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On Reichenbach's common cause principle and Reichenbach's notion of common cause
"... 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 correlation ..."
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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.
The universal constraint set: convention, not fact
 In Dekkers et al
, 2000
"... All languages make the same phonological generalisations. This is the remarkable claim of Optimality Theory (OT). In early generative phonology (Chomsky & Halle 1968), phonological generalisations were expressed by ordered rewrite rules. Each language, however, required its own set of rules as ..."
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All languages make the same phonological generalisations. This is the remarkable claim of Optimality Theory (OT). In early generative phonology (Chomsky & Halle 1968), phonological generalisations were expressed by ordered rewrite rules. Each language, however, required its own set of rules as well as its own ordering. Later, underspecication phonology (Archangeli & Pulleyblank 1989, 1994) emphasised default rules. Universal tendencies in the rules were apparent, but characterising all languages with a single set of rules remained an unreachable dream. In OT, phonological generalisations are expressed as ranked defeasible constraints. Ranking provides so many distinct but plausible grammars that it seems feasible that a universal set of phonological generalisations could account for the diversity of phonological systems. The question we face is no longer whether the assumption of such a universal set is theoretically tenable, but whether it is justiable. There are two senses in which such an assumption could be justied: either as a fact or as a convention. If a fact, it claims that all language users objectively instantiate the same set of generalisations. If a convention, it encourages phonologists to describe languages using an agreed but arbitrary system of generalisations. In this interpretation, the universal constraint set is as arbitrary, but as useful, as the international phonetic alphabet (IPA). This chapter examines seven kinds of argument for one or other status of the universality of phonological constraints. These are the arguments from empirical
Reichenbach’s notion of common cause
, 2008
"... On Reichenbach’s common cause principle and ..."
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Characterizing common cause closed probability spaces
, 2010
"... A classical probability measure space was defined in earlier papers [14], [9] to be 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 classical probability measure space is common cause incomplete if ..."
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A classical probability measure space was defined in earlier papers [14], [9] to be 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 classical probability measure space is common cause incomplete if and only if it contains more than one atom. Furthermore, it is shown that every probability space can be embedded into a common cause closed one; which entails that every classical probability space is common cause completable with respect to any set of correlated events. 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.
1 Common Cause Abduction: Its Scope and Limits
"... ABSTRACT: This article aims to analyse the scope and limits of common cause abduction which is a version of explanatory abduction based on Hans Reichenbach’s Principle of the Common Cause. First, it is argued that common cause abduction can be regarded as a rational mechanism for inferring abductive ..."
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ABSTRACT: This article aims to analyse the scope and limits of common cause abduction which is a version of explanatory abduction based on Hans Reichenbach’s Principle of the Common Cause. First, it is argued that common cause abduction can be regarded as a rational mechanism for inferring abductive hypotheses that aim to account for the surprising correlations of events. Three arguments are presented in support of common cause abduction: the argument from screeningoff, the argument from likelihood, and the argument from simplicity. Second, it is claimed that common cause abduction is a defeasible reasoning, i.e., common cause abductive hypotheses are not always more plausible than separate cause abductive hypotheses. Finally, it is outlined what factors should be taken into account in order to use common cause abduction in a reasonable way.
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 partic ..."
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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. 1 The problem and informal review of results Let T be a theory formal part of which contains classical probability theory (S, p), where S is a Boolean algebra of sets representing random events (with Boolean operations ∪,∩,⊥) and