Supervaluational accounts of truth allow truth to be indeterminate, allowing that even for languages including the liar paradox, ‘‘fixed point’’ interpretations can be found. We apply this kind of account to rational credences, to find non-undermining indeterminate epistemic states even in undermining situations.
To do this, we observe that there are specific assumptions in the implementation of the account of truth which are vital for triviality to be avoided: that we focus only on definite truth value verdicts rather than the sets of precisifications themselves. This means that when we apply the supervaluational Kripkean jump, additional precisifications are added.
When applying this to rational credence, however, we want to focus on the set of credence functions itself (moreover, for credences, the challenge is not avoided by focusing on definite judgements). We thus directly consider an alternative jump which adds additional precise credences (by adding limits of sequences of recommended credences).
We use these considerations to define a notion of underminingness for indeterminate credences and see that non-undermining states can always be found. Our account is very general and could apply to a wide range of target domains.