entry for the Entry for the Stanford Encyclopedia of Philosophy, 2007.

One of the open questions in Bayesian epistemology is how to rationally learn from indicative conditionals (Douven, 2016). Eva et al. (Mind 129(514):461–508, 2020) propose a strategy to resolve this question. They claim that their strategy provides a “uniquely rational response to any given learning scenario”. We show that their updating strategy is neither very general nor always rational. Even worse, we generalize their strategy and show that it still fails. Bad news for the Bayesians.

In this paper, we propose a unified account of conditionals inspired by Frank Ramsey. Most contemporary philosophers agree that Ramsey’s account applies to indicative conditionals only. We observe against this orthodoxy that his account covers subjunctive conditionals as well—including counterfactuals. In light of this observation, we argue that Ramsey’s account of conditionals resembles Robert Stalnaker’s possible worlds semantics supplemented by a model of belief. The resemblance suggests to reinterpret the notion of conditional degree of belief in order to overcome a (...) tension in Ramsey’s account. The result of the reinterpretation is a tenable account of conditionals that covers indicative and subjunctive as well as qualitative and probabilistic conditionals. (shrink)

According to orthodoxy, there are two basic moods of supposition: indicative and subjunctive. The most popular formalizations of the corresponding norms of suppositional judgement are given by Bayesian conditionalization and Lewisian imaging, respectively. It is well known that Bayesian conditionalization can be generalized (via Jeffrey conditionalization) to provide a model for the norms of partial indicative supposition. This raises the question of whether imaging can likewise be generalized to model the norms of ‘partial subjunctive supposition’. The present article casts doubt (...) on whether the most natural generalizations of imaging are able to provide a plausible account of the norms of partial subjunctive supposition. (shrink)

Conditional learning, where agents learn a conditional sentence ‘If A, then B,’ is difficult to incorporate into existing Bayesian models of learning. This is because conditional learning is not uniform: in some cases, learning a conditional requires decreasing the probability of the antecedent, while in other cases, the antecedent probability stays constant or increases. I argue that how one learns a conditional depends on the causal structure relating the antecedent and the consequent, leading to a causal model of conditional learning. (...) This model extends traditional Bayesian learning by incorporating causal models into agents’ epistemic states. On this theory, conditional learning proceeds in two steps. First, an agent learns a new causal model with the appropriate relationship between the antecedent and the consequent. Then, the agent narrows down the set of possible worlds to include only those which make the conditional proposition true. This model of learning can incorporate both standard cases of Bayesian learning and the non-uniform learning required to learn conditional information. (shrink)