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ABSTRACT
Peter Brössel and Franz Huber in 2015 argued that the Bayesian concept of confirmation had no use. I will argue that it has both the uses they discussed—it can be used for making claims about how worthy of belief various hypotheses are, and it can be used to measure the epistemic value of experiments. Furthermore, it can be useful in explanations. More generally, I will argue that more coarse-grained concepts (like confirmation) can be useful, even when we have more fine-grained concepts (like credences).
Acknowledgements
The author is grateful to three referees for this journal for comments on earlier drafts of this paper.
Notes
1 Salmon (Citation1975). This is equivalent to P(E|H) > P(E|–H) assuming that 0 < P(H) < 1, so I will treat them as equivalent. See Fitelson and Hájek (Citation2017).
2 I will usually leave the background beliefs implicit in future.
3 We have more plausibly an explication than an analysis. Indeed this is the example that motivated Carnap to make the distinction; see Carnap (Citation1963, 933–940) and Maher (Citation2007). I will address the question of whether we are analysing, improving, or replacing the ordinary language concept at the end of section 7. Of course, there are alternative explications of confirmation beyond the Bayesian explication. One question for Brössel and Huber is whether they think their analysis undermines these other concepts of confirmation or whether the Bayesian concept has a special problem.
4 Thanks to a referee for comments that led to me setting the issues up in this way, and for various other improvements.
5 I use quotation marks and inverted commas only to help with parsing; the distinction between sentences and propositions will play no role.
6 This passage shows that it is not entirely clear whether Brössel and Huber are working with actual or ideal beliefs. They say that they are focusing on ‘Bayesian confirmation theory qua normative theory’ (Brössel and Huber Citation2015, 738n1). And in order to engage with Hempel, who talks about rational belief, it must be what agents ought to believe that is at issue. But they reject the evidential/inductive probability functions that rationality seems to require (Brössel and Huber Citation2015, 743). So where does the normativity come from? I think they must have in mind a theory according to which conditionalisation is the only normative constraint (plus probabilism). I will assume for simplicity that the agents we are dealing with are sufficiently ideal for the actual/ideal distinction to collapse.
7 Brössel and Huber consider using different probability functions for credence and confirmation, but do not consider objective chance.
8 Something like the Principal Principle (Lewis Citation1980) is needed, though a much weaker version will do the job regarding conditional probabilities.
9 Conditionalisation says that if an agent learns exactly E between t1 and t2, then Pt1(H) = Pt2(H|E).
10 They are different even if the agent is ideal. Deductive logic constrains what agents should believe, but substantive bridging principles are needed to connect deductive logic with belief. Similarly, inductive logic constrains what agents should believe, and substantive bridging principles are also needed here. See Harman (Citation1986).
11 Indeed we might be ignorant of our own beliefs (Williamson Citation2000; Schwitzgebel Citation2011), and perhaps have better access to coarse-grained confirmation relations.
12 I’m using E for both the photographs and the proposition that would be learnt on seeing them.
13 Again, it is rational degrees of belief that are relevant for Brössel and Huber's claim that the Bayesian conception of confirmation is useless for making claims about how ‘worthy of belief various hypotheses are’.
14 The original sentence is: ‘Therefore we cannot use the information that the evidence confirms the hypothesis in order to specify the agent's degrees of belief’.
15 This might look paradoxical—but omitting details from the antecedent of a conditional makes it stronger. See Bradley (Citationforthcoming).
16 We might need to add a ceteris paribus clause here.
17 Brössel and Huber (Citation2015) seem to make these assumptions in the middle of page 746.
18 Garber (Citation1983), Howson and Urbach (Citation1993).
19 Incremental and absolute confirmation were conflated by Hempel (Citation1945) and clarified by Carnap (Citation1962, 477–478).