Online research in philosophy

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

Department of Computer Science, University of California, Los Angeles, Los Angeles, CA 90095, USA judea{at}cs.ucla.edu' + u + '@' + d + ''//--> We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account. Introduction Causal models: a review 2.1 Causal models 2.2 Syntax and semantics (...) The definition of cause Examples A more refined definition Discussion AAppendix: Some Technical Issues A.1 The active causal process A.2 A closer look at AC2(b) A.3 Causality with infinitely many variables A.4 Causality in nonrecursive models. (shrink)

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback-less) models are considered. Composition and effectiveness also hold in Lewis's closest-world semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not (...) in Lewis's closest-world semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...) which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

According to common judicial standard, judgment in favor ofplaintiff should be made if and only if it is more probable than not thatthe defendant''s action was the cause for the plaintiff''s damage (or death). This paper provides formal semantics, based on structural models ofcounterfactuals, for the probability that event x was a necessary orsufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient)causation can be learned from statistical data, and (...) shows how data fromboth experimental and nonexperimental studies can be combined to yieldinformation that neither study alone can provide. Finally, we show thatnecessity and sufficiency are two independent aspects of causation, andthat both should be invoked in the construction of causal explanations for specific scenarios. (shrink)

UCLA Cognitive Systems Laboratory, Technical Report (R-321), June 2005. In Proceedings of International Joint Conference on Artificial Intelligen ce, Edinburgh, Scotland, August 2005.

IN THE PAPER THERE IS AN ATTEMPT TO ESTABLISH THE FOLLOWING THREE PROPOSITIONS: (1) THE CONCEPT OF MIRACLE IS NOT DEFECTIVE; (2) MIRACLES ARE NOT OBSTACLES TO SCIENTIFIC PROGRESS; (3) THE BEST EXPLANATION FOR THE OCCURRENCE OF CERTAIN RADICAL ANOMALOUS EVENTS IS THAT THE AGENCY OF A SUPERNATURAL BEING WAS PART OF THEIR CAUSE. THE ARGUMENT IS NOT INTENDED TO PROVE GOD’S EXISTENCE FROM MIRACLES, BUT ONLY THAT THERE ARE NO "A PRIORI" OBSTACLES TO SUCH A PROOF. THERE COULD BE (...) AMPLE HISTORICAL DOCUMENTATION OR ARCHAEOLOGICAL TRACES TO WARRANT AN INFERENCE THAT MIRACLES HAD TAKEN PLACE, AND THUS PROVING THEISM. (shrink)

This article formulates institutional virtues according to sustainable development (SD) criteria to come up with a paradigmatic set of corporate principles. It aims to answer how a corporation might obtain competitive advantage by combining "going ethical" with "going green." On the one hand, it brings out facts that indicate a forthcoming trend inclined to force relevant actors to comply with SD requirements. On the other hand, it suggests that SD may be implemented as a strategy to gain competitive advantage by (...) the help of the PEARL model through its five fundaments: (1) perception friendliness, (2) environment friendliness, (3) action, (4) relationship, and (5) locality. This article finally shows that although a number of companies (e.g., Bosch, BP, and GE) implement SD as a tool of differentiation, they lack a holistic model that is fully responsive to current dynamics. The PEARL may be implemented as a proactive positioning to gain competitive advantage because transformation of this model into corporate strategy does not only respond to "stakeholder" claims, but also meets the changing characteristic of "societal demands.". (shrink)

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. (...) This, we argue, suggests that Pearl’s logic is either too weak or too strong. (shrink)

Its author was a Carthusian monk. Offered here is a translation, with annotation and an important introduction, of the four books on natural philosophy, the predecessor of modern science.

This book is a compilation of some of the wise sayings of M Fethullah Gülen, each of which is a criterion or pearl of wisdom by which we may seek and find our way in todays world, or a light illuminating our way, to live as a responsible ...

Manipulablity theories of causation, according to which causes are to be regarded as handles or devices for manipulating effects, have considerable intuitive appeal and are popular among social scientists and statisticians. This article surveys several prominent versions of such theories advocated by philosophers, and the many difficulties they face. Philosophical statements of the manipulationist approach are generally reductionist in aspiration and assign a central role to human action. These contrast with recent discussions employing a broadly manipulationist framework for understanding causation, (...) such as those due to the computer scientist Judea Pearl and others, which are non-reductionist and rely instead on the notion of an intervention. This is simply an appropriately exogenous causal process; it has no essential connection with human action. This interventionist framework manages to avoid at least some of these difficulties faced by traditional philosophical versions of the manipulability theory and helps to clarify the content of causal claims. (shrink)

The evidence from randomized controlled trials (RCTs) is widely regarded as supplying the 'gold standard' in medicine-we may sometimes have to settle for other forms of evidence, but this is always epistemically second-best. But how well justified is the epistemic claim about the superiority of RCTs? This paper adds to my earlier (predominantly negative) analyses of the claims produced in favour of the idea that randomization plays a uniquely privileged epistemic role, by closely inspecting three related arguments from leading contributors (...) to the burgeoning field of probabilistic causality-Papineau, Cartwright and Pearl. It concludes that none of these further arguments supplies any practical reason for thinking of randomization as having unique epistemic power. (shrink)

This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be suffcient (...) to establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

This chapter addresses two questions: what are causal relationships? how can one discover causal relationships? I provide a survey of the principal answers given to these questions, followed by an introduction to my own view, epistemic causality, and then a comparison of epistemic causality with accounts provided by Judea Pearl and Huw Price.

In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewis’s well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is (...) the weakest logic of causal counterfactuals that respects Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s. (shrink)

We critically examine Denis Walsh’s latest attack on the causalist view of fitness. Relying on Judea Pearl’s Sure-Thing Principle and geneticist John Gillespie’s model for fitness, Walsh has argued that the causal interpretation of fitness results in a reductio. We show that his conclusion only follows from misuse of the models, that is, (1) the disregard of the real biological bearing of the population-size parameter in Gillespie’s model and (2) the confusion of the distinction between ordinary probability and (...) class='Hi'>Pearl’s causal probability. Properly understood, the models used by Walsh do not threaten the causalist view of fitness. (shrink)

Nancy Cartwright offers an account of causal powers, and argues that it explains some important general features of scientific method. Patricia Cheng argues that this theory is superior as a psychological theory of learning to standard models of conditioning. I extend and develop the theory, and argue that it provides the best explanation of a number of problem cases for philosophical theories of causation, including preemption, overdetermination and puzzles about transitivity. Hitchcock and Halpern & Pearl on ‘actual causes’ Problems (...) and morals 2.1 Puzzles about prevention 2.2 Counterfactuals Causal powers 3.1 Generative causal power 3.2 Preventative causal power Net and component powers ‘Actual’ or ‘successful’ causes Solutions to puzzle cases Conclusion. (shrink)

Judea Pearl (2000) has recently advanced a theory of token causation using his structural equations approach. This paper examines some counterexamples to Pearl's theory, and argues that the theory can be modified in a natural way to overcome them.

Probability theory is important because of its relevance for decision making, which also means: its relevance for the single case. The propensity theory of objective probability, which addresses the single case, is subject to two problems: Humphreys’ problem of inverse probabilities and the problem of the reference class. The paper solves both problems by restating the propensity theory using (an objectivist version of) Pearl’s approach to causality and probability, and by applying a decision-theoretic perspective. Contrary to a widely held (...) view, decision making on the basis of given propensities can proceed without a subjective-probability supplement to propensities. (shrink)

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl (2000) to formalize a (...) causal notion of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman(1976) and Kratzer(1979) will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)

We present a probabilistic extension to active path analyses of token causation (Halpern & Pearl 2001, forthcoming; Hitchcock 2001). The extension uses the generalized notion of intervention presented in (Korb et al. 2004): we allow an intervention to set any probability distribution over the intervention variables, not just a single value. The resulting account can handle a wide range of examples. We do not claim the account is complete --- only that it fills an obvious gap in previous active-path (...) approaches. It still succumbs to recent counterexamples by Hiddleston (2005), because it does not explicitly consider causal processes. We claim three benefits: a detailed comparison of three active-path approaches, a probabilistic extension for each, and an algorithmic formulation. (shrink)

In 2003, the Combined Code emphasised two important aspects of Board contribution: the importance of induction for newly appointed Public Limited Company (PLC) board members, and appropriate training and development for all directors serving on a PLC board and its delegated committees, including the Audit and Remuneration Committees. This paper explores the principles of good induction and re-induction programmes for boards of directors and trustees, and its conclusions draw on the author's previous research on non-executive contribution (Long, 2004; Long et (...) al., 2005) and her recent experience of reviewing board and committee performance and effectiveness through Boardroom Review. (shrink)

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal (...) is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z +. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL. (shrink)

Belief revision theory aims to describe how one should change one’s beliefs when they are contradicted by newly input information. The guiding principle of belief revision theory is to change one’s prior beliefs as little as possible in order to maintain consistency with the new information. Learning theory focuses, instead, on learning power: the ability to arrive at true beliefs in a wide range of possible environments. The goal of this paper is to bridge the two approaches by providing a (...) learning theoretic analysis of the learning power of belief revision methods proposed by Spohn, Boutilier, Darwiche and Pearl, and others. The results indicate that learning power depends sharply on details of the methods. Hence, learning power can provide a well-motivated constraint on the design and implementation of concrete belief revision methods. (shrink)

This paper extends the account of actual causation offered by Halpern and Pearl [2005]. We show that this account yields the wrong judgment in certain classes of cases. We offer a revised definition that incorporates consideration of defaults, typicality, and normality. The revised definition takes actual causation to be both graded and comparative. We then apply our definition to a number of cases.

Artificial Intelligence (AI) and Philosophy of Science share a fundamental problem—that of understanding causality. Bayesian network techniques have recently been used by Judea Pearl in a new approach to understanding causality and causal processes (Pearl, 2000). Pearl’s approach has great promise, but needs to be supplemented with an explicit account of causal interaction. Thus far, despite considerable interest, philosophy has provided no useful account of causal interaction. Here we provide one, employing the concepts of Bayesian networks. With (...) it we demonstrate the failure of one of philosophy’s more sophisticated attempts to deal with the concept of causal interaction, that of Ellery Eells’ Probabilistic Causality (1991). (shrink)

Libet, Gleason, Wright, & Pearl (1983) asked participants to report the moment at which they freely decided to initiate a pre-specified movement, based on the position of a red marker on a clock. Using event-related potentials (ERPs), Libet found that the subjective feeling of deciding to perform a voluntary action came after the onset of the motor “readiness potential,” RP). This counterintuitive conclusion poses a challenge for the philosophical notion of free will. Faced with these findings, Libet (1985) proposed (...) that conscious volitional control might operate as a selector and a controller of volitional processes rather than as an initiator of them. (shrink)

if and only if for every W in V, W is independent of the set of all its non-descendants conditional on the set of its parents. One natural question that arises with respect to DAGs is when two DAGs are “statistically equivalent”. One interesting sense of “statistical equivalence” is “d-separation equivalence” (explained in more detail below.) In the case of DAGs, d-separation equivalence is also corresponds to a variety of other natural senses of statistical equivalence (such as representing the same (...) set of distributions). Theorems characterizing d-separation equivalence for directed acyclic graphs and that can be used as the basis for polynomial time algorithms for checking d-separation equivalence were provided by Verma and Pearl (1990), and Frydenberg (1990). The question we will examine is how to extend these results to cases where a DAG may have latent (unmeasured) variables or selection bias (i.e. some of the variables in the DAG have been conditioned on.) D-separation equivalence is of interest in part because there are algorithms for constructing DAGs with latent variables and selection bias that are based on observed conditional independence relations. For this class of algorithms, it is impossible to determine which of two d-separation equivalent causal structures generated a given probability distribution, given only the set of conditional independence and dependence relations true of the observed distribution. We will describe a polynomial (in the number of vertices) time algorithm for determining when two DAGs which may have latent variables or selection bias are d-separation equivalent. (shrink)

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. (...) We show that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

The American Journal of Bioethics, Volume 12, Issue 9, Page 26-28, September 2012.

A fundamental question in causal inference is whether it is possible to reliably infer the manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most commonly discussed frequentist notions are pointwise consistency and uniform consistency (see, e.g. Bickel, Doksum [2001]). Uniform consistency is in general preferred to pointwise consistency because the former allows us to control the worst case error bounds with a finite sample size. In the sense (...) of pointwise consistency, several reliable causal inference algorithms have been established under the Markov and Faithfulness assumptions [Pearl 2000, Spirtes et al. 2001]. In the sense of uniform consistency, however, reliable causal inference is impossible under the two assumptions when time order is unknown and/or latent confounders are present [Robins et al. 2000]. In this paper we present two natural generalizations of the Faithfulness assumption in the context of structural equation models, under which we show that the typical algorithms in the literature are uniformly consistent with or without modifications even when the time order is unknown. We also discuss the situation where latent confounders may be present and the sense in which the Faithfulness assumption is a limiting case of the stronger assumptions. (shrink)

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend (...) on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004 ) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief. (shrink)

There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...) are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

Artificial Intelligence (AI) and Philosophy of Science share a fundamental problem—understanding causality. Bayesian networks have recently been used by Judea Pearl in a new approach to understanding causality (Pearl, 2000). Part of understanding causality is understanding causal interaction. Bayes nets can represent any degree of causal interaction, and researchers normally try to limit interactions, usually by replacing the full CPT with a noisy-OR function. But we show that noisy-OR and another common model are merely special cases of the (...) general linear systems definition of noninteraction. However, they apply in different situations, and we can measure the degree of causal interaction relative to any such model. (shrink)

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...) that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)

Over the last two decades, philosophers, statisticians, and computer scientists have converged on the fundamental outline of a theory of causal representation and causal inference (Spirtes, Glymour, and Scheines, 2000; Pearl, 2000). Some conditions and assumptions under which reliable inference about the effects of manipulations is possible have been precisely characterized; other conditions and assumptions under which reliable inference about the effects of manipulation is impossible have also been characterized. However, the theory of inference about the effects of manipulations (...) that has been developed does not consider the problem of “defined variables”. In causal modeling, sometimes variables are deliberately introduced as defined functions of others variables. More interestingly, sometimes two or more measured variables are deterministic functions of one another, not deliberately, but because of redundant measurements. In these cases, manipulation of an observed defined variable may actually be an ambiguous description of a manipulation of some underlying variables, although the manipulator does not know that this is the case. In this article we revisit the question of precisely characterizing conditions and assumption under which reliable inference about the effects of manipulations is possible, even when the possibility of “ambiguous manipulations” is allowed. (shrink)

In recent papers we have described a framework for inferring causal structure from relations of statistical independence among a set of measured variables. Using Pearl's notion of the perfect representation of a set of independence relations by a directed acyclic graph we proved..

The framework of causal Bayes nets, currently influential in several scientific disciplines, provides a rich formalism to study the connection between causality and probability from an epistemological perspective. This article compares three assumptions in the literature that seem to constrain the connection between causality and probability in the style of Occam's razor. The trio includes two minimality assumptions—one formulated by Spirtes, Glymour, and Scheines (SGS) and the other due to Pearl—and the more well-known faithfulness or stability assumption. In terms (...) of logical strength, it is fairly obvious that the three form a sequence of increasingly stronger assumptions. The focus of this article, however, is to investigate the nature of their relative strength. The comparative analysis reveals an important sense in which Pearl's minimality assumption is as strong as the faithfulness assumption and identifies a useful condition under which it is as safe as SGS's relatively secure minimality assumption. Both findings have notable implications for the theory and practice of causal inference. 1 Introduction2 Background: Inference of Causal Structure in Markovian Causal Models3 Three Assumptions of Simplicity4 A Comparison of P-minimality and Faithfulness5 A Comparison of P-minimality and SGS-minimality6 Methodological Formulations and Prior Knowledge of Causal Order7 Conclusion. (shrink)

In this paper, I want to substantiate three related claims regarding causal discovery from non-experimental data. Firstly, in scientific practice, the problem of ignorance is ubiquitous, persistent, and far-reaching. Intuitively, the problem of ignorance bears upon the following situation. A set of random variables V is studied but only partly tested for (conditional) independencies; i.e. for some variables A and B it is not known whether they are (conditionally) independent. Secondly, Judea Pearl’s most meritorious and influential algorithm for causal (...) discovery (the IC algorithm) cannot be applied in cases of ignorance. It presupposes that a full list of (conditional) independence relations is on hand and it would lead to unsatisfactory results when applied to partial lists. Finally, the problem of ignorance is successfully treated by means of ALIC, the adaptive logic for causal discovery presented in this paper. (shrink)

The introduction of statistical models represented by directed acyclic graphs (DAGs) has proved fruitful in the construction of expert systems, in allowing efficient updating algorithms that take advantage of conditional independence relations (Pearl, 1988, Lauritzen et al. 1993), and in inferring causal structure from conditional independence relations (Spirtes and Glymour, 1991, Spirtes, Glymour and Scheines, 1993, Pearl and Verma, 1991, Cooper, 1992). As a framework for representing the combination of causal and statistical hypotheses, DAG models have shed light (...) on a number of issues in statistics ranging from Simpson’s Paradox to experimental design (Spirtes, Glymour and Scheines, 1993). The relations of DAGs with statistical constraints, and the equivalence and distinguishability properties of DAG models, are now well understood, and their characterization and computation involves three properties connecting graphical structure and probability distributions: (i) a local directed Markov property, (ii) a global directed Markov property, (iii) and factorizations of joint densities according to the structure of a graph (Lauritizen, et al., 1990). (shrink)

Benj. R. Tucker, the business partner and confrère of E. H. Heywood of Princeton, Mass., has translated and published, in an elegant volume of nearly 500 royal octavo pages, the most renowned of the politico-economical works of the justly celebrated P. J. Proudhon. The title of the work in English is: What is Property? An Inquiry into the Principle of Right and of Government. I am (...) requested to write a review-notice of the work. The temptation is strong to expand into au exhaustive review, but I am not certain of any avenue to the public for such a treatise, and I shall confine myself to the smaller plan. First, as to what is usually put last. The volume as a book is superb. Print, presswork, paper, and binding are at the top of the powers of the bookmaking art, and the price ($3.50, or $6.50, according to style) is not excessive. The work of the translator is also conscientiously and well done, and is nearly faultless from the literary point of view. A few Gallicisms may be pointed out, but they are exceptionally few, and the translator's personality is completely sunk in the labor of love which he evidently had before him. (shrink)

No one lives in a cocoon. Instead, the world constantly invades our lives. In response, we give purpose to these invasions. The image, here, is that of a pearl. What is the purpose of a pearl? The pearl is the oyster’s gift to a grain of sand that gets inside the oyster and disturbs it. Of all the gifts we can give, the greatest is the gift of purpose. It is the pearl of great price. All (...) other gifts are ornaments and baubles. A quite different view of purpose is common. According to this view, the invasions of life come with purposes already attached, and our job is to discover those purposes and reconcile ourselves to them. The image, here, is that of a coin. The coin is an instrument for exchange, and its purpose is predefined. Confronted with a coin, we can be ignorant of its purpose or we can consent to it. But, strictly speaking, we cannot rebel against its purpose: in the very act of rebellion, we tacitly consent to it. The problem with this second view is not that it is wrong but that it is incomplete. Where it applies, it presupposes the first view, because even things like coins do not have their purpose intrinsically but as a gift (in this case, from the national treasury). But, more significantly, very little in life has a predefined purpose. To be sure, most things in life occur against a backdrop of purposes. But just as a house composed of bricks is itself not a brick, so an event that occurs against a backdrop of purposes need not itself have a purpose. For instance, a business that goes bankrupt resides in a socioeconomic context chock-full of purposes (the underlying monetary instruments, trading conventions, and contractual understandings are all purpose-driven). But the merchant whose business goes bankrupt cares little about what purposes apply to business life in general. Nor is the 1 merchant’s ultimate concern with the precise reasons why the business went bankrupt. Even if a compelling, rational explanation can be given for why the business failed (mismanagement, unforeseen new technologies, sabotage, etc.), this doesn’t answer the deeper, existential questions of meaning and purpose that invariably arise when things don’t go our way.. (shrink)

What happened in New York City on September 11, 2001, creates an urgent need for a turn to practical reason, to ethics, to critique, and to a radical,transformative theory and praxis. Contemplation, speculation, pure theory, and contemplative metaphysics in philosophy, while necessary and valuable, are notsufficient in dealing with such an infamous crime against humanity. The central idea running through this paper and much of my work is that there is an essentiallink between rationality and radicalism. The aim of this (...) paper is to explore this link in an argument sketched in three parts: self-appropriation as the pearl of great price in philosophy; a critical theory of society; and a metaphysics and philosophy of religion that are both contemplative and political — a threefold radicality, if you like. This argument seeks to show negatively how the postmodern critique of rationality misfires, and positively how a post-imperial phenomenology, critical theory, and metaphysics/philosophy of religion can do justice to and recognize difference and the otherness of nature, other human beings (especially the exploited and marginalized), being itself, and God.Because in Vietnam the vision of a burning Babeis multiplied, multiplied, the flesh on firenot Christ’s, as Southwell saw it, prefiguringthe Passion upon the Eve of Christmas,but wholly human and repeated, repeated,infant after infant, their names forgotten,their sex unknown in the ashesset alight, flaming but not vanishingnot vanishing as his vision but lingering,cinders upon the earth or living onmoaning and stinking in hospitals three abed;because of this my strong sight,my clear caressive sight, my poet’s sight I was giventhat it might stir me to songis blurredWhy do men then not wreck his rod?Generations have trod, have trod, have trodAnd all is seared with trade, bleared, smeared with toilAnd wears man’s smudge and shares man’s smell, the soilIs bare now, nor can foot feel, being. (shrink)

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These (...) results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)