Relations of Ideas are Matters of Fact: A Unified Theory of Theoretical Unification - PowerPoint PPT Presentation

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Relations of Ideas are Matters of Fact: A Unified Theory of Theoretical Unification

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  1. Relations of Ideas are Matters of Fact: A Unified Theory of Theoretical Unification Kevin T. Kelly Department of Philosophy Carnegie Mellon University kk3n@andrew.cmu.edu

  2. Les relations d'idées sont des questions de fait:Une théorie unifiée d'unification théorique Kevin T. Kelly Department of Philosophy Carnegie Mellon University kk3n@andrew.cmu.edu

  3. I. Relations of Ideas and Matters of Fact

  4. Table of Opposites

  5. Progress

  6. Progress

  7. Progress

  8. Old Wine in New Bottles?

  9. Philosophy of Science 101 Formal Empirical The given number is even. Verifiable The sun will never stop rising. Unverifiable

  10. Wrong Twice! Formal Empirical The given number is even. The current emerald is green. Verifiable The given computation will never halt. The sun will never stop rising. Unverifiable

  11. Aristotelian Excuse Unbounded experience Completed analysis Rational Animal ?? Rational ? Always black? Reason Observation

  12. Leibnizian Doubts Unbounded experience Unbounded analysis ?? ?? Rational ? Always black? Never white? Reason Observation

  13. Bounded Kantian Synthesis 3 2 Unbounded experience 3 4 5 bounded synthesis ?? Always black? 3+2 = 5 ? Never white? Pure intuition Observation

  14. Unbounded Kantian Synthesis Unbounded experience Unbounded Synthesis? ?? ?? Never cross? Always black? Never white? Pure intuition Observation

  15. Kantian Antinomies Physical continuum Geometrical continuum ?? ?? Infinite? Dense? Infinite? Dense? Never white? Beyond all pure intuition Beyond all possible observation

  16. Gödel and Turing Unbounded computation Unbounded reality Input n ?? ?? Never halts? Always black? Never white? Computer Observation

  17. Wrong First Cut Formal Empirical The given number is even. The current emerald is green. Verifiable The given computation will never halt. The sun will never stop rising. Unverifiable

  18. Right First Cut Formal Empirical The given number is even. The current emerald is green. Verifiable The given computation will never halt. The sun will never stop rising. Unverifiable

  19. Unified Epistemology

  20. II.Verification

  21. Conclusion Verification as Halting with the Truth Yes!

  22. Conclusion Verification as Halting with the Truth Maybe you will change your mind.

  23. Conclusion Verification as Halting with the Truth

  24. Conclusion Verification as Halting with the Truth Bang!

  25. Conclusion Verification as Halting with the Truth

  26. Verifiability Yes! Conclusion true Conclusion false

  27. Always green? Classical Problem of Induction I won’t present blue until he says yes! Empirical demon Empirical scientist

  28. Always green? Classical Problem of Induction

  29. Always green? Classical Problem of Induction

  30. Always green? Classical Problem of Induction

  31. Always green? Classical Problem of Induction You lose if you never halt with “yes”!

  32. Always green? Classical Problem of Induction

  33. Always green? Classical Problem of Induction Yes!

  34. Always green? Classical Problem of Induction

  35. Always green? Classical Problem of Induction

  36. Always green? Classical Problem of Induction You lose anyway.

  37. Never halts? “Problem” of Uncomputability Formal demon Formal scientist

  38. Never halts? Similar to the Problem of Induction? Maybe I am in an infinite loop. Or maybe I will halt later… ?

  39. Never halts? Apparently Not Similar I see your program! 666

  40. Never halts? Apparently Not Similar Now I can cleverly calculate a priori what you will do! 666

  41. Never shoots? Never halts? Apparently Not Similar I’m beaten! 666 I’m beaten! chug chug chug 666 21456

  42. Never shoots? Never halts? 666 666 But Maybe Similar After All… Aha! His program is also showing! Aha! His program is also showing! 21456 23455

  43. Never shoots? Never halts? 666 666 666 But Maybe Similar After All… I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! 21456 23455 21456 23455

  44. Never shoots? Never halts? 666 666 666 But Maybe Similar After All… I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! I won’t halt until he halts with “yes” in my a priori simulation of him looking at me! 21456 23455 Self-reference by Kleene fixed point theorem 21456 23455

  45. Never shoots? Never halts? 666 666 666 But Maybe Similar After All… I didn’t halt… I didn’t halt… 21456 23455 I didn’t halt… 21456 23455

  46. Never shoots? Never halts? 666 666 666 But Maybe Similar After All… I still didn’t halt… I still didn’t halt… 21456 23455 I still didn’t halt… 21456 23455

  47. Never shoots? Never halts? 666 666 666 But Maybe Similar After All… I give up! You’ll never halt! 21456 23455 I give up! You’ll never halt! 21456 23455

  48. Never shoots? Never halts? 666 But Maybe Similar After All… The End The End 23455 Bang! 23455

  49. Never shoots? Never halts? 666 But Maybe Similar After All… 23455 23455

  50. Never shoots? Never halts? 666 But Maybe Similar After All… 23455 666 Sucker! 23455