

All the successful theories were developed from experimental results
The more I think about this, the more I’m not sure I 100% agree… For example, special relativity essentially came from the observation that Maxwell’s equations were not Galilean invariant, and instead invariant under this weird other group (what we now call the Lorentz group); and QED essentially came from Dirac wanting to take a “square root” of the Klein-Gordan equation.
(Of course, real history is more intricate than this.)
Well, Con(PA) is a “natural” statement I’d say, and ZFC proves Con(PA).