First, Mahtani argues that both in the game The Mug and in the Sleeping Beauty we should not defer to a trusted person under a particular designation if they do not self-identify under this designation. This invites a more complex Reflection Principle. I respond that there are more parsimonious ways to avoid the challenges posed to the Reflection Principle. Second, Mahtani argues that preferences create a hyperintensional context, which poses a challenge to the Ex-Ante Pareto Principle that can be averted by supervaluation. I respond that such an appeal to supervaluation would block randomization as a fair allocation device.

Stalnaker’s ‘Assertion’ (1978 [1999]) offers a classic account of diagonalization as an approach to the meaning of a declarative sentence in context. Here I explore the relationship between diagonalization and some puzzles in Mahtani’s book The Objects of Credence. Diagonalization can influence how we think about both credence and desirability, so it influences both components of a standard expected utility equation. In that vein, I touch on two of Mahtani’s case-studies, chance and the finite version of the Two Envelope Paradox.

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. Blair is a writer’, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of ‘opacity’. Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for capturing opaque credence assignments without abandoning probabilistic coherence. I draw on ideas from judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’.

I’m so grateful to the commentators for their insightful and constructive responses! Below I continue this exchange with a brief note of reply.