I'm also still bemused with Gödel's second theorem:

*For any formal recursively enumerable (i.e. effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.*That is, any mathematical system that can express addition can not be proven consistent within the system. If it contains a statement proving its consistency, it means it is not consistent. Gödel's first theorem is likewise entertaining, but the basic idea of the second is just hilarious. It says that a mathematical system saying it is consistent is like someone saying "I have never lied." Everyone has lied at some point. Thus, we know that statement to be a lie... Only it's stronger in math.

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