Margherita Benzi Università S. Raffaele di Milano, University of Genoa (Italy)

1. Margherita Benzi Università S. Raffaele di Milano, University of Genoa (Italy) Contexts for Causal Models

2. Plan of the talk • Contrast two views of causality: • absolutistic view = causation is an absolute relation • relativistic view = causes are relative to contexts • Distinguish different kinds of contexts in causal models • Argue against the ‘absolutistic’ view

3. Relativistic positions: P. Suppes • What factors should be considered in investigating the causes of a certain effect? • “Perhaps one of the most puzzling and difficult aspects of the analysis of causality is the problem of how to handle the background that serves as a framework for the occurrence of the particular events under study. If, for example, we study the cause of a match lighting, to what extent must we consider meteorological conditions, the composition of the atmosphere, the absence of meteorites, etc.?” • Dependence on a ‘conceptual framework’: • With respect to one field, framework or background, one event may be a cause of another, and yet, when the field is changed and the framework is extended by the consideration of additional variables, the cause may turn out to be spurious.

4. Absolutistic positions: J. S. Mill • No real distinction between causes and conditions • The real cause is the whole of these antecedents; and we have, philosophically speaking, no right to give the name of cause to one of them exclusively of the others. • Nothing can better show the absence of any scientific ground for the distinction between the cause of a phenomenon and its conditions, than the capricious manner in which we select from among the conditions that which we choose to denominate the cause.

5. Types of Contexts [Hart and Honoré] • Context of Inquiry: different conceptual framework • Context of Occurrence: same conceptual framework, different ‘circumstances’

6. Probabilistic Causality • Test Situations (Cartwright) • Causal Background Contexts (Eells) • Context Unanimity requirement • Context Unanimity vs Objective Homogeneity [Twardy and Korb]

7. (Causal) Bayesian Nets • Relativity wrt the choice of possibly relevant variables (context of inquiry) • Relativity wrt variables in the DAG [‘V’] • Background causal field in bayesian Network: partial reductionism

8. Causal Nets • Background Context In assessing the causal role of X relative to Y, the appropriate background context consists of all variables which are • Direct parents of Y or of any intermediate variable between X and Y, and • Non-descendants of X.

9. A1 A2 A3 A4 A5 Variable A1: Season of the year, valuesspring, summer, fall, winter Variable A2: Rainfall during the season, valuesyes, no Variable A3: Sprinkler during the season, valueson, off Variable A4: Wet pavement, valuesyes, no VariableA5: Slippery pavement, valuesyes, no The standard example

10. Circularity and Reduction • Circularity can eliminated in the model but it can still be present in the considerations that orient the choice of variables (context of Inquiry) • If we eliminate the dependence from the context of Inquiry, we obtain a complete reduction of causes to probabilities

11. Reductionism and Absolutism:The All Embracing Causal Net • Failures of faithfulness can disappear in a more fine-grained description of the domain [Papineau 2001] • Metaphysical Assumption: Nature is not “conspiratorial” • Causal relationships at higher level are fixed by those at the lowest level. Patterns of correlation can thus be misleading about causal structure at any higher level. • But at the bottom level there is no metaphysical room for such failures of faithfulness, since there the causal order is simply constituted by the correlational order. • Causal structures are determined by an extremely rich underlying network of correlations, from which God can read off the causal facts • What if there is no lowest level, if there is no limit to how fine we can cut up our mechanisms? Then reductionists can adopt a limiting procedure.

12. Reductionism and Absolutism:The All Embracing Causal Net • Two relativisations to the granularity of the description [Spohn 2001]: • property of being a direct rather than an indirect cause • where there appears to be a direct or indirect causal dependence within a coarse-grained frame, there may be none within a more fine-grained frame, and vice-versa. • Relativity to the agent

13. Sprinkler Example again • Variable A1: Season of the year, valuesspring, summer, fall, winter • Variable A2: Rainfall during the season, valuesyes, no • Variable A3: Sprinkler during the season, valueson, off • Variable A4: Wet pavement, valuesyes, no • VariableA5: Slippery pavement, valuesyes, no A1 A2 A3 A4 A5

14. Context Dependencies • L0(General background knowledge). the most extensive description of the universe. (“the whole prior state of the universe”, or in “the whole environment”) • L1 (Context of Inquiry). a subset of the set of factors in L0 : ‘L1-factors’In probabilistic causality and Causal modelling, L1-factors seem identifiable as the variables of the domain of interest in a given causal inquiry (factors which are potentially statistically associated. • L2 (Causal models). the selection of a subset of the set of L1-factors the set V of the variables in the DAG). • L3 (Set of the Explicitly Relevant Factors). the set of factors which are more directly ‘causally relevant’ for the assessment of a causal relation (the components of ‘Causal Background Contexts’ in probabilistic causality).

15. Problems with Absolutism • Duplications of causes: truth w.r.t. All-embracive Net and truth w.r.t. Particular models • Forced commitment to physicalism

16. Relativity and Objectivity How to reconcile ‘relativity to the context of Inquiry with objectivity? • Williamson: objective mind-dependent notion of causality (epistemic causality), where objectivity is based on the notion of the ‘most complete’ background knowledge β* • Advantages: • β* is well defined (as long as the indicators of causality can be delimited) • Causality is not tied to a particular agent – indeed This view is compatible with relativistic view if we don’t require that the different ‘Contexts of inquiry’ collapse

17. Conclusion: consequence of AA Epistemological point of view: acceptance of the ‘Absoluteness Assumption’ (a) duplication of causal judgments (w.r.t the true All-embracive Net, and w.r.t the local nets), (b) commitment to some form of very strict physicalism.

18. Conclusion: Avoid Arbitrariness a good reason to reject Absoluteness Assumption Absoluteness assumption is not the only option to avoid arbitrariness. Relativity to context as “relativity to context of Inquiry” objectivity without absoluteness

19. Conclusion objectivity without absoluteness: causal statements will be as objective as any other scientific statement. The price to pay is renouncing to a complete reduction of causes to probabilities, but it is highly dubious that, from an epistemological or a methodological point of view, this reduction offers any real advantage.