This paper presents a new approach to thinking about the famous metamathematical results of Kurt Godel based on two ideas.
The first is that the heuristic structure of Godel's proofs of incompleteness and the unprovability of consistency formalize tropes of ancient Pyrrhonian skepticism, principally methods for constructing undecidability and relative consistency proofs. Second, the intensional content of the Second Incompleteness Theorem is treated as its most important feature and used to characterize Godel's work itself as informal mathematics. These ideas are repackaged in chapter 5 of Imre Lakatos and the Guises of Reason, where Pyrhonnian skepticism plays other important roles. Pyrhonnian skepticism was influential in the scientific revolution and many of their ideas have stood the test of time.