This Statement is False

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Bigand, Gödel, Recursion and Attention

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This Statement is False

  1. 1. THIS STATEMENT IS FALSE Bigand, Gödel, Recursion and Attention Jordan Smith Fall 2013
  2. 2. THIS STATEMENT IS FALSE Bigand Gödel, Recursion and Attention Bigand,
  3. 3. THIS STATEMENT IS FALSE Chan Bigand McAdams
  4. 4. THIS STATEMENT IS FALSE Bigand McAdams
  5. 5. THIS STATEMENT IS FALSE Bigand McAdams
  6. 6. THIS STATEMENT IS FALSE Bigand McAdams
  7. 7. THIS STATEMENT IS FALSE Gödel Gödel, Recursion and Attention Bigand, “the standard proof of the second incompleteness theorem assumes that ProvA(P) satisfies that Hilbert–Bernays provability conditions. Letting #(P) represent the Gödel number of a formula P, the derivability conditions say: 1. If T proves P, then T proves ProvA(#(P)). 2. T proves 1.; that is, T proves that if T proves P, then T proves ProvA(#(P)). In other words, T proves that ProvA(#(P)) implies ProvA(#(ProvA(#(P)))). 3. T proves that if T proves that (P → Q) and T proves P then T proves Q. In other words, T proves that ProvA(#(P → Q)) and ProvA(#(P)) imply ProvA(#(Q)).” THIS STATEMENT IS FALSE
  8. 8. THIS STATEMENT IS FALSE
  9. 9. THIS STATEMENT IS FALSE THIS STATEMENT IS FALSE
  10. 10. THIS STATEMENT IS FALSE
  11. 11. SELF-CONTRADICTION SELF-REFERENCE
  12. 12. SELF-REFERENCE Recursion Bigand, Gödel, Recursion and Attention
  13. 13. SELF-REFERENCE Recursion
  14. 14. SELF-REFERENCE Recursion • • • • • Meter Opera: Pagliacci White Christmas Gould: Fugue Fugue/Counterpoint: • Imitation • Augmentation • Diminuion • Inversion • Retrograde • Invertability
  15. 15. SELF-REFERENCE
  16. 16. SELF-REFERENCE
  17. 17. THIS STATEMENT IS FALSE Attention Gödel, Recursion and Attention Bigand,
  18. 18. THIS STATEMENT IS FALSE Attention
  19. 19. THANK YOU Bigand, Gödel, Recursion and Attention

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