>That is like saying we grounded Einstein's special theory of relativity in the observation that Mercury was a fraction of a second late in its orbit.
You have obviously not comprehended any of Einstein's own popularizations of Relativity. Nor of the history of ideas in mathematics, regarding continuity. The big discontinuity you experience between what you call "formal reasoning" (can you define that, by the way?) and common sense, is just that -- your experience.