Externalism and Exploitability
According to Bayesian orthodoxy, an agent should update – or at least should plan to update – her credences by conditionalization. Some have defended this claim by means of a diachronic Dutch book argument. They say: an agent who doesn’t plan to update her credences by conditionalization makes herself vulnerable (by her own lights) to a diachronic Dutch book, i.e., a sequence of bets which, when accepted, pose a risk of monetary loss without any possibility of monetary gain. Here, I will argue that this argument is in tension with an attractive conception of evidence: namely, evidence externalism, i.e., the view that an agent’s evidence can entail non-trivial propositions about the external world.
I show two things. First, I show that there are two constraints on updating plans – transparency and reflectiveness – which are individually necessary and jointly sufficient for any updating plan to be immune to diachronic Dutch books. Very roughly, if an agent complies with a transparent updating plan, she is certain about exactly what evidence she has; if an agent complies with a reflective updating plan, she cannot engage in biased inquiry, i.e., an inquiry which, by her own lights, is guaranteed to raise her credence in favour of a proposition. Second, I show that an evidence externalist must countenance possible situations where the plan of updating by conditionalization violates one or both of these constraints. The upshot: if the evidence externalist is right, then an agent who plans to update by conditionalization can be (by her own lights) vulnerable to a diachronic Dutch book.