Balazs Gyenis

When Can Statistical Theories Be Causally Closed

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbachs Common Cause Principle (RCCP).

Causal Completeness in General Probability Theories

A general probability space is defined to be causally complete if it contains common cause type variables for all correlations it predicts between compatible variables that are causally independent with respect to a causal independence relation defined between variables. The problem of causal completeness is formulated explicitly and several propositions are presented that spell out causal (in)completeness of certain classical and non-classical probability spaces with respect to a causal independence relation that is stronger than logical independence.

How Do Macrostates Come About

This paper is a further consideration of Hemmo and Shenker’s ideas about the proper conceptual characterization of macrostates in statistical mechanics. We provide two formulations of how macrostates come about as elements of certain partitions of the system’s phase space imposed on by the interaction between the system and an observer, and we show that these two formulations are mathematically equivalent. We also reflect on conceptual issues regarding the relationship of macrostates to distinguishability, thermodynamic regularity, observer dependence, and the general phenomenon of measurement.

Is it the Principal Principle that Implies the Principle of Indifference

Hawthorne et al. (Br J Philos Sci, http://bjps.oxfordjournals.org/lookup/doi/10.1093/bjps/axv030) argue that the Principal Principle implies a version of the Principle of Indifference. We show that what the Authors take to be the Principle of Indifference can be obtained without invoking anything which would seem to be related to the Principal Principle. In the Appendix we also discuss several Conditions proposed in the same paper.