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

2. Planetary retrograde motion Mars Earth Sun Astronomy 1543 Only at solar opposition

3. Ptolemaic Explanation  Retrograde path is due to an epicycle. Retrograde path is due to an epicycle. Can happen regardless of the position of the sun Can happen regardless of the position of the sun epicycle

4. Copernican Explanation “Lapped” competitor appears to backtrack against the bleachers. “Lapped” competitor appears to backtrack against the bleachers. Lapping only happens when the center of the track is opposite. Lapping only happens when the center of the track is opposite. lapping  epicycle

5. Copernicus Victorious Explains the data rather than merely accommodating them. Explains the data rather than merely accommodating them. Has fewer adjustable parameters. Has fewer adjustable parameters. Is more falsifiable (failure of correlation would rule it out). Is more falsifiable (failure of correlation would rule it out). Is “simpler”. Is “simpler”.

6. More Victories for Simplicity universal gravitation vs. divided cosmos universal gravitation vs. divided cosmos wave theory of light vs. particles and aether wave theory of light vs. particles and aether oxygen vs. phlogiston oxygen vs. phlogiston natural selection vs. special creation natural selection vs. special creation special relativity vs. classical electrodynamics special relativity vs. classical electrodynamics chaos vs. infinite series of random variables chaos vs. infinite series of random variables

7. Ockham’s Razor Which theory is true?

8. Ockham Says: Choose the Simplest! Looks good. Feels good!

9. Skeptical Challenge What about this?

10. Puzzle An indicator must be sensitive to what it indicates. An indicator must be sensitive to what it indicates. simple

11. Puzzle An indicator must be sensitive to what it indicates. An indicator must be sensitive to what it indicates. complex

12. Puzzle But Ockham’s razor points at simplicity no matter what. But Ockham’s razor points at simplicity no matter what. simple

13. Puzzle But Ockham’s razor always points at simplicity. But Ockham’s razor always points at simplicity. complex

14. Paradox If we know that the truth is simple, we don’t need Ockham’s razor. If we know that the truth is simple, we don’t need Ockham’s razor. simple

15. Paradox If we don’t know that the truth is simple, what good is Ockam’s razor? If we don’t know that the truth is simple, what good is Ockam’s razor? complex

16. Weird Science Simplicity must somehow point at the truth now. Simplicity must somehow point at the truth now.

17. Weird Science Hmm, how could that work? Hmm, how could that work?

18. Metaphysicians for Ockham Mysticism: the simple world calls to us… Mysticism: the simple world calls to us… Leibniz: God creates a simple world and creates humans who expect it to be simple. Leibniz: God creates a simple world and creates humans who expect it to be simple. Kant: simple minds create simple worlds. Kant: simple minds create simple worlds. With friends like those….

19. Darwin, the New Savior If our simplicity bias wasn’t right, we would have been squished long ago!

20. Darwin, the New Savior If Darwin happens to be wrong, then science should be abandoned?

21. Collapse of Scientific Naturalism (Koons 1999) 1.All truths are natural truths. 2.Science can know all natural truths. 3.Naturalistic knowledge is belief that tracks the truth. 4.Science mainly uses Ockham’s razor. 5.So Ockham’s razor must track the truth. 6.The tracking relation must have some causal explanation (by O.R.). 7.A truth-tracking method must work whichever theory happens to be true. 8.But only some of the possible theories explain the tracking relation, unless it is known a priori. 9.It isn’t. Contradiction.

22. Moral Koons is onto something. Naturalists who expect too much from science tie science to weird metaphysical speculations. Solution: Dump short-run tracking as the justification of scientific method. Dump short-run tracking as the justification of scientific method. It’s enough that Ockham’s razor be our best possible means for finding the hidden truth. It’s enough that Ockham’s razor be our best possible means for finding the hidden truth. Maybe that can be known a priori. Maybe that can be known a priori.

23. Challenge How could you know that a fixed pointer helps you find something unless you already know that it points at what you are looking for? Ummm… simple

24. Response It happens every day! simple

25. Asking for Directions I’m lost

26. Asking for Directions

27. Ask!

28. Where’s …

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

30. Asking for Directions Goal

31. Best Route Goal

32. Disregarding Advice is Worse Goal

33. Disregarding Advice is Worse Extra U-turn Goal

34. Disregarding Advice is Worse Extra U-turn Goal

35. Is That What Ockham Does?

36. Bean Counting

38. May come at any time…

39. Bean Counting May come at any time…

40. Bean Counting May come at any time…

41. Bean Counting May come at any time…

42. Bean Counting May come at any time…

43. Bean Counting May come at any time…

44. Bean Counting May come at any time…

45. Analogy Beans = “empirical effects”. Beans = “empirical effects”. Count = complexity of true model. Count = complexity of true model. Appearance times = elusiveness of effects. Appearance times = elusiveness of effects.

46. Polynomial Models Data = ever tighter open intervals around Y at rational values of X. Data = ever tighter open intervals around Y at rational values of X. X Y

47. Polynomial Models 0: no effect 0: no effect

48. Polynomial Models 1: constant effect 1: constant effect

49. Polynomial Models 2: constant + linear effect 2: constant + linear effect

50. Polynomial Models 3: constant + linear + quadratic effect 3: constant + linear + quadratic effect

51. Retractions U-turn = model retraction; U-turn = model retraction; Freeway = retraction-efficient truth-finding method. Freeway = retraction-efficient truth-finding method. H H

52. How Ockham’s Razor Helps No matter which theory is true, Ockham’s razor never retracts more than any other convergent method. No matter which theory is true, Ockham’s razor never retracts more than any other convergent method. Any non-Ockham method does worse. Any non-Ockham method does worse.

53. Over-counting is Inefficient Suppose you over-count. Suppose you over-count. 31

54. Over-counting is Inefficient Where is that extra marble, anyway? Where is that extra marble, anyway? 31

55. Over-counting is Inefficient If you never say 2 you’ll never converge to the truth…. If you never say 2 you’ll never converge to the truth…. 31

56. Over-counting is Inefficient That’s it. You should have listened to Ockham. That’s it. You should have listened to Ockham. 3 222 1

57. Over-counting is Inefficient Oops! Well, no method is infallible! Oops! Well, no method is infallible! 3 222 1

58. Over-counting is Inefficient If you never say 3, you’ll never converge to the truth…. If you never say 3, you’ll never converge to the truth…. 3 222 1

59. Over-counting is Inefficient Embarrassing to be back at that old theory, eh? Embarrassing to be back at that old theory, eh? 3 2223 1

60. Over-counting is Inefficient And so forth… And so forth… 3 22234 1

61. Over-counting is Inefficient And so forth… And so forth… 3 222345 1

62. Over-counting is Inefficient And so forth… And so forth… 3 2223456 1

63. Over-counting is Inefficient And so forth… And so forth… 3 22234567 1

64. The Score You: You: 3 22234567 1 At moment of over-count

65. The Score Ockham: Ockham: 22234567 3 saved retracation At moment of over-count

66. Moral Ockham’s razor keeps one on the straightest path to the truth. Ockham’s razor keeps one on the straightest path to the truth. Argument is a priori and mathematical, not hidden and metaphysical. Argument is a priori and mathematical, not hidden and metaphysical. Insistence on truth in the short run saddles science with a priori metaphysical commitments. Insistence on truth in the short run saddles science with a priori metaphysical commitments.