Bayesian confirmation theory tells you to update your credences by conditionalizing on any new evidence you encounter. However, conditionalization depends on your prior credences, and Bayesianism does not tell you what those prior credences should be. (The only requirement is that your prior credences must be probabilistically coherent.) Two people with different initial credences—different “starting points,” so to speak—could reach radically different conclusions when they conditionalize on the same evidence. One person could regard evidence E as strong support for hypothesis H; another could regard E as strong evidence against H, even though both individuals are following the conditionalization rule. Is there no objective fact of the matter whether E really confirms H? Is any initial credence as good as any other, or are some starting points more reasonable than others? The Bayesian theory of confirmation, by itself, gives no answer to these questions.
These unanswered questions have engendered an ongoing debate between two schools of thought within Bayesianism confirmation theory. Subjective Bayesians argue that there are no rational requirements for prior credences except probabilistic coherence (i.e., conformity to the rules of probability). Objective Bayesians, on the contrary, see the subjectivity of Bayesianism as a serious problem for the theory. In order to make it more objective, they have tried to identify rational requirements or rules for prior credences, in addition to the minimum requirement of probabilistic coherence. When relevant statistical frequencies are known, we can use a statistical syllogism to determine the appropriate prior credence for a hypothesis. Similarly, if the objective chance of an event is known, and we have no other evidence regarding whether it has occurred, our credence in the event ought to match its objective chance of occurring. (Philosopher David Lewis called this truism the principal principle.David Lewis (1980), “A subjectivist’s guide to objective chance,” in R.C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Vol II (Berkeley, UCP: 263-293)) But how should we determine prior probabilities when we don’t know the objective chances and we have no relevant statistical data? How should we assign prior credences to hypotheses when we have no evidence at all?
In cases where prior credences cannot be determined by objective chances or statistical frequencies, objective Bayesians usually appeal to the so-called principle of indifference, which says that when you have no evidence to decide between multiple hypotheses, you should assign the same probability to each of those hypotheses. Depending on how the hypotheses in question are enumerated, however, the principle of indifference yields contradictory results, and there is no consensus on how to resolve that issue.For examples and further discussion of this problem, see Section 2.1 The Principle of Indifference in Jonathan Weisberg (2021), “Formal Epistemology,” The Stanford Encyclopedia of Philosophy.
My own opinion, for what it’s worth, lies somewhere between the subjectivist and objectivist positions. On the one hand, I agree with objective Bayesians that mere probabilistic coherence is insufficient to make one’s starting point reasonable. On the other hand, I’m not optimistic that they will succeed in finding strict rules of rationality for prior credences, beyond the rules of probabilistic coherence. As I see it, the difference between “reasonable” and “unreasonable” starting points is largely a matter of common sense, which cannot be formulated into a precise (much less concise) set of rules.
In some cases, when people disagree in their prior probabilities, methods of non-deductive argumentation such as argument by analogy and inference to the best explanation might help to resolve the disagreements. However, these modes of non-deductive inference rely on common sense in a similar way, and they too exhibit a degree of subjectivity. For example, as we saw in the previous chapter, argument by analogy often relies on common-sense judgments about which similarities are relevant and which are not. (See the section on Assessing Analogies.) Likewise, inference to the best explanation depends on subjective judgments about which explanatory virtues should be weighed more heavily (in cases where rival explanations exhibit different virtues). It also depends on common-sense intuitions, such as the intuition that simplicity and other virtues make an explanation more likely to be true. To the extent that subjective judgments and common-sense intuitions are requisite features of non-deductive reasoning in general, it is unsurprising—and, perhaps, inescapable—that they show up in the Bayesian framework as well.
Such controversies notwithstanding, Bayesian methodology remains useful in a broad range of cases where its subjectivity isn’t a problem: for example, when working out the implications of our own beliefs, and when engaging in philosophical debates in which there is some level of agreement on the relevant prior probabilities. Moreover, even when there is disagreement on what the priors should be, the inherent subjectivity of Bayesianism doesn’t render it useless. It may, for example, enable us to estimate just how high or low someone’s prior credence must be in order to rationally believe or disbelieve some controversial proposition in light of shared evidence. We’ll see how this works in the next chapter.