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We show that representing imprecise probabilities by using probability constraints closed under merely finite consequence, the probability filter model, avoids objections by Walley to the credal set model. We show that it encompasses the model of sets of desirable gambles.

What happens when we use a decision theory to judge itself? Theories that diverge from Expected Utility Theory often recommend using EUT, thus undermining themselves.

We argue that accuracy-theoretic considerations still tell the risk-sensitive to update by conditionalization.

We note that strict propriety follows from weak propriety, given truth-directedness, thus closing an argumentative gap in the literature.

This argues that evidence gathering is epistemically irrational for the (Buchak-style) risk-avoidant agent. To do this we consider how accuracy should be measured once risk-awareness is rationally permissible.

We show that Moss’s model of uncertainty is at least as expressively powerful as every other current imprecise probability framework. And we give a Dutch Book argument for certain failures of consistency.

This provides a new proposal for what to do at limit stages of the revision theory of truth: one shouldn’t only consider definite verdicts that are brought about, but more general closed properties. This is important if one wishes to consider a revision theory for probability.

We investigate how to assign semantic probability values to sentences by tracking how often a sentence is true in transfinite sequences; particularly sequences from Gupta and Belnap’s revision theory of truth.

In addition to specific responses to Caie’s paper, this presents some bullets that need to be bitten if one adopts a consequentialist view of epistemic utility. Further such bullets are also presented in my thesis (ch.7)

This presents a Kripke-style construction for a language with self-referential probability as well as an ω-complete axiomatisation. It also follows Stern in arguing that principles like introspection should be formulated using a truth predicate.