The fallacy of faulty instantiation—also called the fallacy of “accident” and the fallacy of “reference class”—occurs when a person misapplies a general rule to a new case. This fallacy can be committed several ways.

First, a person can take a property that correctly describes most members of a group, that is, rightly describes the typical members of the group, and projects that property onto an atypical or unrepresentative case. For example, it is true (in America) that you introduce yourself to another person by extending your hand. But offering to shake hands with a man missing his arms would be a fallacious application of that general rule. Applying the rule to this atypical case would not be taken as an act of friendship, but one of mocking. It is in this sense that some statisticians use the phrase “fallacy of reference class.” Most Americans generally welcome shaking hands as an act of friendly introduction. But obviously most armless Americans would not. The rule refers to the class of Americans generally, not to the class of armless Americans.

Second, a person can misapply a rule by applying it in a way it was not meant to apply. Specifically, a person can apply a rule to non-essential features of a case rather than essential ones. This is the origin of the label “accident,” which has an older meaning of non-essential (“accidental”) features of a case. For example, from the rule that people like fresh food it doesn’t follow that my dinner guests will all like fresh rat meat on their pizza tonight. The rule “people like fresh food” means that regarding foods people normally prefer, they like those foods fresh. It doesn’t apply to a food that is inherently repellent.

Third, a person can attempt to refute or disprove a rule by deliberately misapplying it to an atypical case. For example, a proponent of gun control faced with the objection that guns deter crime, might fallaciously attempt to rebut this by saying, “Are you kidding? Despite the fact that any U.S. President is surrounded by gun-toting secret service agents, a number of them have been targets of assassins.” This refutation is silly, however. Guns may well deter ordinary criminals, such as robbers and rapists, because such criminals are motivated by self-interest, and the most important self-interest is survival. But assassins are typically motivated by by ideological fervor or desire for fame, and as such are quite atypical.

Note in a case such as the above, the speaker isn’t attempting to prove a contrary rule (“Guns invite attack”), but merely to disprove (however fallaciously) a general rule (“Guns deter attack”), that is, establish a negation of a general rule (“It is not the case that guns deter attack”).