Abstract: Humeans about chance often endorse the Best-Systems account, according to which chances are but summaries of the patterns found in the totality of local matters of fact. More thoroughgoing subjectivists like de Finetti, on the other hand, rationalize chance-talk by appealing to certain symmetries in an agent’s credences. In this talk, I will explore the extent to which these two different approaches can inform each other. I will explain how de Finetti’s framework admits a Humean interpretation where the underlying symmetries in the agent’s prior can be seen as implicitly providing a Best-Systems theory of chance. This perspective gives rise to hybrid views of chance lying somewhere on the spectrum between traditional Best-Systems conceptions of chance and de Finetti’s ‘radical’ subjectivism, where each position on that spectrum depends on the degree to which one allows Best-Systems probabilities to be sensitive to the agent’s inductive assumptions.
As we will see, the interactions between the Best-Systems view and de Finetti’s account of chance are especially fruitful in the context of computationally bounded Bayesian agents: i.e., Bayesian agents with computable priors. I will discuss a recent criticism of Humean conceptions of chance due to Gordon Belot, who shows that there are several chance-credence principles in the spirit of Lewis’ Principal Principle that computationally bounded Bayesian agents cannot obey. On the other hand, we will see that, on de Finetti’s conception of chance, ergodic decomposition theorems supply a general version of the Principal Principle, which applies to computable and uncomputable priors alike. De Finetti’s conception of chance is thus largely unaffected by Belot’s impossibility results: computationally bounded Bayesian agents automatically obey a version of the Principal Principle. So, with a healthy dose of subjectivism, Humeans about chance needn’t be too worried about these results. Our discussion will raise a number of questions about the right formulation of the Principal Principle, the extent to which computationally bounded Bayesian agents can entertain, and defer to, uncomputable chances, and the right constraints to impose on theories of chance when the underlying agents are computationally bounded.
This is joint work with Krzysztof Mierzewski.
Jowett Society Organising Committee: Ryan Kendall, Charlotte Dorneich, Amit Karmon | Jowett Society Website
