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Fetzer’s Solution to the Reference Class Problem Causality, Probability, and Counterfactuals Lorenzo Casini Philosophy, Kent

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2 Outline Two questions (What is RCP) Two problems (Why does RCP really matters) Fetzer’s solution of MRCP A possible defence of Fetzer’s proposal Applying Fetzer’s solution to CBNs Summary

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3 Two Problems: MRCP: existence of a relevant reference class ERCP: justifying a probability value as the right one I will focus on: solution of MRCP, which is Ontologically acceptable (reference class description points to something out-there-in-the-world) Epistemologically acceptable (relevant reference class is knowable in principle)

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4 Two Questions: What is p that x is A given that x is a ‘such-and-such’ event? Many Rs admissible many answers: What is p that x is A because x is a ‘such-and-such’ event? ( and related counterfactual) Unique answer requires unique R Fetzer: MRCP is about single-case true statistical explanations

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5 Fetzer’s (and Pearl’s) recipe: Explanatory relevance is nomic or causal relevance (‘this x is A because it is R’ if ‘being R c being A’) R is a complete set of causally relevant factors Factors are objective (mind independent) S-R is only a guide to C-R

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6 Fetzer’s solution to MRCP Probability is the disposition of a set-up to: give an outcome on a single trial generate long-run frequencies for the possible outcomes Such disposition is possessed by every member of a maximally specific reference class R

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7 Ontology The classifying of x as member of R at t entails necessarily: x’s possession of a permanent dispositional property χ at t Syntax (i) (subjunctive conditional) (ii) (causal conditional) Semantics of of worlds where is true over worlds where is true is n

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8 Hypothesising F is C-R if Testing Causal conditionals are corroborated if frequency distribution approximates normal distribution (Bernoulli’s theorem) F is C-R if, for : Notice: Testing requires randomness assumption (i.e.: K’s maximal specificity)

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9 Possible defence of Fetzer’s proposal Existence: O.Either there are many reference classes at different t or the relevant one is the closest to the outcome which occurs with p=1 (Hanna, 1982) A.Completeness assumption refers to a set-up type at under assumption that nothing interferes Explanation: O.Completeness is too demanding—prevents any explanation to be true (Humphreys, 1982) A.F.’s proposal is suitable for HPs on repeatable and controlled conditions

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10 Knowability: O.type-level probabilities say nothing about single-case propensities (Pollock, 1990) A.F.’s proposal is epistemologically acceptable if evidence can confirm completeness of R Testability: O.Completeness is untestable in principle (Gillies, 2002) A.For frequencies to confirm completeness, we must assume underlying conditions (causal structure & dispositional strength) are stable

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11 In sum: assume randomness of outcomes stability of causal structure & dispositional strength sequences are long enough (Tests are reliable) then, we can distinguish causally relevant properties among prima facie causally relevant ones if R is objectively homogeneous, no other statistically relevant property will be causally relevant

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12 Applying Fetzer’s solution to CBNs Causal graph on Any is probabilistically independent, given, of any set of variables not containing its descendents (CMC) Pearl: the relevant R is the sum total of and (X is deterministically dependent on its known and unknown causes) But: what do correspond to? how to know whether CMC holds for ? Plus: no genuinely statistical explanations! Do we need determinism to solve MRCP?

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13 Under Fetzer’s dispositional interpretation is single-case, objective, testable F.’s solution involves time reference (applicable to dynamic BNs?) Only are objective (mind independent) ( play the role of ceteris-paribus clauses: ‘nothing interferes’) Counterfactual analysis needs no deterministic assumptions to solve MRCP: e.g.: ‘R’=‘L.F’, x belongs to R and brings about O with probability m. Had x belonged to, would O have occurred with probability n, where ?

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14 Summary MRCP is about the existence of a complete reference class description which explains the probabilistic possession by an individual of a certain attribute via a statistical disposition Single-case dispositional claims have their truth conditions in (intensional) limiting frequencies over possible-worlds. When these are true (/corroborated), we know (/have good reasons to believe in): completeness of reference class (thereby solving MRCP—without determinism), and the ontology of single-case dispositions (which give causal conditionals the desired explanatory power)

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15 Open issues Still, when it comes to testing… remain F.’s solution does not rely on (extensional) limiting frequencies, yet on other (not less) controversial assumptions. To what extent can we rely on (in/)stability of causal structure & dispositional strength to (dis/)confirm completeness? extend propensity claims corroborated within a population (where unknown causes might be ‘friendly’) to other populations/individuals?

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16 Thank you What is What is your Reference Class, darling? reference

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17 References Cartwright, N. (2003), “What makes a capacity a disposition?” Causality: Metaphysics and Methods discussion paper 10/03, London School of Economics Centre for Philosophy of Natural and Social Science Dawid, A. P. (2000a), “Causal Inference Without Counterfactuals”, Journal of the American Statistical Association, 95: 407-424 Dawid, A. P. (2000b), “Causal Inference Without Counterfactuals: Rejoinder”, Journal of the American Statistical Association, 95: 444-448 Fetzer, J. H. (1970), “Dispositional Probabilities”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 473-482 Fetzer, J. H. (1981), Scientific Knowledge. Causation, Explanation, and Corroboration, Boston Studies in the Philosophy of Science, D. Reidel Publishing Company, Dordrecht, Vol. 69 Fetzer, J. H. (1982), “Probabilistic Explanations”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2: 194-207 Gillies, D. (2000), “Varieties of Propensities”, British Journal for the Philosophy of Science, 51: 807-835 Gillies, D. (2002), “Causality, Propensity, and Bayesian Networks”, Synthese, 132: 63-88 Hájek, A. (2007), “The Reference Class Problem is Your Problem Too”, Synthese, 156: 563-585 Halpern, J. Y., Pearl, J. (2005), “Causes and Explanations: A Structural-Model Approach. Part II: Explanations”, British Journal for the Philosophy of Science, 56: 843-887 Hanna, J. F. (1982), “Probabilistic Explanation and Probabilistic Causality”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2: 181-193 Humphreys, P. (1982), “Aleatory Explanations Expanded”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2: 208-223 Pearl, J. (2000a), Causality. Models, Reasoning, and Inference, Cambridge University Press Pearl, J. (2000b), “Causal Inference Without Counterfactuals: Comment”, Journal of the American Statistical Association, 95: 428-431 Pollock, J. L. (1990), Nomic Probability and the Foundations of Induction, Oxford University Press Reichenbach, H. (1949), The Theory of Probability, University of California Press Williamson, J. (2006), “Dispositional versus Epistemic Causality”, Minds and Machines, 16: 259-276 Williamson, J. (2007), “Causality”, in Gabbay, D. and Guenthner, F. (eds.): Handbook of Philosophical Logic, Springer, 14: 89-120

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