That wisdom and ignorance are often outwardly indistinguishable can be demonstrated by the following thought experiment. Imagine that just before a game of Paper-Scissors-Rock I announce, “I am going to play Rock,” when it is also understood that I am trying to win. If my opponent is a small child or an idiot, he will play Paper without even suspecting the possibility of deceit. A less credulous opponent will assume that the intention of saying I will play Rock is to entice him to play Paper which I will defeat with Scissors and so he should play Rock. A third opponent may think of doing the same—before suspecting that I have anticipated him: The real intention of my suspicious announcement about Rock is to make him think I am going to play Scissors as a means of enticing him to play Rock which I will defeat with Paper—and so he should play Scissors. In theory, this laborious and increasingly confusing process could go on forever but a final example will suffice: A fourth player may exist who suspects that all of the above has been foreseen by me and figures in my elaborate ruse: My real intention in saying I will play Rock is to entice him to quickly run through the first two possibilities and then choose, like the third player, to play Scissors—which I will defeat with Rock. And so, being the most thoughtful and skeptical of all my opponents, he follows the example of the idiot and plays Paper. He is not deterred by the fact that doing so looks stupid; actually, it is the very "stupidity" of playing Paper that makes it such a shrewd decision for him—it is the one move I would never expect of my intelligent opponent. For a similar reason, he assumes I believe he would never think me stupid enough to play Rock after announcing the intention to do so—for which very reason Rock is for me the most shrewd and likely move. The results can therefore be tabulated as follows,
In this example it will of course be noticed that the stupidest play and the shrewdest play are disparate in essence but identical in aspect. Montaigne, in his Essays, applies a similar observation to two different religious types: Those, on the one hand, who being “made from simple minds, incurious and unlearned” keep within the tenets of their faith and are never troubled by atheistical misgivings and, on the other hand, the philosophers who, “by long and reverent research penetrate through to a deeper, darker light of Scripture and know the sacred and mysterious secret of our ecclesiastical polity.” According to Montaigne, doubt always arrises from, “minds of middling vigour and middling capacity.” Francis Bacon would have agreed. “A little philosophy inclineth man’s mind to atheism,” he said, “but depth in philosophy bringeth men’s minds about to religion.”