8 - SAMPLING

Summary

Introduction

As some of our earlier discussions have indicated, one major variety of reasoning in which we engage is inductive reasoning, whereby a conclusion is drawn on the basis of experience that is in some way incomplete. We decide that something will be a certain way because we, and perhaps others, have found it to be that way in the past. What we are drawing from for our evidence is what we take to be a representative sample of cases of the thing in question. The better the sample, or range and depth of experience, the more justified is the conclusion drawn from it. The most public way in which we see this kind of reasoning is through the reported results of opinion polls.

As early as the Port Royal Logic (1662) logicians have identified invalid inductions as a species of fallacy. Inductions based on fewer than all instances, we are told, often lead us into error. But we inevitably have to reason on the basis of fewer than all instances, so the opportunities for error are extensive. The question is how few instances we can accept before the conclusion we draw is unjustified, and the answer will depend on the contexts involved and the types of things we are reasoning about. The fallacy that arises when we conclude too much on too little evidence has come to be called the Hasty Generalization.