When is it responsible to generalize from a single instance?

Abstract

Although large samples are always better than small samples and always confer greater justification on general claims than small samples, this paper argues for situations where even a small sample can justifiably be thought to be representative of the population and we are justified in believing, or having a pro-attitude towards, a general claim by generalizing from it. It is not fallacious to make inductive inferences in these situations from small samples. I will describe three such scenarios. On the other hand, when it cannot justifiably be thought to be representative of the population then it is always fallacious, irrespective of other considerations. I will describe one such scenario in which generalizing from a small sample has been claimed to be justified on the grounds of cognitive economy and will show that this claim is false unless the scenario reduces to one of the first three. Since generalizing from a single instance is a limiting case of generalizing from a small sample, I will focus on generalizing from a single instance. Whatever can be shown with regard to a single instance follows a fortiori for all small samples. As it turns out, it is very difficult for a reasoner reasoning in good conscience to commit to a fallacy of hasty generalization, and if a fallacy can only be committed by insincere reasoners and cannot be made by reasoners reasoning in good conscience, then it is not very interesting, as it is not really an error in reasoning. The reason for this is that for the reasoner to have reasoned fallaciously, they must have knowingly ignored evidence, and this is something that a sincere reasoner is not likely to have done. Equally, the charge that someone has committed this fallacy is not easy to substantiate and amounts to accusing the reasoner of insincerity.