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.

Cases where every credence undermines its own adoption seem to lead to epistemic dilemmas. We move to considering indeterminate credences and look at what is determinately recommended of you. By doing this, we propose that the epistemic dilemmas are avoided.

We investigate the supervaluational Kripkean account of truth and show how it can apply to finding rational indeterminate credences in undermining scenarios. Our construction is general and could apply to a whole range of domains.