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.
This thesis discusses self-referential probabilities in some gory detail. We discuss a number of semantics models and initial work on how rationality considerations should apply in such cases.