 But would God be the right sort of something? If we are only seeking an a priori proof of something (anything at all!), then why not rest content with a mathematical demonstration that there exists an integer between a square and a cube? There must exist such an integer because 25 is a square and 27 is a cube and only one integer can be between 25 and 27. Therefore, something exists. Why does this come off as a mathematical joke?