The document discusses the distinction between property causal relations and token causal relations in probabilistic causality. It argues that the property-token distinction is useful for explaining token causal relations. Specifically, explaining a token causal relation involves locating it within a broader property causal relation and showing how it fits within an established nomic or statistical pattern.

1. PROBABILISTIC CAUSALITY AND EXPLANATION or how explaining probabilistic causes Federica Russo [email_address] UCL

2. 1 In this talk I will ...  briefly recall the main features of the probabilistic theory of causality  sketch the distinction property causal relations vs. token causal relations … and I will argue ...  the property-token distinction is useful for the purpose of explanation

3. 2 Some background ... Probabilistic Causality denotes any type of Indeterministic Causality (Salmon 1990) Aleatory causality Processes and interactions Statistical causality Constant conjunction and statistical regularities two possible approaches :

4. 3 Some background ... The probabilistic theory of causality states that causes raise the probability of their effects However … The squirrel’s kick The plant and the defoliant P(E|C)>P(E|  C) In general squirrel’s kicks don’t cause golf balls to drop in the cup In general spraying a defoliant doesn’t cause plants to survive

5. 4 How the property-token distinction works ... Smoking causes coronaries in the adult American population Do you still want to defend the probabilistic theory of causality? You should distinguish two concepts of cause, then! C causes E P(E|C) > P(E|  C) However, this condition is not necessary nor sufficient for the token relation about John. John’s smoking caused him a coronary vs.

6. 5 Explaining a token causal relation is... … to trace back to the causes that made the effect happen Strenuous exercise (E) --- Smoking (S) +++ High Cholesterol Intake (C) + Heart attack (H) Suppose John had an heart attack, the most explanatory causal factor is smoking. P(H|S  C  E) >>> P(H|  S  C  E) P(H|S  C  E) > P(H|S  C  E) And in fact in general smoking causes heart attacks ...

7. 6 Explaining a token causal relation... … to locate the phenomenon in a nomic pattern The token causal hypothesis John’s smoking caused him a coronary is more likely if (our belief in ?) the property causal relation Smoking causes coronaries holds and is strong The token causal relation is subsumed under the corresponding property causal relation But, this is a Covering Law Model !! In other words:

8. 7 Connecting Property and Token causal relations if C is a causal factor of magnitude m for producing E in a population P then S{c(t 1 ) token caused e(t 2 )| c(t 1 ) and e(t 2 ) occured in the population P} = m The hypothesis that c token caused e is better supported as the strength (or our belief in?) of the property causal relation increases. The Connecting Principle (Sober&Papineau 1986)

10. Selected References Cartwright N. (1979) "Causal Laws and Effective Strategies", Nous, 13, pp. 419-37. (1989) Nature's Capacities and their Measurement , Clarendon Press, Oxford. Edwards A.W.F. (1972) Likelihood. An Account of the Statistical Concept of Likelihood and its Application to Scientific Inference , Cambridge University Press, Cambridge. Eells E. (1991), Probabilistic Causality , Cambridge University Press, Cambridge. Gillies D. (2000) Philosophical Theories of Probability , Routledge, London. Hacking I. (1965) Logic of Statistical Inference , Cambridge University Press, Cambridge. Hempel C.G. (1965) Aspects of Scientific Explanation and Other Essays , Free Press, New York. Koopman B.O. (1940) "The Axioms and Algebra of Intuitive Probability", Annals of Mathematics, 41, pp. 269- 292. Salmon W.C. (1971) Statistical Explanation and Statistical Relevance , Pittsburgh Univerity Press, Pittsburgh. (1984) Scientific Explanation and the Causal Structure of the World , Princeton University Press. (1990) " Causal Propensities: Statistical Causality vs. Aleatory Causality", Topoi, 9, pp. 95-100. Sober E. (1984) "Two Concepts of Cause", PSA 1984 vol 2, pp. 405-424. Sober E. and Papineau D. (1986) "Causal Factors, Causal Influence, Causal Explanation", Proceedings and Addresses of Aristotelian Society, 60, pp. 97-136. Suppes P. (1970) A Probabilistic Theory of Causality , North Holland Publishing Company, Amsterdam. Comments? Mailto : Russo@lofs.ucl.ac.be