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Ockham’s Razor without Circles, Evasions, or Magic

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  1. Ockham’s Razor without Circles, Evasions, or Magic Kevin T. Kelly Department of Philosophy Carnegie Mellon University www.cmu.edu

  2. I. The Simplicity Puzzle

  3. Which Explanation is Right? ???

  4. Ockham Says: Choose the Simplest!

  5. But Maybe… Gotcha!

  6. The Simplicity Puzzle • An indicator must be sensitive to what it indicates. simple

  7. The Simplicity Puzzle • An indicator must be sensitive to what it indicates. complex

  8. The Simplicity Puzzle • But Ockham’s razor always points at simplicity. simple

  9. The Simplicity Puzzle • But Ockham’s razor always points at simplicity. complex

  10. A. Circular Accounts

  11. Prior Probability • Assign high prior probability to simple theories. On the presumption of simplicity, presume simplicity.

  12. Miracle Argument • Phenomenon e: Venus appears to bob back and forth about the sun against the fixed stars. Venus Sun

  13. Miracle Argument • e would not be a miracle given S; • e would be a miracle given C. q C S

  14. Miracle Argument • e would not be a miracle given S; • e would be a miracle given C. q’ C S

  15. However… • e would not be a miracle given C(q); Why not this? q C S

  16. Bayesian Explanation • Ignorance (over theories) • + Ignorance (over parameter settings in each theory) • = Knowledge (against complex parameter settings). Simple theory q Complex theory q q q q q q Bayesian q

  17. = The Old Paradox of Indifference • Ignorance (over blue, non-blue) • + Ignorance (over ways of being non-blue) • = Knowledge (that the truth is blue as opposed to any other color) Blue Not-Blue Bayesian

  18. In Any Event… The coherentist foundations of Bayesianism have nothing to do with short-run truth-conduciveness.

  19. B. Evasive Accounts

  20. Theoretical Virtues • Simple theories have virtues: • Testable • Unified • Explanatory • Symmetrical • Bold • Compress data

  21. Theoretical Virtues • Simple theories have virtues: • Testable • Unified • Explanatory • Symmetrical • Bold • Compress data • But to conclude that the virtuous theory is true is wishful thinking. Kelly Maximus

  22. Bayesian Convergence • Too-simple theories get shot down… Updated opinion Theories Complexity

  23. Bayesian Convergence • Plausibility is transferred to the next-simplest theory… Updated opinion Plink! Theories Complexity Blam!

  24. Bayesian Convergence • Plausibility is transferred to the next-simplest theory… Updated opinion Plink! Theories Complexity Blam!

  25. Bayesian Convergence • Plausibility is transferred to the next-simplest theory… Updated opinion Plink! Theories Complexity Blam!

  26. Bayesian Convergence • The true theory is nailed to the fence. Updated opinion Zing! Theories Complexity Blam!

  27. Over-fitting • Empirical estimates based on complex models have greater expected distance from the truth. Truth Unconstrained aim at the true value

  28. Over-fitting • Empirical estimates based on complex models have greater expected distance from the truth. Pop! Unconstrained aim at the true value

  29. Overfitting • Empirical estimates based on constrained models can have lower expected distance from the truth… Clamped aim at the true value

  30. Convergence • But alternative strategies also converge: • Any finite variant of a convergent strategy converges(Reichenbach, Salmon).

  31. Over-fitting • Empirical estimates based on constrained models can have lower expected distance from the truth… (Akaike, Vapnik, Sober and Forster, etc.) Pop! Clamped aim at the true value

  32. Over-fitting • ...even if the simple theory is knownto be false… You missed! Clamped aim at the true value

  33. Makes Sense… …when loss of an answer is similar in nearby distributions. Close is good enough! Loss Similarity of Probability distributions p

  34. But Truth Matters… …when loss of an answer is discontinuous with similarity---e.g., in causal prediction. Not now! Loss Similarity of Probability distributions p

  35. C. Magical Naturalism Truth

  36. Leibniz Simple B(Simple) Kant Simple B(Simple) Ouija board Simple B(Simple) Magic • Simplicity indicates truth via an unknown cause. God

  37. Metaphysicians for Ockham Magic • Ockham says: explain Ockham’s razor without undetected causes.

  38. Metaphysicians for Ockham Magic • Ockham says: explain Ockham’s razor without undetected causes.

  39. II. A New Direction

  40. Ancient Hint “Living in the midst of ignorance and considering themselves intelligent and enlightened, the senseless peoplegoround and round, following crooked courses, just like the blind led by the blind.” Katha Upanishad, I. ii. 5, c. 600 BCE. Truth

  41. Diagnosis of Standard Accounts • Short-run Reliability: too strong. Truth • Long-run Convergence: too weak. Truth

  42. Natural Alternative • Short-run Reliability: too strong. Truth • Straightest Convergence: just right? Truth • Long-run Convergence: too weak. Truth

  43. III. Navigation by Fixed Directions complex

  44. Asking for Directions Where’s …

  45. Asking for Directions Turn around. The freeway ramp is on the left.

  46. Goal Asking for Directions

  47. Goal Best Route

  48. Best Route to Any Goal

  49. Disregarding Advice is Bad Extra U-turn

  50. Best Route to Any Goal …so fixed advice can help you reach a hidden goal without circles, evasions, or magic.