In ‘The logic of partial supposition’ (Analysis vol. 81), Benjamin Eva and Stephan Hartmann investigate partial imaging, a credence-revision method which combines the partiality familiar from Jeffrey Conditioning(The Logic of Decision, 1983) with the formal notion of imaging familiar from Lewis’s ‘Causal decision theory’ (1981). They argue that because partial imaging is non-monotonic, it ‘fail[s] to provide a plausible account of the norms of partial subjunctive suppositions’.In this note, I present a notion of partial imaging that does satisfy monotonicity, and (...) discuss some of the applications and ramifications. The account frames conditioning as a form of imaging, and rejects Gärdenfors’s principle of linearity in ‘Imaging and conditionalization’ (1982). (shrink)

Accuracy-first epistemology says that the rational update rule is the rule that maximizes expected accuracy. Externalism says, roughly, that we do not always know what our total evidence is. It’s been argued in recent years that the externalist faces a dilemma: Either deny that Bayesian Conditionalization is the rational update rule, thereby rejecting traditional Bayesian epistemology, or else deny that the rational update rule is the rule that maximizes expected accuracy, thereby rejecting the accuracy-first program. Call this the Bayesian Dilemma. (...) Here is roughly how the argument goes. Schoenfield (2017) has shown that following Metaconditionalization maximizes expected accuracy. But if externalism is true, Metaconditionalization is not Bayesian Conditionalization. Therefore, the externalist must choose between the rule that maximizes expected accuracy (Metaconditionalization) and Bayesian Conditionalization. I am not convinced by this argument; once we make the premises fully explicit, we see that it relies on assumptions that the externalist has every reason to reject. Still, I think that the Bayesian Dilemma is a genuine dilemma. I give a new argument—I call it the continuity argument—that doesn’t make any assumptions the externalist rejects. Roughly, I show that if you're sufficiently confident that you will correctly identify your evidence, then you'll expect adopting a rule that I call Accurate Metaconditionalization to be more accurate than adopting Bayesian Conditionalization. (shrink)