Concrete Causation About the Structures of Causal Knowledge Inaugural-Dissertation zur Erlangung des Doktorgrades der Philosophie an der Ludwig-Maximilians-Universität München vorgelegt von Roland Poellinger, München http://logic.rforge.com Referent: Prof. Dr. Godehard Link (Lehrstuhl für Philosophie, Logik und Wissenschaftstheorie, LMU München) Korreferent: Prof. Dr. Thomas Augustin (Institut für Statistik, LMU München) Tag der mündlichen Prüfung: 13.02.2012 I would like to thank the Alexander von Hum- boldt Foundation, which partially supported my work through funding the Munich Cen- ter for Mathematical Philosophy (MCMP) at LMU Munich. I am especially thankful to the LMU working group MindMapsCause, that has shaped many of my thoughts in valuable discussions. Title image: tommy leong/Fotolia.com, R. Poellinger Contents 1Reasoningaboutcausation 1 1.1 Causalpowers......................... 2 1.2 Causalprocesses ....................... 4 1.3 Natural experiments . 6 1.4 Logical reconstruction . 7 1.5 Correlation and probabilistic causation . 10 1.6 Counterfactual analysis . 14 1.7 Rankingtheory ........................ 19 1.8 Agency, manipulation, intervention . 22 1.9 Decisions to take . 28 2 Causation and causality: From Lewis to Pearl 33 2.1 What is a theory of causation about? . 33 2.2 Hume’s counterfactual dictum . 34 2.3 A possible worlds semantics with similarity . 36 2.4 From counterfactual dependence to veritable causes . 40 2.5 Pearl’s reply to Hume ................... 42 2.6 Pearl’sagenda........................ 43 2.7 From modeling to model . 54 2.8 Triggering causes, bringing about effects . 58 2.9 Computing observational data for causal inference . 62 2.10 About the identifiability of effects in causal models . 72 2.11 Singular causation and the actual cause . 78 3 Causality as epistemic principle of knowledge organization 85 3.1 The total system and the modality of interventions . 86 3.2 Subnets for epistemic subjects . 88 3.3 Organizing Data in causal knowledge patterns . 91 3.4 Causal knowledge patterns: design and manipulation . 95 3.5 Reviewing the framework . 113 viii Contents 4 Modelingwithcausalknowledgepatterns 115 4.1 Causal decision theory, or: Of prisoners and predictors . 115 4.2 Meaningful isomorphisms . 130 4.3 Epistemic contours and the Markov assumption, revisited 134 A Random variables (stochastic variables) 137 B Technicalities: Implications of d-separation 141 References 151 Register of names 157 Chapter 1 Reasoning about causation Felix qui potuit rerum cognoscere causas Vergil, Georgica (II, 490) Philosophers have been thinking systematically about cause and ef- fect since the very beginnings of philosophy as a discipline. Availing itself of mathematical methods and formal semantics in the last century, epistemology at once had the means to shape prevailing problems in sym- bolic form, express its achievements with scientific rigor, and sort issues within formal theories from questions about intuitions and basal pre- misses. David Lewis was among the first ones to utilize symbolic tools and approach causality within a framework of formal semantics.1 After Bertrand Russell had famously and brusquely turned his back on any further pursuit of establishing criteria for causal analysis in his treatise On the Notion of Cause (1913), David Lewis re-thought the words of an earlier mind: In 1740 David Hume had listed causation among one of the principles that are “to us the cement of the universe” and thus “of vast consequence [. ] in the science of human nature”.2 Hume gives various hints about what his account of causation might be – one way of read- ing suggests that he argues for an innate human causal sense by which we discover the relation of causation in our surroundings.3 Although Hume is later sharply criticized for this empiricist account by Immanuel Kant, who in turn claims that causal principles are of synthetic a priori 1Cf. especially [Lewis 1973a]. 2These statements are from An Abstract of a “Treatise of Human Nature”. 3Cf. [Garrett 2009]. 2 Reasoning about causation nature,4 David Lewis refers back to one specific counterfactual explica- tion of the semantics of causal statements in Hume’s writings, moreover bases his thoughts on Humean supervenience, and unfolds a detailed method for causal analysis in the framework of his possible worlds se- mantics. Approaching the field from a computer science perspective in the 1980s, Judea Pearl introduces networks of belief propagation as the basis for Bayesian inference engines in an AI engineering context.5 His interventionist account of causation, most elaborately presented in his book Causality (2000/2009), draws on structural transformations of formal causal models for the identification of cause-effect relations. As a defendant of a thicker concept of causation, Nancy Cartwright de- cisively rejects Pearl’s thin, formal approach and makes a case for a family-like understanding of causal concepts. In the following chapters the line of thought from Lewis to Pearl shall be traced, partly by examining their replies to one another, before I want to make the attempt to locate causation and causality in the ontological landscape and try to pave the way for an epistemic under- standing of the relation of causation, finally applying this conception to examples from recent and older philosophical literature. An overview on ways of implementation and applications of the suggested methods will conclude this text. Before getting into technical details, a short list of important approaches towards the analysis of causal concepts (and their most prominent advocates) shall be given – especially as a point of reference and distinction for what follows. What suggestions have fueled the philosophical discussion? 1.1 Causal powers One metaphysical approach towards causality, which has recently gained interest again, is the ascription of essential causal powers or capacities to objects of reality.6 As an answer to the Humean view of the world as consisting of distinct and discrete objects, causal powers theorists argue for the metaphysically real category of dispositions, which are necessar- ily separate from their token instantiations but at the same time linked to those instantiations of themselves through a necessary causal rela- tion. Before this background, powers are seen like enduring states with 4Cf. [Watkins 2009] or also [de Pierris & Friedman 2008]. 5Cf. e. g. [Pearl 1982]. 6Cf. for this and the following [Mumford 2009]. Reasoning about causation 3 the hidden disposition to objectively produce events or states by singu- larly contributing observable quantities to their manifestations – most times in combination with other contributing or also counteracting pow- ers. One question that arises within this framework seems to be the question about the nature of the connection between powers and their manifestations. Can one realistically postulate a certain disposition if it, for example, never manifests itself? And if one sees causation as an asymmetric relation, is there a way to understand the directedness of powers as necessary causal directedness from cause towards effect? Con- troversial questions seem to remain open as yet, but if powers of this sort are understood as basic building blocks of reality, one need not stick to events as relata of causal claims – e. g., explanations of equilibria (two stellar bodies orbiting one another at a stable distance and like exam- ples) are easily given by determining the contributions of each power to the situation under examination. And as Cartwright claims, gen- eral causal statements are best understood as compact statements about the capacities involved, as in “aspirins relieve headaches.”7 Finally, in distinction from other theories of causal relations, the main goal of the theory of causal powers is to say what and where causality really is, and – from the point of view of causal powers theorists – thus distances itself as a metaphysical enterprise from other theories that only settle for a description of the symptoms of (supposedly existing) actual causation. Another contribution to this line of reasoning was made by Karl Pop- per in 1959. Popper argues against the nowadays so popular subjective interpretation of probability in favor of an objective yet not frequentist interpretation of probability with dispositional character as “a property of the generating conditions”.8 He compares these propensities to phys- ical forces: I am inclined to accept the suggestion that there is an analogy between the idea of propensities and that of forces – especially fields of forces. But I should point out that although the labels ‘force’ or ‘propensity’ may both be psychological or anthropomor- phic metaphors, the important analogy between the two ideas does not lie here; it lies, rather, in the fact that both ideas draw atten- tion to unobservable dispositional properties of the physical world, and thus help in the interpretation of physical theory.9 7[Mumford 2009, p. 272] refers with this example to Cartwright’s Nature’s Capacities and Their Measurement (1989, Oxford: Clarendon). 8Cf. [Popper 1959, p. 34]. 9Cf. [Popper 1959, pp. 30–31]. 4 Reasoning about causation This view of (conditional) probabilities as causal dispositions has been famously criticized in 1985 by Paul Humphreys, who replies to Pop- per with a detailed illustration of an argument that shows how the determination of dependency between variables must fail for the propen- sity interpretation of probability – due to the fact that dependency is necessarily