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# Oxford Presentation

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### Oxford Presentation

1. 1. Federica Russo Université Catholique de Louvain Centre for Philosophy of Natural and Social Science - LSE Overview: Philosophy of probability: theory and interpretations Philosophy of causality: probability and causality My research project: some ideas in progress
2. 2. Philosophy of probability: theory and interpretations <ul><li>Axioms: </li></ul><ul><li>Let S be a collection of sentences and P a probability function satisfying Kolmogorov axioms : </li></ul><ul><li>1. P (A)  0 </li></ul><ul><li>2. P (A) = 1 if A is true in all models </li></ul><ul><li>3. P (A  B) = P (A) + P (B) if A, B mutually exclusive </li></ul>
3. 3. <ul><li>Consequences: </li></ul><ul><li>a. P (  A) = 1  P (A) </li></ul><ul><li>b. P (A) = P (B) if in all models A  B </li></ul><ul><li>c. P (A  B) = P (A) + P (B)  P (A  B) </li></ul><ul><li>Conditional probability: </li></ul><ul><li>P (A | B) = P (A  B) / P (B) if P (B)  0 </li></ul><ul><li>Bayes’ Theorem: </li></ul><ul><li>P (B | A) = P (A | B) P (B) / P (A) </li></ul><ul><li>Unconditional independence: </li></ul><ul><li>A and B are unconditional independent iff </li></ul><ul><li>P (A | B) = P (A) or </li></ul><ul><li>P (A | B) = P (B) or </li></ul><ul><li>P (A | B) = P (A) P (B) </li></ul><ul><li>Conditional independence: </li></ul><ul><li>A is conditional independent of B given C iff </li></ul><ul><li>P (A | B  C) = P (A | C) </li></ul>
4. 4. Interpretations of probability <ul><li>Logical interpretation </li></ul><ul><ul><li>Probability is the ratio between favourable cases and equipossible cases </li></ul></ul><ul><li>Subjective interpretation </li></ul><ul><ul><li>Probability a quantitative expression of degree of knowledge, degree of belief, degree of confirmation </li></ul></ul><ul><li>Objective interpretation </li></ul><ul><ul><li>Probability is a quantitative expression of an objective feature of the world </li></ul></ul>Agent-dependent notion  Epistemological interpretations Agent-independent notion  Metaphysical interpretation
5. 5. Dutch Book arguments <ul><li>Within subjective interpretation: probabilities are degrees of belief </li></ul><ul><li>Goal: justify 2 epistemological principles </li></ul><ul><ul><li>Probability laws are coherence conditions on degrees of belief </li></ul></ul><ul><ul><li>Conditionalization is a rule of probabilistic inference </li></ul></ul><ul><li>Assumption: degrees of belief are betting quotients </li></ul><ul><li>A Dutch Book is such that the bettor looses whatever happens </li></ul><ul><li>Synchronic Dutch Book theorem: the bettor is not liable to the Dutch Book iff his betting quotients satisfy probability axioms </li></ul><ul><li>Diachronic Dutch Book theorem: conditionalization is the only coherent dynamic rule for updating probabilities </li></ul>
6. 6. Varieties of Bayesianism <ul><li>Subjective Bayesianism </li></ul><ul><li>coherence is the only constraint on probability functions </li></ul><ul><li>Objective Baysianism </li></ul><ul><li>knowledge and lack of knowledge are empirical and logical constraints on probability functions </li></ul>
7. 7. Philosophy of causality: probability and causality <ul><li>Motivation for the probabilistic approach </li></ul><ul><li>Probabilistic theories of causality </li></ul><ul><li>vs. </li></ul><ul><li>Theories of probabilistic causality </li></ul>
8. 8. Suppes: causal relations among events <ul><li>Causes precede effects in time by definition </li></ul><ul><li>Causes increase the probability of the effect: P(E | C) > P(E) </li></ul><ul><li>Genuine causes are not spurious </li></ul>
9. 9. Suppes: causal relations among quantitative properties <ul><li>Restate former definitions in terms of random variables and probability distributions </li></ul><ul><li>Causation implies correlation </li></ul>
10. 10. Traditional problems <ul><li>Improbable consequences </li></ul><ul><li>Levels of causation: </li></ul><ul><ul><li>type causation vs . token causation </li></ul></ul><ul><li>Negative causes </li></ul><ul><li>Deterministic causality vs. Indeterministic causality </li></ul>
11. 11. My research project: some ideas in progress <ul><li>Causality: metaphysics, epistemology, or methodology? </li></ul><ul><li>Causal modelling: metaphysics, epistemology or methodology? </li></ul>
12. 12. <ul><li>My project: </li></ul><ul><li>Is in the epistemology of causality </li></ul><ul><li>Attempts to extrapolate a notion of causality </li></ul><ul><li>My methodology: </li></ul><ul><li>Analysis of modelling </li></ul><ul><li>Analysis of case studies </li></ul>
13. 13. Intermezzo: what is a causal model? <ul><li>Causal models have two parts: </li></ul><ul><li>A set of equations </li></ul><ul><li>A graph </li></ul><ul><li>Equations functionally relate variables </li></ul><ul><li>Graphs are a device for laying out pictorially what is hypothesized to cause what </li></ul>
14. 14. Causal models: an example C 3 =  1 C 2 +  2 C 1 +  i Child mortality and mother’s education C 1 = mother’s edication C 2 = socioeconomic status C 3 = child mortality
15. 15. Two claims about causality <ul><li>What is causality? </li></ul><ul><li>causality is a measure of change </li></ul><ul><li>Where does causality come from? </li></ul><ul><li>causality comes from the causal hypotheses </li></ul>
16. 16. Related problems <ul><li>What about probability? </li></ul><ul><li>objective Bayesian approach </li></ul><ul><li>What about determinism? </li></ul><ul><li>determinism is a heuristic principle </li></ul>