One thing to notice about this discussion is that Theaetetus does not dig in his heels and insist that the ignorant members of the jury do know that the per- son is innocent provided only that they believe it and it is true. Faced with the counterexample, he retreats at once. Why is this? Why not stay with the defi- nition and reject the counterexample as false? The answer is that for many concepts, there is general agreement about their application to particular cases, even if there is no general agreement about a correct definition. To take an extreme example, everyone agrees that Hitler was a dictator (even Hitler), and no one supposes that Thomas Jefferson was a dictator (even his enemies). So any definition of “dictator” must be wrong if it implies that Hitler was not a dictator or that Thomas Jefferson was a dictator. Of course, people do dis- agree about borderline cases, so there might be no perfectly exact definition of “dictator.” Nonetheless, any definition that does not square with the clear cases can be refuted by citing one of these clear cases as a counterexample.

Ethics is an area where arguments often turn on counterexamples. Con- sider the traditional moral precept “Do unto others as you would have them do unto you.” This principle captures an important moral insight, but, if taken quite literally, it is also subject to counterexamples. Jones, a sadomasochist, en- joys beating other people. When asked whether he would like to be treated in that way, he replies, “Yes.” It is obvious that the Golden Rule was not in- tended to approve of Jones’s behavior. The task, then, is to reformulate this rule to avoid this counterexample. That is not as easy as it might seem.

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No discussion of counterexamples is complete without a mention of the Morgenbesser retort. Though the exact story is now shrouded in the mists of time, it has come down to us from the 1950s in the following form: In a lec- ture, a British philosopher remarked that he knew of many languages in which a double negative means an affirmative, but not one language in which a double affirmative means a negative. From the back of the room came Morgenbesser’s retort: “Yeah, yeah.”