Deference and Infinite Frames

This paper concerns three recent results concerning probabilistic deference. The results show interesting things about how various kinds of deference work on finite frames, but in each case the results do not naturally generalise to infinite frames. The non-generalisation raises interesting philosophical questions about the epistemological significance of the original results, and in the conclusion I briefly note reasons for thinking that epistemologists should be interested in what happens on infinite frames. The main priority, however, is simply showing that the finite and infinite frames behave differently in all three cases.