It is straightforward to prove that someone is an astronomer, or is sane, but how do you prove that someone is not an astronomer, or is insane? The first proof is trivial, the second perhaps impossible, Leibniz explained. How in general do you prove that someone is insane? What would such a proof even look like? Natural phenomena are of no help here. God, who, of course, as a consequence of His nature, has infinite knowledge of the universe, including the universe inside the human head, knows the answer, but the limitations of man prevent man from receiving that knowledge from Him. “I hazard to suggest that man is, in this respect, on his own.” There were now exactly three hours until the predicted eclipse. Leibniz would, in that time, he wrote, rap on the window, gain entry to the observatory, ask the old man simply, How did you come to lose your eyes and how do you claim to see the stars without them?, and then at the stroke of noon incline his head toward the heavens. If Leibniz deemed the man’s story sane, and the solar eclipse furthermore occurred, then the old man was certainly sane. If Leibniz deemed the man’s story insane, yet the eclipse occurred, then, too, the old man was certainly sane. If Leibniz deemed the man’s story insane, and the eclipse furthermore failed to occur, then the old man was probably, but only probably, as it would be no demonstration, insane. And if Leibniz deemed the man’s story sane, but the eclipse failed to occur, then the old man was possibly (but only possibly!) sane, although, in truth, in that case, at once the thorniest case and the most common, and, added Leibniz, actually even the quintessential case here on Earth, we would know more or less nothing at all.

“At that moment,” Leibniz wrote, “I rapped on the window.”