York Hagmayer: Causal Bayes Nets in the Psychology of Causal Learning and Reasoning Theoretical Inspirations and Empirical Challenges

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1 Clark Glymour (Keynote Lecture): Brain Troubles Abstract: The brain is a natural device with parts, sub-parts, and sub-sub-parts influencing one another in various combinations and degrees to produce thought, emotion and action. It is a device we cannot experiment upon in any direct way except in the occasions of neuro-surgery, where discovery is not forbidden but systematic experimentation is. The development in the latter half of the 20th century of a variety of physical methods for indirect measurements of physiological processes in the brain opened the prospect of inferring aspects of brain function without penetrating human skulls. Until about a decade ago, these measurement methods were used almost exclusively to try to identify regions of the brain whose activity is characteristic of particular tasks or anomalies, without attempting to infer how in the course of a task various regions of the brain influence one another. In the last ten years the ambition has extended to attempts to determine some of the relevant causal connections. Challenging a long history of statistical shibboleths, these efforts push on the boundaries of what is possible with available computational and statistical methods. After introducing the background, this lecture will discuss some of the current statistical and computational methods that attempt to infer causal connections among brain regions from indirect physiological measurements chiefly fmri how they are tested, their limitations, their sensitivities to the processing of data, and open challenges. Frederick Eberhardt: The Search for Causes Abstract: On the basis of the causal Markov and faithfulness conditions causal Bayes nets provide an axiomatic framework for the development of causal discovery algorithms. The framework remains silent on the interpretation of a cause, but can (and is!) applied successfully in many scientific disciplines. With the possible exception of the Markov condition, all the assumptions of this framework have been varied, replaced or shown to be "non-essential" to causal discovery. As a result we have a set of axiomatic systems for causal discovery. If it is one thing that these systems of axioms characterize, what is it? To what extent can one maintain realist commitments to causation? Using a variety of examples I will argue that even at the level of medium-sized dry goods, Reichenbach's challenge of "coordination" between formal model and the real world exposes unexpected and, at least to me, uncomfortable features of the causal Bayes net framework. York Hagmayer: Causal Bayes Nets in the Psychology of Causal Learning and Reasoning Theoretical Inspirations and Empirical Challenges Abstract: Causal Bayes nets have been developed in philosophy, statistics and computer sciences to provide a formalism to represent causal structures, to infer causal structure from available evidence and to derive predictions for unobserved variables and the consequences of potential interventions (Glymour & Cooper, 1999; Spirtes, Glymour & Scheines, 1993, 2000). Within cognitive science causal Bayes nets are considered rational models of causal learning and reasoning (e.g., Griffiths & Tenenbaum, 2005, 2009). Within psychology causal Bayes nets have been used to derive predictions for experiments. They also inspired psychological theories of causal learning, reasoning and categorization (e.g., Gopnik, Glymour, et al., 2004;

2 Rehder, 2003; Sloman, 2005; Waldmann, 1996). These theoretical models assume that adults as well as children represent causal structures in terms of causal models or maps, which share at least some properties with causal Bayes nets. For example, both assume that only directed causal relations among causes and their immediate effects are represented. One crucial assumption made by causal Bayes nets is the Markov assumption, which informally states that variables are independent of other variables that are not their direct or indirect effects conditional on their immediate causes. Despite its importance, peopleʼs belief in the Markov assumption and its implications for relations of conditional independence within different causal structures has rarely been empirically investigated. Only in the last couple of years there is growing empirical evidence that people may not share the Markov assumption (e.g., Rehder & Burnett, 2005; Rottman & Hastie, subm.; Hagmayer & Waldmann, 2004; Walsh & Sloman 2008). They rarely perceive the two effects of a common cause to be conditionally independent or the last effect in a causal chain to be independent of the first cause conditional on the intermediate event. Given several causes of the same effect, they show limited discounting of a second cause after the presence of a first cause explaining an observed effect has been established. I will discuss some implications of these findings for causal Bayes nets as rational models and psychological theories of causal reasoning inspired by Bayes nets. Stephan Hartmann (with Jan Sprenger): New Solutions to the Old Evidence Problem Abstract: One of the most troubling and tenacious challenges for the Bayesian philosopher of science is the Problem of Old Evidence (Glymour 1980). The problem arises for anyone who wants to model belief revision and theory appraisal in science by means of Bayesian Conditionalization. This paper addresses the problem headon: We first discuss different varieties of the problem. Next we present those solution attempts where confirmation occurs through conditionalizing on the proposition that the theory T entails the evidence E. Apart from discussing the classical proposals by Garber (1983), Jeffrey (1983) and Niiniluoto (1983), we present our own model which improves upon the previous models in terms of parsimony, intuitive access and plauibsility of the assumptions. Finally, we present a second solution from a different modeling angle -- the relevant probability shift now occurs by learning the constraint p'(e T)=1, instead of by conditionalizing on a particular proposition. This proposal builds on an idea which Garber (1983) discusses under the label of an "evolving probability model", but he does not pursue it further and dismisses it rather quickly. Vera Hoffmann-Kolss: Actual Causation and Causal Intuitions Abstract: The philosophical debate on actual causation often follows what can be called a Socratic strategy of concept analysis. A definition of actual causation is proposed and shown to deliver intuitively correct results when applied to a number of cases. It is then confronted with possible intuitive counterexamples and revised if necessary. In several of his works, Clark Glymour argues that this strategy is not adequate for developing a philosophical account of actual causation (Glymour et al. 2010; Glymour and Wimberly 2007). The number of causal structures that would have to be considered in order to corroborate a proposed analysis by far exceeds the number of examples which can reasonably be surveyed. Moreover, if the causal

3 structures under consideration reach a certain degree of complexity, causal intuitions are not as uncontroversial as is often assumed. Glymour therefore favours a Euclidean approach, according to which philosophical theories of actual causation do not aim to give a strict definition of this notion, but have the form of formal axiomatic systems whose theorems provide informative or interesting insights about the concept of causation. In this paper, I raise a challenge for Euclidean theories of actual causation. One requirement on formal theories of actual causation is that they consider actual causation as a non-vague notion: once the events c and e are specified, the theory is supposed to provide a decision procedure answering the question whether c qualifies as an actual cause of e. I argue, however, that our intuitive notion of actual causation is vague and allows for borderline cases. This raises difficulties for current analyses of actual causation and calls the Euclidean strategy into question. References: Glymour, C., Danks, D., Glymour, B., Eberhardt, F., Ramsey, J., Scheines, R., Spirtes, P., Teng, C.M. and Zhang, J. (2010), 'Actual Causation: A Stone Soup Essay', Synthese 175: Glymour, C. and Wimberly, F. (2007), 'Actual Causes and Thought Experiments', in J.K. Campbell, M. O'Rourke and H.S. Silverstein (eds.), Causation and Explanation: MIT Press: Conor Mayo-Wilson: When is Clark Glymour's Brain like a Planet?: Causation on "Macro" and "Micro" scales Abstract: In a recent collaboration with Joseph Ramsey and others, Glymour (i) describes six problems that arise in causal inference from fmri data and (ii) develops a causal discovery algorithm, called IMaGES, that aims to minimize the six sources of error. Although Glymour and collaborators focus on brain troubles, I argue that the six problems arise for causal inference in a variety of microscopic systems, even those that occur in the social sciences. This suggests that, although the algorithm was developed for causal inference in neuroscience, IMaGES might be applicable in a variety of applied sciences. In the second half of the talk, I briefly outline a second approach to causal discovery at the micro-scale ; the approach is inspired by Glymourʼs work on mental causation, in which he suggests causal time series of macro- scopic aggregates of microscopic processes are the appropriate model for mental causation. Mental states may be aggregates of microscopic brain states, but clearly, the aggregation function is unknown. In contrast, in economics, the functional relationship between macroeconomic variables like gdp and micro-economic ones concerning firm spending is sometimes known. I suggest that, when such aggregation functions are known, causal discovery algorithms can be employed at the macro-scale level to yield non-trivial constraints on micro-scale causation. Paul Näger: Causal Unfaithfulness and Quantum Experiments Abstract: In his "Markov Properties and Quantum Experiments" Clark Glymour (2006) shows that experiments with entangled quantum objects are not compatible with the conjunction of the Causal Markov Condition and the Causal Faithfulness

4 Condition. He argues for a violation of the former because violations of the latter cannot be explained in usual ways. In this talk we further investigate the second horn of the dilemma. We argue, first, that if the Causal Markov Condition holds, every possible causal structure must violate faithfulness. Second, we show which of the known ways to violate faithfulness can explain the unfaithfulness of the quantum realm. Finally, we present two new kinds of unfaithfulness, which can correctly account for the situation. Our considerations make explicit that there are viable explanations of the unfaithfulness associated with entangled objects and that Glymour's second horn is a plausible way to understand causation in the quantum realm. Gerhard Schurz & Alexander Gebharter: Causality as a Theoretical Concept Abstract: In this paper we demonstrate that causality, if characterized by Spirtesʼ, Glymourʼs, and Scheinesʼ (1993) causal Markov and minimality conditions, satisfies recent standards for theoretical concepts. First of all, it explains two otherwise unexplainable statistical phenomena and, thus, can be justified as something ontologically real by an inference to the best (available) explanation (IBE). Secondly, we show that while these two axioms alone are empirically empty, adding principles of faithfulness, or time directedness, or intervention assumptions to these core axioms excludes certain logically possible probability distributions and, thus, produces an enriched theory of causality that possesses empirical content, on the basis of which not only particular causal models, but the general theory of causality as a whole becomes independently testable. Matthias Unterhuber: Does Formal Learning Theory Espouse Laws of Nature, Ceteris Paribus? Abstract: Kevin Kelly and Clark Glymour proposed formal learning theory as a framework for discovery problems in the sciences. I shall argue in this paper that despite that fact formal learning theory naturally gives one an account of laws of nature. I will contrast the resulting notion of laws of nature with alternative accounts of laws of nature, such as Lewisʼ Best System Analysis. I shall in particular inquire which role the notion of ceteris paribus hypotheses, as suggested by Glymour (2002), plays in that framework and in which way this notion of cp hypothesis relates to other accounts of cp laws in the literature References Glymour, C. (2002). A Semantics and Methodology for Ceteris Paribus Hypotheses. Erkenntnis, 57, Sylvia Wenmackers: On Glymourʼs Problem of Old Evidence: A New Theory for Theory Change Abstract: The problem of old evidence was first identified by Clark Glymour [1980] in his book Theory and Evidence. In the third chapter, Why I am not a Bayesian, Glymour considers Bayesian confirmation theory and investigates whether it is successful in helping us to understand scientific reasoning. He identified several shortcomings, one of which was the problem of old evidence / new theories. This

5 problem arises from the discrepancy between descriptive, historical examples, in which old evidence does seem to lend positive confirmation to new theories, and the normative, Bayesian position, in which old evidence cannot confirm new theories, because old evidence already has probability unity once the update rule based on conditionalization has been applied to it. Many later authors have called Glymourʼs problem simply the problem of old evidence. Both Garber [1983] and Jeffrey [1983] argued that the Bayesian background assumption of logical omniscience is too strong. Weakening the assumption should allow us to model agents that discover that the new theory entails the old evidence. Also Glymour [1980] observed that scientists are not perfect logicians and he believed this to be the relevant observation, but he doubted that this ʻsemirationalityʼ can be captured in the Bayesian framework. Another popular response is to introduce counterfactual degrees of belief. Both Christensen [1999] and Joyce [1999] considered a measure of confirmation that is equal to the difference between the probability of the hypothesis of interest, H, given the actual old evidence, E, minus the probability of this hypothesis, H, given the counterfactual assumption, E. As Glymour already argued, however, it is far from trivial to establish a historically accurate estimate of such counterfactual probabilities. A minority of philosophers have stressed the importance of the other side of the problem: the problem of new theories. Talbott [2008] summarizes it as follows: Suppose that there is one theory H 1 that is generally regarded as highly confirmed by the available evidence E. It is possible that simply the introduction of an alternative theory H 2 can lead to an erosion of H 1 's support. *...+This sort of change cannot be explained by conditionalization. Observe that the problem of new theories runs deeper than the problem of logical omniscience: even if the latter problem were solved, the former would remain. In joint work (in progress) with Jan-Willem Romeijn, we offer an analysis that proceeds in three parts: (1) New theories pose a problem for Bayesianism in itself, because they involve a language change, which requires a departure from the orthodox Bayesian approach. Of any alternative approach, we require that it be conservative in cases that do not involve theory change. Such an alternative framework was proposed by Romeijn [2005]. (2) Moreover, it is unclear that old evidence remains unchanged within the context of the new theory. Among other things, we aim to provide a precise model that illustrates Jeffreyʼs [1983] qualitative comment, uttered in response to the problem of old evidence: What is the ʻnew evidenceʼ on which we are to condition? (Remember: the senses are not telegraph lines on which the external world sends observation sentences for us to condition upon.) (3) Finally, we offer a conservative extension of the Bayesian framework that dissolves the composite problem of new theories and old evidence. In particular, our framework is compatible with Glymourʼs observation that in important historical examples old evidence does offer positive confirmation to new theories. Although Glymour had good reasons not to identify as a Bayesian in 1980, we are curious

6 whether he still objects to being a Bayesian (in the extended sense) in References [Christensen, 1999] D. Christensen, Measuring Confirmation, Journal of Philosophy 96 (1999) [Garber, 1983] D. Garber, Old evidence and logical omniscience in Bayesian confirmation theory, Minnesota studies in the philosophy of science, Vol. 10, University of Minnesota Press, Minneapolis (1983) [Glymour 1980] C. Glymour Why I am not a Bayesian, Chapter 3 in Theory and Evidence, Princeton University Press, Princeton (1980) pp [Jeffrey, 1983] R. Jeffrey, Bayesianism with a human face, Testing Scientific Theories, Minnesota Studies in the Philosophy of Science, Vol. 10, University of Minnesota Press, Minneapolis (1983) pp [Joyce, 1999] J. Joyce, The Foundations of Causal Decision Theory, Cambridge University Press, Cambridge (1999). [Romeijn 2005] J. W. Romeijn, Theory Change and Bayesian Statistical Inference, Philosophy of Science 72 (2005) [Talbott, 2008] W. Talbott, Bayesian Epistemology, Stanford Encyclopedia of Philosophy (2008).