1. Levels of causation and the interpretation of probability Seminar 1 Federica Russo Philosophy, Louvain & Kent

2. 2 Overview The problem, the questions, and the perspective Probabilistic squirrels and twofold causality Metaphysical answers to epistemological questions Epistemological answers to epistemological questions Probabilistic causal claims

3. 3 The problem Compare: Smoking causes lung cancer Smoking caused me to develop cancer The questions Are there distinct levels of causation? If so, how are they related? The perspective Making epistemological sense of the levels without any metaphysical burden

4. 4 Probabilistic squirrels Type-level causation P(B|S) < P(B)Squirrels’ kicks are negative causes for birdies Token- level causation P(b|s) > P(b)The squirrel’s kick is a positive cause for the birdie

5. 5 Twofold causality solves the problem: Two distinct levels of causation: type- and token-level Two levels, two analyses Different mechanisms may operate at different levels

6. 6 Levels of squirrels Type-level squirrels Squirrels’ kicks are preventatives for birdies Token-level squirrels The squirrel’s kick we witnessed caused the birdie How do we know about the token-squirrel? Eells: draw it’s probability trajectory!

7. 7 Metaphysical answers to epistemological questions

8. 8 Token probability trajectories face two problems: The exact specification of the causal context and of all the factors involved The reference to several hypothetical populations

9. 9 Epistemological answers to epistemological questions Can we make epistemological sense of the levels without metaphysical burden? A statistical understanding of the levels: At the type-level, causal relations joint probability distributions are represented by joint probability distributions At the token-level, causal relations realisations are realisations of joint probability distributions

10. 10 The connecting principle The rough idea (Sober 1986): “If a token event of type C is followed by a token event of type E, then the support of the hypothesis that the first event token-caused the second increases as the strength of the property causal relation of C to E does.”

11. 11 The connecting principle The formulation: If C is a causal factor of magnitude m for producing E in a population P, then S {C t1 token caused E t2 |C t1 and E t2 occurred in the population P } = m

12. 12 The connecting principle reformulated If c is a causal factor of magnitude m for producing e in a population P, then S(H| E) is proportional to m. Notation: c, e :causes and effects at the type-level E :evidence  type-level causal relation with strength m H :hypothesis  token-level causal relation

13. 13 The connecting principle reformulated The strength m The replacement of equality by proportionality The measure of support S(H|E)

14. 14 Likelihood and support The Fisherian concept of Likelihood: A predicate of hypotheses in the light of data Edwards’ definition of support :

15. 15 Epistemological morals The connecting principle allows to compute likelihood the likelihood of token hypotheses, not their strength – this is metaphysics Type-level causation Type-level causation is epistemologically primitive Token-level causation Token-level causation is ontologically primitive

16. 16 Probabilistic Probabilistic causal claims Type and token claims are probabilistic What interpretation of probability? Frequency–cum- Objective Bayesian interpretation Type level: express frequency of occurrence Token level: express belief in what did or will happen

17. 17 To sum up and conclude There is a genuine distinction between type- and token-level causal claims To make sense of it, we don’t need metaphysical assumptions about different mechanisms operating at the two levels The connecting principle allows us to relate type- and token-level epistemologically