Tim opens with a brief point about the postulation of a very low entropy past state. He contrasts the claim that, if this state is not the initial state of the world, that the entropy profile of the universe will be symmetric (intuitively, with a global minimum at the moment of the past hypothesis) and the claim that the macroscopic profile of the universe will be symmetric in the same way. David takes some time to respond to this point.
David then turns the discussion to the inferential role of the past hypothesis. He starts by identifying two kinds of inferences that can be used to determine the state of the world at times other than the present: Inference by Prediction/Retrodiction (in which one takes facts about the present and applies the laws to determine facts about the past or future) and Inference by Measurement (in which one takes facts about the present plus facts about certain past events and determines facts about the past or future). Inference by Measurement is, David points out, much stronger, but its appeal to certain past events is in need of justification. David argues that the event postulated by the past hypothesis is precisely the privileged past state that can do this inferential work. Tim asks whether these inference types really exhaust the relevantly available inference procedures. He also wonders whether the sorts of inferences David wants to call inferences by measurement really always have to appeal to facts about states other than the present, specifically the past hypothesis. There is a long discussion of the predictive centrality/fundamentality of the past hypothesis and of the nature of records.
