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# 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