cathode rays are deflected toward a positively charged plate because cathode rays are negatively charged particles).

On my account of evidence, or that of the explanatory B-concept, e' is (explanatory) evidence that h, but the “his­torical” e is not. As I noted in chapter 1, however, epistemic reasons for believing the truth of a hypothesis are some­times proposed that are not explanatory. And they may be good reasons. For example, the fact that the third Cavendish Professor of Physics at Cambridge (Thomson) believed h to be true (even before he conducted his experiments) might be a good reason (before the experiments) to believe that h is true. In the present case, however, the alleged histor­ical fact about the success of simple theories in claim e is a speculation, not something established or even shown to be probable.

Perhaps, then, the Epistemological Claim at the begin­ning of section 5 can be defended without invoking a dubious historical argument from the success of simple theories. Can one show in some other way that the simplicity of a theory makes it probable, or even that it increases its probability?

8.