In this, the second of our esteemed series of paradoxes, we delve into the depths of prophets and the intricacies of incompleteness.
This proof is a masterclass in self-referential logic, where the statement "This sentence is not true" is not true.
Assume that the statement is false. Then, by our earlier work, we have that the statement must be true.
But wait, that's not possible! We've created a paradox, a self-contained contradiction.
The mathematicians at Proof 3 have taken issue with this proof, calling it "a juggling act with truth and falsehoods."
For a more in-depth exploration of paradoxes, see Paradoxes of Logic.
For a more concrete approach to the incompleteness theorem, see Proof 4: The Unsettling of Set Theory.
This proof is dedicated to the memory of Gödel's cat, who was not impressed.
