Lucas on Gödel’s proof

Summary of the second paragraph here.

Thesis: In any formal system* there exists a proposition that (a) is not provable in a formal system and (b) we can know to be true. 

1.) Given any formal system, let proposition (P) be this formula is unprovable in the system

2.) If P is provable, a contradiction occurs.

3.) Therefore, P is known to be unprovable.

4.) If P is known to be unprovable it is known to be true.

5.) Therefore, P is (a) unprovable in a system and (b) known to be true.


*sufficient to give us arithmetic.

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