David summarizes his distinction between inference by prediction/retrodiction and inference by measurement, and reiterates that this can make plausible the claim that the special status of the Past-Hypothesis can ground the asymmetry in our epistemic relations to the past and future. He goes through some objections to this view that came up in the class before, which he and Tim then discuss. David relates this epistemic asymmetry to the time-asymmetries in causation, counterfactual...

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...

Barry Loewer is the guest lecturer for this class. Tim starts by recapitulating the notion of typicality introduced in the previous lecture. Tim, David and Barry then engage in a debate about Tim's view of the nature of statistical explanation. Barry then gives a summary of the difference between his and David's view of statistical mechanics and Tim's view. He starts by arguing that one main point of contention is the "imperialistic" nature of his and David's project. A second main point of...

Tim and David begin by continuing their discussion of the 'Stosszahlansatz', the assumption that the number of particle collisions in a given subregion is just proportional to the volume of that region. They summarize the debate up to this point and attempt to clarify the nature of their disagreement about its explanatory value. Tim then takes over and gives a short primer on the mathematics of measure theory, connecting it with the purely mathematical notion of a "probability measure" and...

Time Maudlin starts by distinguishing and characterizing three different classes of explanations of thermodynamic phenomena previously studied in the seminar (appeals to symmetry principles, to random walks in the phase space, or to features of the actual micro-dynamics of isolated systems). He explains the various ways in which the standard measure over phase space comes into play in these explanations. David Albert then examines the various ways in which one might justify appealing to this...

In this lecture, Tim Maudlin continues the statistical mechanical account of the velocity distribution of particles in a monatomic gas, and how this distribution evolves over time. David Albert and Tim disagree about the status of the 'Stosszahlansatz'', the assumption that the location of particles in the system, and the locations of critical regions required to impact on other particles, are statistically independent of each other. Tim argues that when an assumption of statistical...

David Albert begins with a brief discussion of an issue raised in the last lecture- whether you can define an entropy for a non-equilibrium system. He and Tim Maudlin agree that while the steps along the reversible route must involve equilbrium states, partitioning can still be used to define the entroy of a non-equilibrium system. Tim returns to the discussion of statistical mechanics began in the last lecture, addressing how we can calculate and explain the velocity distribution of gas...

In this lecture, David Albert continues his introduction to thermodynamics, explaining how the entropy of a system is defined and determined in thermodynamic terms. This requires distinguishing between reversible and irreversible paths between two states of a system, and envisaging how pistons and heat baths can be used to mimic the irreversible transfer of heat between a warm body and a cool one. Tim Maudlin and David disagree on whether the entropy of a non-equilibrium system can be...

This is the second lecture in the joint NYU/Columbia graduate course on philosophy of statistical explanation and cosmology. It's David Albert's first lecture, and in it he introduces the main ideas he'll discuss in the class, with some contrast between his approach and that of our other lecturer, Tim Maudlin (NYU).