Probabilistic   Squirrels : A Novel Defence of Twofold Causality Federica Russo [email_address] Centre de Philosophie des ...
Overview <ul><ul><ul><ul><li>Suppes’ Probabilistic Causality: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Main concepts a...
Suppes’ Probabilistic Theory <ul><li>B arometer Reading,  R ain, and  A ir Pressure </li></ul><ul><ul><ul><ul><ul><li>P (R...
Is Suppes’ Theory Adequate? <ul><li>P regnancy,  T hrombosis, and  C ontraceptive Pills </li></ul><ul><ul><ul><ul><ul><li>...
The Golf Environment: Improbable Consequences <ul><ul><ul><ul><li>Clumsy golf players: </li></ul></ul></ul></ul><ul><ul><u...
The Golf Environment: Negative Causes <ul><ul><li>Nuisance  Squirrels: </li></ul></ul><ul><ul><ul><ul><li>Squirrels’ kicks...
Probabilistic Squirrels save PT, seemingly <ul><ul><ul><ul><li>Population-level causation </li></ul></ul></ul></ul><ul><ul...
<ul><ul><ul><ul><li>Priors: P (E) = .90 ; P (C) = .15 ; P (E    C) = .10 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Hen...
Suppes’: causal relations among quantitative properties <ul><ul><ul><li>X, Y, Z  Random variables </li></ul></ul></ul><ul>...
Quantitative Barometric Changes <ul><ul><ul><ul><ul><li>X : number of rainy days </li></ul></ul></ul></ul></ul><ul><ul><ul...
Quantitative Probabilistic Squirrels <ul><li>1 if the ball falls into the cup </li></ul><ul><li>Cup X </li></ul><ul><li>0 ...
Quantitative Squirrels are negative causes <ul><li>P (X = 1 | Y = 1) = .66  <   P (X = 1 | Y = 0) = .94 </li></ul>Squirrel...
The probability of a birdie  given  the squirrel’s kick  does  exist
Still, do you want the squirrel  to be a token  positive  cause?
Token probability trajectories face two problems: <ul><li>the exact specification  </li></ul><ul><li>of the causal context...
Sketch of a solution <ul><li>Do we really need a fully developed  token probabilistic theory? </li></ul><ul><li>Maybe no …...
To sum up … <ul><ul><ul><ul><ul><li>The probabilistic theory of causality  </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><...
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Kul Wedsem Presentation

  1. 1. Probabilistic Squirrels : A Novel Defence of Twofold Causality Federica Russo [email_address] Centre de Philosophie des Sciences UCL
  2. 2. Overview <ul><ul><ul><ul><li>Suppes’ Probabilistic Causality: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Main concepts and some criticisms </li></ul></ul></ul></ul><ul><ul><ul><ul><li>The Golf Environment: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Improbable Consequences, Negative Causes, </li></ul></ul></ul></ul><ul><ul><ul><ul><li>and Twofold Causality </li></ul></ul></ul></ul><ul><ul><ul><ul><li>The Fallacy of Probabilistic Squirrels: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>A Bayesian Argument </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Probabilistic Quantitative Squirrels: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>A Novel Defence of Twofold Causality </li></ul></ul></ul></ul>
  3. 3. Suppes’ Probabilistic Theory <ul><li>B arometer Reading, R ain, and A ir Pressure </li></ul><ul><ul><ul><ul><ul><li>P (R | B) > P (R) The barometer </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>-prima facie- causes rain </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>P (R | B  A) = P (R | A) The barometer is a spurious cause of rain, </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>P (R | B  A)  P (R | B) i.e. has no real effect </li></ul></ul></ul></ul></ul>
  4. 4. Is Suppes’ Theory Adequate? <ul><li>P regnancy, T hrombosis, and C ontraceptive Pills </li></ul><ul><ul><ul><ul><ul><li>P (T | C) > P (T) Contraceptive pills cause thrombosis </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>But </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>P (T | C) < P (T) Contraceptive pills may prevent thrombosis </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Since </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>P (T | P) > P (T) Pregnancy may also cause thrombosis </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>And </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>P (P | C) < P (P) Contraceptive pills prevent pregnancy </li></ul></ul></ul></ul></ul>
  5. 5. The Golf Environment: Improbable Consequences <ul><ul><ul><ul><li>Clumsy golf players: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Hitting a tree-limb makes a birdie </li></ul></ul></ul></ul><ul><ul><ul><ul><li>even more improbable </li></ul></ul></ul></ul><ul><ul><ul><ul><li>If the birdie occurs, </li></ul></ul></ul></ul><ul><ul><ul><ul><li>relativisation of causal concepts </li></ul></ul></ul></ul><ul><ul><ul><ul><li>to the causal backgroud is helpful </li></ul></ul></ul></ul>
  6. 6. The Golf Environment: Negative Causes <ul><ul><li>Nuisance Squirrels: </li></ul></ul><ul><ul><ul><ul><li>Squirrels’ kicks lower </li></ul></ul></ul></ul><ul><ul><ul><ul><li>the probability of birdies </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Nevertheless </li></ul></ul></ul></ul><ul><ul><ul><ul><li>A squirrel’s kick </li></ul></ul></ul></ul><ul><ul><ul><ul><li>may cause a birdie </li></ul></ul></ul></ul>
  7. 7. Probabilistic Squirrels save PT, seemingly <ul><ul><ul><ul><li>Population-level causation </li></ul></ul></ul></ul><ul><ul><ul><ul><li>P (E | C) < P (E) Squirrels’ kicks are negative causes </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Token-level causation </li></ul></ul></ul></ul><ul><ul><ul><ul><li>P (e | c) > P (e) The squirrel’s kick is a </li></ul></ul></ul></ul><ul><ul><ul><ul><li>positive cause </li></ul></ul></ul></ul>
  8. 8. <ul><ul><ul><ul><li>Priors: P (E) = .90 ; P (C) = .15 ; P (E  C) = .10 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Hence: P (E | C) = .66 < P (E) =.90 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Squirrels are negative causes </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Update: P n (C) = .90 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Jeffrey’s Rule </li></ul></ul></ul></ul><ul><ul><ul><ul><li>P n (e) = P (e | h) P n (h) + P (e |  h) P n (  h) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>P n (E) = .69 < P (E) = .90 </li></ul></ul></ul></ul><ul><ul><ul><ul><li>The squirrel is still a negative cause! </li></ul></ul></ul></ul>Bayesian squirrels reveal a fallacy
  9. 9. Suppes’: causal relations among quantitative properties <ul><ul><ul><li>X, Y, Z Random variables </li></ul></ul></ul><ul><ul><ul><li>P (X ≤ x) </li></ul></ul></ul><ul><ul><ul><li>P (Y ≤ y) Probability distributions </li></ul></ul></ul><ul><ul><ul><li>P (Z ≤ z) </li></ul></ul></ul><ul><ul><ul><li>cov (X, Y) Measure of association between X and Y </li></ul></ul></ul><ul><ul><ul><li> (X, Y) Standardized measure of association between X and Y </li></ul></ul></ul>
  10. 10. Quantitative Barometric Changes <ul><ul><ul><ul><ul><li>X : number of rainy days </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Y : height of the barometer reading </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Z : index of air pressure change </li></ul></ul></ul></ul></ul><ul><ul><li>P (X ≤ x | Y ≤ y) > P (X ≤ x) The barometer is a prima facie cause </li></ul></ul><ul><ul><li>(X, Y) > 0 </li></ul></ul><ul><ul><li>P (X ≤ x | Y ≤ y, Z ≤ z) = P (X ≤ x | Z ≤ z) The barometer is a spurious cause </li></ul></ul><ul><ul><li> (X, Y | Z = z) = 0 </li></ul></ul>
  11. 11. Quantitative Probabilistic Squirrels <ul><li>1 if the ball falls into the cup </li></ul><ul><li>Cup X </li></ul><ul><li>0 if the ball does not </li></ul><ul><li>1 if the squirrel kicks the ball </li></ul><ul><li>Squirrel Y </li></ul><ul><li>0 if the squirrel does not </li></ul>
  12. 12. Quantitative Squirrels are negative causes <ul><li>P (X = 1 | Y = 1) = .66 < P (X = 1 | Y = 0) = .94 </li></ul>Squirrel –Y- Cup – X- 1 0 Tot 1 .10 .80 .90 0 .05 .05 .10 Tot .15 .85 1
  13. 13. The probability of a birdie given the squirrel’s kick does exist
  14. 14. Still, do you want the squirrel to be a token positive cause?
  15. 15. Token probability trajectories face two problems: <ul><li>the exact specification </li></ul><ul><li>of the causal context and </li></ul><ul><li>of all the factors involved </li></ul><ul><li>the reference to </li></ul><ul><li>different hipothetical corresponding type-populations </li></ul>
  16. 16. Sketch of a solution <ul><li>Do we really need a fully developed token probabilistic theory? </li></ul><ul><li>Maybe no … </li></ul><ul><li>Is a Bayesian framework promising? </li></ul><ul><li>Maybe yes … </li></ul>
  17. 17. To sum up … <ul><ul><ul><ul><ul><li>The probabilistic theory of causality </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>is sound, consistent, and promising </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Twofold causality is defensible </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Probabilistic squirrels are acquitted, </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>provided that we adopt: </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>a twofold conception of causality and </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>a Bayesian framework </li></ul></ul></ul></ul></ul>ACQUITTED!

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