Induction

§4.3

An induction is an argument in which a universal conclusion pertaining to all objects of a certain sort is inferred from premises about particular objects of that sort. For example, you might infer from premises about particular men being mortal, to the conclusion that all men are mortal.

It is either primarily or exclusively from induction that we acquire the universal knowledge that then gets applied in deductions. However, whereas deduction is well understood, the nature of induction and the standards by which inductive inferences can be assessed are subject to a great deal of confusion and controversy. For example, it is debated whether inductive arguments can ever establish their conclusions with certainty. It is hard to see how they could, since it is not clear what it is about knowing that some (or even many) members of a group have a certain feature that can assure us that the other members of the group must have it as well. On the other hand, since all or most of our deductive arguments depend on induced propositions, and arguments are only as good as their premises, if induction cannot establish conclusions with certainty, then we cannot be certain of the conclusions of (almost any) deductions either. As a result, few if any arguments would be able to establish their conclusions with certainty, and almost all of the things that we think we know by inference would be cast into doubt.

Most contemporary philosophers embrace this skeptical conclusion. A few go further, arguing that induction not only fails to give us certainty but fail to give us any reason whatsoever to believe their conclusions. If they are right, then much of what we ordinary take ourselves to know is not only uncertain, but entirely unfounded. Most philosophers reject this position. Many hold that, though induced conclusions are never certain, they can have such a high degree of probability that we can think of them as certain for most purposes. Some hold that induction can establish certainty, but only when the premises are considered in the context of a great deal of background knowledge that is too vast to be enumerated into premises.

These differing views of the status of induced conclusions are based on differing views of what (if anything) it is about knowing facts about particulars that gives us reasons to believe universal conclusions. For example, the philosophers who have the most positive view of induction tend to focus on the processes by which we form concepts (such as “man” and “moral”) in the first place and classify particular things under them. Some of them stress the role played in this process by an awareness of cause and effect and argue that it is an understanding of causes and of the reasons we had for forming the relevant concepts that justify us in inferring from facts about some instances of those concepts to universal conclusions applying to all the instances. Philosophers who have a less positive attitude towards induction usually think we know less about cause and effect in the first place and tend to regard the classification of particulars into kinds as unfounded. The different theories of the nature of induction, lead to differences of opinion about some of the standards that should be employed in evaluating inductive arguments. For all of these reasons, induction is a difficult subject to cover briefly, and I will not say much about it here. However, I will mention a few factors which all but the most skeptical philosophers agree are crucial to the strength of an inductive inference.

First, as with the case of statistical arguments (discussed above) inductive arguments cannot be assessed in isolation from the rest of one’s knowledge. In particular, no matter how many members of a certain kind one might know to have a certain trait, one cannot rationally infer that all members of the kind have it, if one knows of any member that doesn’t (or if one has good reason to suspect that any member doesn’t). So, to induce that all the members of a kind have a certain trait, it is not sufficient that you know that some members have it, it must be that all the members you know about have it.

Second, you must be on guard against the possibility that it is a coincidence that all the members you know about have the trait. This can easily occur when you don’t know many members, so (all other things being equal) knowing about more members the more of the members of a kind one is aware of, the stronger one’s inductions about it will be.

However, even when one knows something to be true of a great many members of a kind, it is still easy for this to be a coincidence. For example, consider the case of a teacher who has a great deal of experience with autistic children but who has never taught other children. Suppose that this teacher found that a certain pedagogical technique was extremely effective with all of the students on which he tried it. Does this put him in a position to infer that this technique works well for all children? No, because all of the students on which he has tried the technique have something in common other than being children—their autism. Moreover, this common trait is one that there is reason to think might make a difference to which techniques are effective. The teacher would not be in a position to draw a conclusion about children in general until he has tried the technique on children who do not have the disability. Indeed, he will not have a very strong inference about all children, until the group of children on which he has tried the technique is diverse enough that all of its members do not share any trait (other than being children) that there is reason to think might be relevant to which techniques they respond well to. In general, when assessing inductions, you should consider whether the examples used have anything in common that might be relevant to the conclusion other than that they are members of the kind being induced about.