In this important book, Ellery Eells explores and refines philosophical conceptions of probabilistic causality. In a probabilistic theory of causation, causes increase the probability of their effects rather than necessitate their effects in the ways traditional deterministic theories have specified. Philosophical interest in this subject arises from attempts to understand population sciences as well as indeterminism in physics. Taking into account issues involving spurious correlation, probabilistic causal interaction, disjunctive causal factors, and temporal ideas, Professor Eells advances (...) the analysis of what it is for one factor to be a positive causal factor for another. A salient feature of the book is a theory of token level probabilistic causation in which the evolution of the probability of a later event from an earlier event is central. This will be a book of crucial significance to philosophers of science and metaphysicians; it will also prove stimulating to many economists, psychologists, and physicists. (shrink)

After clarifying the probabilistic conception of causality suggested by Good (1961-2), Suppes (1970), Cartwright (1979), and Skyrms (1980), we prove a sufficient condition for transitivity of causal chains. The bearing of these considerations on the units of selection problem in evolutionary theory and on the Newcomb paradox in decision theory is then discussed.

This paper discusses Simpson's paradox and the problem of positive relevance in probabilistic causality. It is argued that Cartwright's solution to Simpson's paradox fails because it ignores one crucial form of the paradox. After clarifying different forms of the paradox, it is shown that any adequate solution to the paradox must allow a cause to be both a negative cause and a positive cause of..

John Dupré (1984) has recently criticized the theory of probabilistic causality developed by, among others, Good (1961-62), Suppes (1970), Cartwright (1979), and Skyrms (1980). He argues that there is a tension or incompatibility between one of its central requirements for the presence of a causal connection, on the one hand, and a feature of the theory pointed out by Elliott Sober and me (1983), on the other. He also argues that the requirement just alluded to should be given (...) up. I defend the theory against Dupré's criticisms and conclude with comments on Dupré's appraisal of the bearing of his arguments on the nature of probabilistic causal laws. (shrink)

It is possible for a causal factor to raise the probability of a second factor in some situations while lowering the probability of the second factor in other situations. Must a genuine cause always raise the probability of a genuine effect of it? When it does not always do so, an "interaction" with some third factor may be the reason. I discuss causal interaction from the perspectives of Giere's counterfactual characterization of probabilistic causal connection (1979, 1980) and the "contextual (...) unanimity" model developed by, among others, Cartwright (1979) and Skyrms (1980). I argue that the contextual unanimity theory must exercise care, in a new way that seems to have gone unnoticed, in order to adequately accommodate the phenomenon, and that the counterfactual theory must be substantially revised; although it will still, pending clarification of a second kind of revision, be unable to accommodate a kind of interaction exemplified in cases like those described by Sober (1982). (shrink)

In an earlier paper (Dupré 1984), I criticized a thesis sometimes defended by theorists of probabilistic causality, namely, that a probabilistic cause must raise the probability of its effect in every possible set of causally relevant background conditions (the "contextual unanimity thesis"). I also suggested that a more promising analysis of probabilistic causality might be sought in terms of statistical relevance in a fair sample. Ellery Eells (1987) has defended the contextual unanimity thesis against my (...) objections, and also raised objections of his own to my positive claims. In this paper I defend and amplify both my objections to the contextual unanimity thesis and my constructive suggestion. (shrink)

According to Nancy Cartwright, a causal law holds just when a certain probabilistic condition obtains in all test situations which in turn satisfy a set of background conditions. These background conditions are shown to be inconsistent and, on separate account, logically incoherent. I offer a corrective reformulation which also incorporates a strategy for problems like Hesslow's thrombosis case. I also show that Cartwright's recent argument for modifying the condition to appeal to singular causes fails.Proposed modifications of the theory's (...) class='Hi'>probabilistic condition to handle effects with extreme probabilities (0 or 1) are found unsatisfactory. I propose a unified solution which also handles extreme causes. Undefined conditional probabilities give rise to three good, but non-equivalent, ways of formulating the theory. Various formulations appear in the literature. I give arguments to eliminate all but one candidate. Finally, I argue for a crucial new condition clause, and show how to extend the results beyond a simple probabilistic framework. (shrink)

The main aim of this paper is to provide some probabilistic notions on causality proposed to be applied to the nomic statements which intend to give account of the indeterministic processes within the domain of a scientific theory. In general, such statements are, in more or less extent, idealized statements which rest on a variety of unrealistic suppositions. I try to show how the probability distribution over the final states of an indeterministic process changes accordingly as the nomic (...) statement in question is de-idealized by means of addition of the causally relevant factors. In order to illustrate the study I take few nomic statements from population genetics. Besides, in the course, I attempt to contrast the ideas embraced here with some of the notions of Humphreys´ ontic conceptions of causality and explanation, which are contrary to the epistemic view adopted here about those subjects. (shrink)

A formulation of probabilistic causality is given in terms of the theory of abstract dynamical systems. Causal factors are identified as invariants of motion of a system. Repetition of an experiment leads to the notion of stationarity, and causal factors yield a decomposition of the stationary probability law of the experiment into ergodic components. In these, statistical behaviour is uniform. Control of identified causal factors leads to a corresponding statistical law for the events, which is offered as a (...) notion of probabilistic causality. After a suggestion by Feller, randomization is identified as mixing, formulated in above terms. (shrink)

It is argued in this paper that although much attention has been paid to causal chains and common causes within the literature on probabilistic causality, a primary virtue of that approach is its ability to deal with cases of multiple causation. In doing so some ways are indicated in which contemporary sine qua non analyses of causation are too narrow (and ways in which probabilistic causality is not) and an argument by Reichenbach designed to provide a (...) basis for the asymmetry of causation is refined. The importance of referring causal claims to an abstract model is also emphasized. (shrink)

Using Bayesian network causal models, we provide a simple general account of probabilistic causal interaction. We also detail problems in the leading accounts by Ellery Eells, and any others which require valence reversals, contextual unanimity, or average effects.

The elements of structural models used in the social sciences are built up from four fundamental assumptions. It is then shown how the central idea of qualitative probabilistic causality follows as a special case of this covariational account. The relationships of both instrumentalism and common cause arguments for scientific realism to these structures is demonstrated. It is concluded that a predictivist argument against a thoroughgoing instrumentalism can be given, and hence why the difference between experimental and non-experimental contexts (...) is important to arguments for scientific realism. (shrink)

Probabilistic accounts of causality have long had trouble with ‘spurious’ evidential correlations. Such correlations are also central to the case for causal decision theory—the argument that evidential decision theory is inadequate to cope with certain sorts of decision problem. However, there are now several strong defences of the evidential theory. Here I present what I regard as the best defence, and apply it to the probabilistic approach to causality. I argue that provided a probabilistic theory (...) appeals to the notions of agency and effective strategy, it can avoid the problem of spurious causes. I show that such an appeal has other advantages; and argue that it is not illegitimate, even for a causal realist. (shrink)

The scheme of abstract dynamical systems will represent repetitive experimentation: There is a basic space of events X1 and the denumerable product … contains all possible sequences of events x = (x1, x2, … ). There are projections qn which give the nth member of x: qn (x) = xn. A transformation T is defined over X by the equation qn (Tx)= q n+1 (x). It removes the sequence by one step, T(x1,x2,…) = (x2,x3,…) and is known as the shift (...) transformation. It comes as an abstraction of the dynamical transformations of classical theories. Here it represents the performance of ‘the next’ experiment. (shrink)

This paper argues that if the world is irreducibly stochastic, then both Salmon's S-R model of explanation and Fetzer's C-R model of explanation have the following undesirable consequence: the objective probability (associated with the model's relevance condition) of any actual macro-event is either undefined or else, if defined, it equals one--so that the event is not even a candidate for a probabilistic explanation. This result follows from the temporal ambiguity of ontic probability in an irreducibly stochastic world. It is (...) argued further that an analogous difficulty faces those theories of probabilistic causality which depend upon the notions of contributing and counteracting causes. Because of the problem of temporal ambiguity, it is not possible to objectively label a particular event as a contributing (or a counteracting) cause of some subsequent event. The argument is carried through in detail for a recent theory of probabilistic causality proposed by Paul Humphreys. (shrink)

This article considers the popular thesis that a more proportional relationship between a cause and its effect yields a more abstract causal explanation of that effect, which in turn produces a deeper explanation. This thesis is taken to have important implications for choosing the optimal granularity of explanation for a given explanandum. In this article, I argue that this thesis is not generally true of probabilistic causal relationships. In light of this finding, I propose a pragmatic, interest-relative measure of (...) explanatory depth. This measure uses a decision-theoretic model of information pricing to determine the optimal granularity of explanation for a given explanandum, agent, and decision problem. (shrink)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, (...) but none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, (...) but none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

Comienzo este artículo mostrando que las teorías neohumeanas de la causalidad probabilista basadas en la noción de relevancia estadlstica (como la teoria de Suppes, 1970) se encuentran con múltiples e insuperables dificultades. Luego analizo brevemente algunas versiones de la causalidad probabilista que relativizan o prescinden de dicha noción: la de Cartwright, que postula la existencia de capacidades causales, y las de Salmon y Dowe, quienes, aunque se proponen no abandonar el suelo humeano, creen necesario introducir una ontología de propensiones. Y (...) concluyo que el análisis de estas versiones demuestra que la causalidad probabilista constituye un nuevo y serio obstáculo para el enfoque humeano o neohumeano de la causalidad.In this paper I first show that the neohumean theories of probabilistic causality based on the notion of statistical relevance (as that of Suppes, 1970) run into many and unsolvable difficulties. Then I briefty analyze some accounts of probabilistic causality which relativize or avoid this notion: the Cartwright’s account, claiming the existence of causal capacities, and those of Salmon and Dowe, though trying to remain on a Humean ground, believe that the introduction of an ontology of propensities is required. I finally conclude that the analysis of these accounts shows that probabilistic causality constitutes a new and serious obstacle to the Humean or neohumean view of causality. (shrink)

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump (...) in computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

Within the last decade a new crop of theories of probabilistic causality has taken root. While these theories differ from each other in small ways, the basic principles underlying them are the same. These common principles form what I call the received view of probabilistic causality. ;In the first four chapters of the dissertation I examine and criticize the work of three proponents of the received view: Nancy Cartwright, Ellery Eells, and Paul Humphreys. Due to a (...) number of epistemic and pragmatic problems that each of these theories face, I argue that they are inadequate theories of probabilistic causality. ;In chapter six I examine the minimal set of principles that underlie these three theories--the received view of probabilistic causality. I show that the received view is an inadequate basis for a theory of probabilistic causality. The central problem for the received view is due to the interpretation of probability that the received view adopts--a physical-propensity interpretation of the probability calculus. I show that there are four problems with using the propensity interpretation of probability in a theory of probabilistic causality. I also argue that a theory of probabilistic causality should use relative frequencies in place of propensities. ;In the final chapter of the dissertation, I sketch an epistemic theory of probabilistic causality that has a number of advantages over the received view. First, the epistemic theory takes seriously and responds to the epistemic and pragmatic problems raised against Cartwright, Eells, and Humphreys' theories of probabilistic causality. Second, the epistemic theory adopts a relative frequency interpretation of probability and avoids the problems associated with using a propensity interpretation of probability. Finally, the epistemic theory provides an account of how we can make justified inferences regarding causal relations. ;I support my theory with examples from contemporary medical science. In particular, I provide a detailed historical examination of the attempt by medical scientists to determine whether Helicobacter pylori is a causal factor for various forms of gastric illness. (shrink)

This paper examines a promising probabilistic theory of singular causation developed by David Lewis. I argue that Lewis' theory must be made more sophisticated to deal with certain counterexamples involving pre-emption. These counterexamples appear to show that in the usual case singular causation requires an unbroken causal process to link cause with effect. I propose a new probabilistic account of singular causation, within the framework developed by Lewis, which captures this intuition.