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

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