The common cause principle states that correlations have prior common causes which screen off those correlations. I argue that the common cause principle is false in many circumstances, some of which are very general. I then suggest that more restricted versions of the common cause principle might hold, and I prove such a restricted version.

In the paper it will be shown that Reichenbach’s Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ , respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of ${\mathcal{O}}_{a}$ and ${\mathcal{O}}_{b}$ (...) and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models. (shrink)

My Ph.D. dissertation written under the supervision of Prof. Tomasz Placek at the Institute of Philosophy of the Jagiellonian University in Kraków. In one of its most basic and informal shapes, the principle of the common cause states that any surprising correlation between two factors which are believed not to directly influence one another is due to their common cause. Here we will be concerned with a version od this idea which possesses a purely probabilistic (...) formulation. It was introduced, in the form of a general principle, by Hans Reichenbach in his posthumously published book "The Direction of Time". The central notion of the principle in Reichenbach's formulation, and of the current essay, is that of screening off: two correlated events are screened off by a third event if conditioning on the third event makes them probabilistically independent. Reichenbach's principle marks also the beginning of a new field of philosophy: namely, that of ``probabilistic causality''. For the most part, the current essay can be seen as an effort at checking how far one can go with the purely statistical notions revolving around Reichenbach's idea of common cause. In short, the answer is ``surprisingly far''; in some classes of probability spaces all correlations between ``interesting'' events possess explanations of such sort. However, this fact lends itself to opposing interpretations; more on that in the conclusion. Chapters 6 and 7 contain mathematical results concerning these issues. The screening-off condition requires an equality of a probabilistic nature to hold; chapter 8 is a short discussion of slightly weakened versions of the condition, which hold if the sides of the above mentioned equality differ to a small degree. In chapter 2, after some mathematical preliminaries, we study the various formulations of the principle which might be said to stem from the original idea of Reichenbach. We also examine a few of the most salient counterarguments, which undermine at least some of the formulations. Chapter 3 is of a formal nature, dealing with various probabilistic notions which can be thought of as generalizations of Reichenbach's concept of common cause. The next chapter concerns the relationship between the idea of common causal explanation and the Bell inequalities. In chapter 5 we briefly present the form of Reichenbach's principle which can be found in the field of representing causal structures by means of directed acyclic graphs. (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)

Reichenbach’s Common Cause Principle is the claim that if two events are correlated, then either there is a causal connection between the correlated events that is responsible for the correlation or there is a third event, a so called (Reichenbachian) common cause, which brings about the correlation. The paper reviews some results concerning Reichenbach’s notion of common cause, results that are directly relevant to the problem of how one can falsify Reichenbach’s Common (...) Cause Principle. Special emphasis will be put on the question of whether EPR-type correlations can have an explanation in terms of Reichenbachian common causes. Most of the results to be recalled indicate that falsifying Reichenbach’s Common Cause Principle is much more tricky than one may have thought and that, contrary to some claims in the literature, there is no conclusive proof yet that the EPR correlations predicted by ordinary, non-relativistic quantum mechanics cannot have a common cause; furthermore, recent results about possible Reichenbachian common causes of correlations predicted by quantum field states between spacelike separated local observable algebras in algebraic quantum field theory strongly indicate that there may very well exist Reichenbachian common causes of superluminal correlations predicted by quantum field theory. (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 Reichenbachs definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle. (shrink)

If $\mathcal{A}$ (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $\mathcal{A}$ (V 1 ), B∈ $\mathcal{A}$ (V 2 ) correlated in the normal state φ there exists (...) a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2 , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle. (shrink)

Reichenbach’s Common Cause Principle is the claim that if two events are correlated, then either there is a causal connection between the correlated events that is responsible for the correlation or there is a third event, a so called (Reichenbachian) common cause, which brings about the correlation. The paper reviews some results concerning Reichenbach’s notion of common cause, results that are directly relevant to the problem of how one can falsify Reichenbach’s Common (...) Cause Principle. Special emphasis will be put on the question of whether EPR-type correlations can have an explanation in terms of Reichenbachian common causes. Most of the results to be recalled indicate that falsifying Reichenbach’s Common Cause Principle is much more tricky than one may have thought and that, contrary to some claims in the literature, there is no conclusive proof yet that the EPR correlations predicted by ordinary, non-relativistic quantum mechanics cannot have a common cause; furthermore, recent results about possible Reichenbachian common causes of correlations predicted by quantum field states between spacelike separated local observable algebras in algebraic quantum field theory strongly indicate that there may very well exist Reichenbachian common causes of superluminal correlations predicted by quantum field theory. (shrink)

Despite the platitude that analytic philosophy is deeply concerned with language, philosophers of science have paid little attention to methodological issues that arise within historical linguistics. I broach this topic by arguing that many inferences in historical linguistics conform to Reichenbach's common cause principle (CCP). Although the scope of CCP is narrower than many have thought, inferences about the genealogies of languages are particularly apt for reconstruction using CCP. Quantitative approaches to language comparison are readily understood as (...) methods for detecting the correlations that serve as premises for common cause inferences, and potential sources of error in historical linguistics correspond to well-known limitations of CCP. (shrink)

The Common Cause Principle, stating that correlations are either consequences of a direct causal link between the correlated events or are due to a common cause, is assessed from the perspective of its viability and it is argued that at present we do not have strictly empirical evidence that could be interpreted as disconfirming the principle. In particular it is not known whether spacelike correlations predicted by quantum field theory can be explained by properly (...) localized common causes, and EPR correlations are known to be unexplainable only by common causes that are required to satisfy conditions that are empirically not tested. (shrink)

Reichenbach’s Common Cause Principle is the claim that if two events are correlated, then either there is a causal connection between the correlated events that is responsible for the correlation or there is a third event, a so called common cause, which brings about the correlation. The paper reviews some results concerning Reichenbach’s notion of common cause, results that are directly relevant to the problem of how one can falsify Reichenbach’s Common (...) class='Hi'>Cause Principle. Special emphasis will be put on the question of whether EPR-type correlations can have an explanation in terms of Reichenbachian common causes. Most of the results to be recalled indicate that falsifying Reichenbach’s Common Cause Principle is much more tricky than one may have thought and that, contrary to some claims in the literature, there is no conclusive proof yet that the EPR correlations predicted by ordinary, non-relativistic quantum mechanics cannot have a common cause; furthermore, recent results about possible Reichenbachian common causes of correlations predicted by quantum field states between spacelike separated local observable algebras in algebraic quantum field theory strongly indicate that there may very well exist Reichenbachian common causes of superluminal correlations predicted by quantum field theory. (shrink)

The Common Cause Principle, stating that correlations are either consequences of a direct causal link between the correlated events or are due to a common cause, is assessed from the perspective of its viability and it is argued that at present we do not have strictly empirical evidence that could be interpreted as disconfirming the principle. In particular it is not known whether spacelike correlations predicted by quantum field theory can be explained by properly (...) localized common causes, and EPR correlations are known to be unexplainable only by common causes that are required to satisfy conditions that are empirically not tested. (shrink)

The Common Cause Principle, stating that correlations are either consequences of a direct causal link between the correlated events or are due to a common cause, is assessed from the perspective of its viability and it is argued that at present we do not have strictly empirical evidence that could be interpreted as disconfirming the principle. In particular it is not known whether spacelike correlations predicted by quantum field theory can be explained by properly (...) localized common causes, and EPR correlations are known to be unexplainable only by common causes that are required to satisfy conditions that are empirically not tested. (shrink)

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V1) andA(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal (...) correlations predicted by the vacuum state between events inA(V1) andA(V2) have a genuinely probabilistic common cause, then the local algebrasA(V1) andA(V2) must be statistically independent in the sense of C*-independence. (shrink)

The Common Cause Principle was introduced by HansReichenbach, in The Direction of Time, which was publishedposthumously in 1956. Suppose that two events A and Bare positively correlated: p(A∩B)>p(A)p(B)p(A∩B)>p(A)p(B)p(A\textbackslashcap B)>p(A)p(B). Suppose,moreover, that neither event is a cause of the other. Then,Reichenbach’s Common Cause Principle (RCCP) states that Aand B will have a common cause that renders them conditionallyindependent. Reichenbach incorporated his RCCP into a new probablistictheory of causation, and used it to describe (...) a (purported)macrostatistical temporal asymmetry in analogy with the second law ofthermodynamics. The principle is significant because it posits aconnection between causal structure and probabilistic correlations,thus facilitating causal inference from observed correlations.However, RCCP has been controversial, and a number of counterexampleshave been proposed. RCCP is often seen as an antecedent of theCausal Markov Condition, which plays a central role in causalmodeling and causal inference. RCCP has also been taken to captureassumptions about the behavior of classical systems that appear to beviolated in quantum mechanics. (shrink)

Suppose that two geysers, about one mile apart, erupt at irregular intervals, but usually erupt almost exactly at the same time. One would suspect that they come from a common source, or at least that there is a common cause of their eruptions. And this common cause surely acts before both eruptions take place. This idea, that simultaneous correlated events must have prior common causes, was first made precise by Hans Reichenbach (Reichenbach 1956). It (...) can be used to infer the existence of unobserved and unobservable events, and to infer causal relations from statistical relations. Unfortunately it does not appear to be universally valid, nor is there agreement as to the circumstances in which it is valid. (shrink)

We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (RPCC) for genuinely indeterministic systems. We first argue that the RPCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological (...) claim. We briefly review the most entrenched or classical positions, including Salmon’s ‘interactive forks’, van Fraassen’s scepticism, and Cartwright’s generalisation of the fork criterion. We then go on to review the results of the ‘Budapest school’ on the existence of formally defined screening­ off events for any correlation —by means of the ideas of probability space extensibility and (Reichenbachian common cause) completability. We distinguish the Budapest doctrine clearly from any of the classical conceptions, and thus present an overall framework for discussions of causal inference in quantum mechanics. We argue that this review is preliminary essential work for a thorough assessment of the conditions under which RCCP may be a reliable tool for causal inference in a genuinely probabilistic (indeterministic) context. (shrink)

The Principle of Common Cause (PCC) puts forward the idea that events which occur simultaneously and are correlated have a prior common cause which screens off the correlation. I endorse the view that the PCC does qualify as a principle that can be used as a tool in explaining improbable coincidences. However, though there are epistemological advantages in common cause explanations of correlated events, the PCC is not impeccable. This paper offers a (...) preliminary assessment of the PCC advocated by Reichenbach, and then attempts to illustrate three scenarios in which the principle might be inadequate in explaining correlated events. The paper also compares the Common Cause Principle and the Causal Markov Condition (CMC), and examines the advantages of CMC over the Common Cause Principle. (shrink)

Anything other than paraphrasing the well-known Heraclitean aphorism would not be more appropriate to portray the crux of the contribution of the three philosophers of the Budapest School, Gábor Hofer-Szabó, Miklós Rédei and Lázló E. Szabó, in the ongoing discussion of the principle of the common cause . Indeed, ‘common causes love to hide’ and for that reason critics and aspirant falsifiers of PCC find correlations which, at a first level of analysis, might lack a (...) class='Hi'>common cause explanation. But as the authors argue such correlations do not amount to disconfirming evidence for the principle, since PCC does not specify where to search for a common cause of a correlation; it just states that there is one. PCC is neither falsifiable, nor verifiable; it is a metaphysical doctrine that can only be assessed for its plausibility in the light of theories of empirical science. This idea fosters the investigation of the existence of common causes of correlations in two fundamental physical t .. (shrink)

I present two relatively independent sets of remarks on common causes and the violation of Bell inequalities in algebraic quantum field theory. The first set of remarks concerns the possibility of reconciling Reichenbachian ideas on common causes with quantum field theory in the face of an already known difficulty: the event shown to satisfy statistical relations for being the common cause of two correlated events has been associated with the union, rather than the intersection, of the (...) backward light cones of the correlated events. I explore a way of overcoming this difficulty by considering the common cause to be a conjunction of suitably located events. But I show that this line of thought too is beset with interpretational problems. My second set of remarks concerns the type of inequality one may derive from the common-common cause hypothesis: I argue, on grounds of interpretation, that the Clauser-Horne type, and not the Bell type, of inequalities emerge more naturally in this context. (shrink)

The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the (...) common cause principle, by proving results that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field. (shrink)

Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbach’s groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter program—to take the probabilistic relationships constitutive of the principle of the common cause and (...) use them to ground the direction of causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scale—the worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) correlations in quantum mechanics. (shrink)

We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (PCC) for genuinely indeterministic systems. We first argue that the PCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological (...) claim. We briefly review the most entrenched or classical positions, including Salmon’s ‘interactive forks’, van Fraassen’s scepticism, and Cartwright’s generalisation of the fork criterion. We then go on to review the results of the ‘Budapest school’ on the existence of formally defined screening-off events for any correlation —by means of the ideas of probability space extensibility and (Reichenbachian common cause) completability. We distinguish the Budapest doctrine clearly from any of the classical conceptions, and thus present an overall framework for discussions of causal inference in quantum mechanics. The framework, however preliminary, is essential work for a thorough assessment of the conditions under which PCC may be a reliable tool for causal inference in a genuinely probabilistic (indeterministic) context. (shrink)

This paper deals with Hans Reichenbach's common cause principle. It was propounded by him in, and has been developed and widely applied by Wesley Salmon, e.g. in and. Thus, it has become one of the focal points of the continuing discussion of causation. The paper addresses five questions. Section 1 asks: What does the principle say? And section 2 asks: What is its philosophical significance? The most important question, of course, is this: Is the principle (...) true? To answer that question, however, one must first consider how one might one argue about it at all. One can do so by way of examples, the subject of section 3, or more theoretically, which is the goal of section 4. Based on an explication of probabilistic causation proposed by me in,, and, section 4 shows that a variant of the principle is provable within a classical framework. The question naturally arises whether the proved variant is adequate, or too weak. This is pursued in section 5. My main conclusion will be that some version of Reichenbach's principle is provably true, and others may be. This may seem overly ambitious, but it is not. The paper does not make any progress on essential worries about the common cause principle arising in the quantum domain; it only establishes more rigorously what has been thought to be plausible at least within a classical framework. (shrink)

We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause principle against certain attempts of (...) falsification. Some open problems concerning possible strengthening of the common cause completability result are formulated. (shrink)

Elliot Sober ([2001]) forcefully restates his well-known counterexample to Reichenbach's principle of the common cause: bread prices in Britain and sea levels in Venice both rise over time and are, therefore, correlated; yet they are ex hypothesi not causally connected, which violates the principle of the common cause. The counterexample employs nonstationary data—i.e., data with time-dependent population moments. Common measures of statistical association do not generally reflect probabilistic dependence among nonstationary data. I demonstrate (...) the inadequacy of the counterexample and of some previous responses to it, as well as illustrating more appropriate measures of probabilistic dependence in the nonstationary case. A challenge to the principle of the common causeSober's argument and the attempts to rescue the principleProbabilistic dependenceNonstationary time seriesProbabilistic dependence in nonstationary time seriesDo Venetian sea levels and British bread prices violate the principle of the common cause? (shrink)

There is no EPR-like funny business if (contrary to apparent fact)our world is as indeterministic as you wish, but is free from theEPR-like quantum mechanical phenomena such as is sometimes described interms of superluminal causation or correlation between distant events.The theory of branching space-times can be used to sharpen thetheoretical dichotomy between EPR-like funny business and noEPR-like funny business. Belnap (2002) offered two analyses of thedichotomy, and proved them equivalent. This essay adds two more, bothconnected with Reichenbachs principle of (...) the common cause, theprinciple that sends us hunting for a common-causal explanation ofdistant correlations. The two previous ideas of funny business and thetwo ideas introduced in this essay are proved to be all equivalent,which increases ones confidence in the stability of (and helpfulnessof) the BST analysis of the dichotomy between EPR-like funny businessand its absence. (shrink)

Nancy Cartwright believes that we live in a Dappled World– a world in which theories, principles, and methods applicable in one domain may be inapplicable in others; in which there are no universal principles. One of the targets of Cartwright’s arguments for this conclusion is the Causal Markov condition, a condition which has been proposed as a universal condition on causal structures.1 The Causal Markov condition, Cartwright argues, is applicable only in a limited domain of special cases, and thus cannot (...) be used as a universal principle in causal discovery. I have no dispute with any of these claims here. Rather, I wish to argue for a very limited thesis: that the Causal Markov condition is applicable in the specific domain of microscopic quantum mechanical systems; further, that the condition can fruitfully be applied to the much discussed EPR setup. This is perhaps a surprising conclusion, for it is precisely in this domain that Cartwright’s arguments against the Causal Markov condition have been considered to be the most successful. (shrink)

A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if (...) one weakens slightly Reichenbach's definition of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle. (shrink)

I consider the problem of extending Reichenbach's principle of the common cause to more than two events, vis-a-vis an example posed by Bernstein. It is argued that the only reasonable extension of Reichenbach's principle stands in conflict with a recent proposal due to Horwich. I also discuss prospects of the principle of the common cause in the light of these and other difficulties known in the literature and argue that a more viable version (...) of the principle is the one provided by Penrose and Percival (1962). (shrink)

In a recent article, Elliot Sober responds to challenges to a counter-example that he posed some years earlier to the Principle of the Common Cause (PCC). I agree that Sober has indeed produced a genuine counter-example to the PCC, but argue against the methodological moral that Sober wishes to draw from it. Contrary to Sober, I argue that the possibility of exceptions to the PCC does not undermine its status as a central assumption for methods that endeavor (...) to draw causal conclusions from statistical data. 1 The PCC and the counter-example 2 Making non-stationary time series stand still 3 Sober's alternative. (shrink)

The principle of common cause asserts that positive correlations between causally unrelated events ought to be explained through the action of some shared causal factors. Reichenbachian common cause systems are probabilistic structures aimed at accounting for cases where correlations of the aforesaid sort cannot be explained through the action of a single common cause. The existence of Reichenbachian common cause systems of arbitrary finite size for each pair of non-causally correlated events (...) was allegedly demonstrated by Hofer-Szabó and Rédei in 2006. This paper shows that their proof is logically deficient, and we propose an improved proof. (shrink)

The most serious candidates for common causes that fail to screen off and thus violate the causal Markov condition refer to quantum phenomena. In her seminal debate with Hausman and Woodward, Cartwright early on focussed on unfortunate non-quantum examples. Especially, Hausman and Woodward’s redescriptions of quantum cases saving the CMC remain unchallenged. This paper takes up this lose end of the discussion and aims to resolve the debate in favour of Cartwright’s position. It systematically considers redescriptions of ICC structures, (...) including those by Hausman and Woodward, and explains why these are inappropriate, when quantum mechanics is true. It first shows that all cases of purported quantum ICCs are cases of entanglement and then, using the tools of causal modelling, it provides an analysis of the quantum mechanical formalism for the case that the collapse of entangled systems is best described as a causal model with an ICC. (shrink)

The likelihood justification of cladistic parsimony suggested in Sober (1984) is here shown to be incomplete. Even so, cladistic parsimony remains a counter-example to the principle of the common cause formulated by Reichenbach (1956) and Salmon (1975, 1979, 1984).

The Principle of common cause has its significance in providing explanations of phenomena in terms of causal theories. Though the principle has its own epistemological advantages, there can be certain situations where the principle might fail. In the first part of the paper, I offer a preliminary assessment of the PCC and then I turn to make an attempt to illustrate those scenarios where the PCC might misguide us in providing explanation of phenomena in terms (...) of common cause. (shrink)

According to Reichenbach’s principle of common cause, positive statistical correlations for which no straightforward causal explanation is available should be explained by invoking the action of a hidden conjunctive common cause. Hofer-Szabó and Rédei’s notion of a Reichenbachian common cause system is meant to generalize Reichenbach’s conjunctive fork model to fit those cases in which two or more common causes cooperate in order to produce a positive statistical correlation. Such a generalization is (...) proved to be unsatisfactory in the light of a probabilistic conception of causation. Accordingly, an alternative model for systems of multiple common causes is offered, which is capable of emulating the explanatory efficacy of Reichenbachian common cause systems, while overcoming their major conceptual shortcomings at the same time. (shrink)

Sober (1984) has considered the problem of determining the evidential support, in terms of likelihood, for a hypothesis that is incomplete in the sense of not providing a unique probability function over the event space in its domain. Causal hypotheses are typically like this because they do not specify the probability of their initial conditions. Sober's (1984) solution to this problem does not work, as will be shown by examining his own biological examples of common cause explanation. The (...) proposed solution will lead to the conclusion, contra Sober, that common cause hypotheses explain statistical correlations and not matchings between event tokens. (shrink)

The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this study, an extended interpretation of the principle is proposed, according to which common causes should be invoked to explain positive correlations whose values depart from the ones that one would expect to obtain in accordance to her probabilistic expectations. In addition, a probabilistic model for common causes is tailored which satisfies the (...) generalized version of the principle, at the same time including the standard conjunctive-fork model as a special case. (shrink)

The aim of this article is to analyze the main contributions of Wesley C. Salmon to the philosophy of science, that is, his concepts of causation, common cause, and theoretical explanation, and to provide a critique of them. This critique will be based on a comparison of Salmon's concepts with categories developed by Hegel in his Science of Logic, and which can be applied to the issues treated by Salmon by means of the above given three concepts. It (...) is the author's contention that by means of Hegelian categories it becomes possible to provide a critique of Salmon's philosophy of science and at the same time to enlarge the concept framework of philosophy of science. (shrink)

This article aims to analyze 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 inferential mechanism that enables us to accept hypotheses that aim to account for the surprising correlations of events. Three arguments are presented in support of common cause abduction: the (...) argument from screening-off, 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. (shrink)

We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common (...) cause of the correlation. The main result we prove is that a quantum probability space is common cause closed if and only if it has at most one measure theoretic atom. This result improves earlier ones published in [1]. The result is discussed from the perspective of status of the Common Cause Principle. Open problems on common cause closedness of general probability spaces (L, ϕ) are formulated, where L is an orthomodular bounded lattice and ϕ is a probability measure on L. (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)

The common cause principle states that common causes produce correlations amongst their effects, but that common effects do not produce correlations amongst their causes. I claim that this principle, as explicated in terms of probabilistic relations, is false in classical statistical mechanics. Indeterminism in the form of stationary Markov processes rather than quantum mechanics is found to be a possible saviour of the principle. In addition I argue that if causation is to be (...) explicated in terms of probabilities, then it should be done in terms of probabilistic relations which are invariant under changes of initial distributions. Such relations can also give rise to an asymmetric cause-effect relationship which always runs forwards in time. (shrink)

When two causally independent processes each have a quantity that increases monotonically (either deterministically or in probabilistic expectation), the two quantities will be correlated, thus providing a counterexample to Reichenbach's principle of the common cause. Several philosophers have denied this, but I argue that their efforts to save the principle are unsuccessful. Still, one salvage attempt does suggest a weaker principle that avoids the initial counterexample. However, even this weakened principle is mistaken, as can (...) be seen by exploring the concepts of homology and homoplasy used in evolutionary biology. I argue that the kernel of truth in the principle of the common cause is to be found by separating metaphysical and epistemological issues; as far as the epistemology is concerned, the Likelihood Principle is central. (shrink)