From these three premises we can validly infer that John committed the crime. Suppose, however, that we discover that John could not have com- mitted the crime. (Three bishops and two judges swear that John was some- where else at the time.) Now, from the fact that John did not commit the crime, we could not immediately conclude that Joan committed it, for that would lead to an inconsistency. If she committed the crime, then, according to premise 3, she would have committed a motiveless crime, but that con- flicts with premise 2, which says that motiveless crimes do not occur. So the discovery that John did not commit the crime entails that at least one of the premises in the argument must be abandoned, but it does not tell us which one or which ones.
This same phenomenon occurs when we are dealing with counterevidence to a complex system of beliefs. Counterevidence shows that there must be something wrong somewhere in the system, but it does not show exactly where the problem lies. One possibility is that the supposed counterevidence is itself in error. Imagine that a student carries out an experiment and gets the result that one of the fundamental laws of physics is false. This will not shake the scientific community even a little, for the best explanation of the student’s result is that she messed things up. Given well-established principles, she could not have gotten the result she did if she had run the experiment cor- rectly. Of course, if a great many reputable scientists find difficulties with a supposed law, then the situation is different. The hypothesis that all of these scientists, like the student, simply messed up is itself highly unlikely. But it is surprising how much contrary evidence will be tolerated when dealing with a strong explanatory theory. Scientists often continue to employ a theory in the face of counterevidence. Sometimes this perpetuates errors. For years, in- struments reported that the levels of ozone above Antarctica were lower than before, but scientists attributed these measurements to bad equipment, until finally they announced an ozone hole there. Still, there is often good reason to hold on to a useful theory despite counterevidence, as long as its defects do not make serious trouble—that is, give bad results in areas that count. Good judgment is required to determine when it is finally time to shift to a different explanation.