As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.

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 Reichenbach's Common Cause Principle. (shrink)

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

This paper considers the importance of unification in the context of developing scientific theories. I argue that unifying hypotheses are not valuable simply because they are supported by multiple lines of evidence. Instead, they can be valuable because they guide experimental research in different domains in such a way that the results from those experiments inform the scope of the theory being developed. I support this characterization by appealing to the early development of quantum theory. I then draw some comparisons (...) with discussions of robustness reasoning. (shrink)

We argue against the common view that it is impossible to give a causal account of the distant correlations that are revealed in EPR-type experiments. We take a realistic attitude about quantum mechanics which implies a willingness to modify our familiar concepts according to its teachings. We object to the argument that the violation of factorizability in EPR rules out causal accounts, since such an argument is at best based on the desire to retain a classical description of nature that (...) consists of processes that are continuous in space and time. We also do not think special relativity prohibits the superluminal propagation of causes in EPR, for the phenomenon of quantum measurement may very well fall outside the domain of application of special relativity. It is possible to give causal accounts of EPR as long as we are willing to take quantum mechanics seriously, and we offer two such accounts. (shrink)

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

The paper extends the framework of outcomes in branching space-time (Kowalski and Placek [1999]) by assigning probabilities to outcomes of events, where these probabilities are interpreted either epistemically or as weighted possibilities. In resulting models I define the notion of common cause of correlated outcomes of a single event, and investigate which setups allow for the introduction of common causes. It turns out that a deterministic common cause can always be introduced, but (surprisingly) only special setups permit the introduction of (...) truly stochastic common causes. I analyse next the Bell-Aspect experiment and derive the Bell-CH inequalities. I observe that we postulate there not a common cause for outcomes of a single event but rather a common common cause that accounts for outcomes of many events, where 'events' mean 'measurements with (different) directions of polarization'. Since the inequalities are violated, I claim that no causal story can be told about the Bell correlations, where causality is subliminal and restricted by screening-off condition. Similarly, given certain intuitive principles, no deterministic story can be told about these correlations. (shrink)

A probability space is common cause closed if it contains a Reichenbachian common cause of every correlation in it and common cause incomplete otherwise. It is shown that a probability space is common cause incomplete if and only if it contains more than one atom and that every space is common cause completable. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the principle is only falsifiable if conditions on the common cause (...) are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause. (shrink)

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it (...) which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle. (shrink)

The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause Principle.