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Church’s Thesis and Hume’s Problem: Justification as Performance

Church’s Thesis and Hume’s Problem: Justification as Performance. Kevin T. Kelly Department of Philosophy Carnegie Mellon University kk3n@andrew.cmu.edu. Further Reading.

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Church’s Thesis and Hume’s Problem: Justification as Performance

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  1. Church’s Thesis and Hume’s Problem:Justification as Performance Kevin T. Kelly Department of Philosophy Carnegie Mellon University kk3n@andrew.cmu.edu

  2. Further Reading • (With C. Glymour) “Why You'll Never Know Whether Roger Penroseis a Computer”,Behavioral and Brain Sciences, 13: 1990. • The Logic of Reliable Inquiry, Oxford: Oxford University Press, 1996. • (with O. Schulte)“Church's Thesis and Hume's Problem,” in Logic and Scientific Methods, M. L. Dalla Chiara, et al., eds. Dordrecht: Kluwer, 1997. • (with O. Schulte and C. Juhl)“Learning Theory and the Philosophy of Science”,Philosophy of Science 64: 1997. • “The Logic of Success”, British Journal for the Philosophy of Science, 51:2000. • “Uncomputability: The Problem of Induction Internalized,” Theoretical Computer Science 317: 2004. • Computability and Learnibility, Textbook manuscript, 2005.

  3. Fateful First Cut

  4. Painful Progress

  5. Slight Rearrangement

  6. Philosophy of Science 101

  7. Wrong Twice!

  8. Classical Excuse Unbounded experience Completed analysis Rational Animal ?? Rational ? Always black? Reason Observation

  9. But Maybe… Unbounded experience Unbounded analysis ?? ?? Rational ? Always black? Never white? Reason Observation

  10. Kant 3 2 Unbounded experience 3 4 5 temporal intuition ?? Always black? 3+2 = 5 ? Never white? Intuition Observation

  11. Oops! Unbounded experience spatial intuition ?? ?? Never cross? Always black? Never white? Intuition Observation

  12. After Turing Unbounded computation Unbounded reality Input n ?? ?? Never halts? Always black? Never white? Computer Observation

  13. Bad First Cut

  14. Good First Cut

  15. Computational Epistemology

  16. .5 Verification as “Support” 1.0 Deductive verification Inductive verification

  17. Paradigms Evolve • Objective support by evidence.

  18. Paradigms Evolve… • Objective support by evidence. • Coherent personal opinion. • “Rational” update.

  19. Paradigms Evolve… • Objective support by evidence. • Coherent personal opinion. • “Rational” update.

  20. But Leading Metaphors Matter • Myopic • Bedrock = “rationality” intuitions • Success = being “rational” • Truth-finding performance deferred or ignored • Problem complexity ignored • Little resemblance to computability

  21. Verification as Halting Conclusion Data

  22. Verification as Halting Yes! Conclusion Data

  23. Verification as Halting Conclusion Data

  24. Verification as Halting Conclusion Data

  25. Verification as Halting Bang! Conclusion Data

  26. Verification as Halting Conclusion Data Can’t take it back.

  27. Verifiability Yes! Conclusion true Conclusion false

  28. Always green? Laws are Not Verifiable

  29. Always green? Laws are Not Verifiable

  30. Always green? Laws are Not Verifiable

  31. Always green? Laws are Not Verifiable

  32. Always green? Laws are Not Verifiable You must halt with “yes” if it’s true!

  33. Always green? Laws are Not Verifiable You must halt with “yes” if it’s true!

  34. Always green? Laws are Not Verifiable Yes!

  35. Always green? Laws are Not Verifiable

  36. Always green? Laws are Not Verifiable

  37. Never shoots? A Purely Formal Problem

  38. Never shoots? Analogy? I ain’t a’ shootin’, yeller belly!

  39. Never shoots? Apparently Not Game’s up, J.R.! Yer program’s showin’! 666

  40. Never shoots? 666 Apparently Not Now shaddup! I’m calculatin’ a-preeorey-like what yer gonna do.

  41. Never shoots? Never shoots? 666 Apparently Not ?!!! 21456 23455

  42. Never shoots? Never shoots? 666 But Then Again… I got it! Two kin play that opry oary game! 21456 23455

  43. Never shoots? Never shoots? 666 21456 23455 21456 23455 But Then Again… I won’t shoot ‘til I see him shoot in this here opry oary sim-yooo-laytion! 666

  44. Never shoots? Never shoots? 666 21456 23455 21456 23455 But Then Again… 666 I ain’t a’ shootin’.

  45. Never shoots? Never shoots? 666 21456 23455 But Then Again… 666 I still ain’t a’ shootin’. 21456 23455

  46. Never shoots? Never shoots? 666 21456 23455 But Then Again… 666 You check that there opry oary all you want… 21456 23455

  47. Never shoots? Never shoots? 666 But Then Again… 666 21456 23455 An’ all you’ll see is I ain’t a-shootin’ 21456 23455

  48. Never shoots? Never shoots? 666 But Then Again… Aw, shucks, J.R. I reckon You ain’t never gonna shoot. 666 21456 23455 Aw, shucks, J.R. I reckon you ain’t never gonna shoot. 21456 23455

  49. Never shoots? Never shoots? 666 23455 23455 But Then Again… 666 Bang!

  50. Never shoots? Never shoots? 666 23455 But Then Again… 666 23455

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