Bigand, Gödel, Recursion and Attention

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Bigand, Gödel, Recursion and Attention
Jordan Smith
Fall 2013

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Bigand Gödel, Recursion and Attention
Bigand,

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Chan
Bigand
McAdams

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Bigand
McAdams

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Bigand
McAdams

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Bigand
McAdams

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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

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THIS STATEMENT IS FALSE

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11. SELF-CONTRADICTION
SELF-REFERENCE

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Recursion
Bigand, Gödel, Recursion and Attention

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Recursion

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Recursion
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Meter
Opera: Pagliacci
White Christmas
Gould: Fugue
Fugue/Counterpoint:
• Imitation
• Augmentation
• Diminuion
• Inversion
• Retrograde
• Invertability

15. SELF-REFERENCE

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Attention Gödel, Recursion and Attention
Bigand,

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Attention

19. THANK YOU
Bigand, Gödel, Recursion and Attention