Induction (logic)

Induction (logic), in logic, process of drawing a conclusion about an object or event that has yet to be observed or occur, on the basis of previous observations of similar objects or events. For example, after observing year after year that a certain kind of weed invades our yard in autumn, we may conclude that next autumn our yard will again be invaded by the weed; or having tested a substantially large sample of coffee makers, only to find that each one of them has a faulty fuse, we conclude that all the coffee makers in the batch are defective. In these cases we infer, or reach a conclusion based on observations. The observations or assumptions on which we base the inference—the annual appearance of the weed, or the sample of coffee makers with faulty fuses—constitute the premises or assumptions.

In an inductive inference, the premises provide evidence or support for the conclusion; this support can vary in strength. The argument’s strength depends on how likely it is that the conclusion will be true, assuming all of the premises to be true. If assuming the premises to be true makes it highly probable that the conclusion also would be true, the argument is inductively strong. If, however, the supposition that all the premises are true only slightly increases the probability that the conclusion will be true, the argument is inductively weak.

The actual truth or falsity of the premises or the conclusion is not at issue. The degree of strength instead depends on whether, and how much, the likelihood of the conclusion’s being true would increase if the premises were true. So, in induction, as in deduction, the emphasis is on the form of support that the premises provide to the conclusion. However, induction differs from deduction in a crucial aspect. In deduction, for an argument to be correct, if the premises were true, the conclusion would have to be true as well. In induction, however, even when an argument is inductively strong, the possibility remains that the premises are true and the conclusion false. To return to our examples, even though it is true that this weed has invaded our yard every year, it remains possible that the weed could die and never reappear. Likewise, it is true that all of the coffee makers tested had faulty fuses, but it is possible that the remainder of the coffee makers in the batch are not defective. Yet it is still correct, from an inductive point of view, to infer that the weed will return, and that the remainder of the coffee makers have faulty fuses.

Thus, strictly speaking, all inductive inferences are deductively invalid. Yet induction is not worthless; in both everyday reasoning and scientific reasoning (see scientific method) regarding matters of fact—for instance in trying to establish general empirical laws—induction plays a central role. In an inductive inference, for example, we draw conclusions about an entire group of things, or a population, on the basis of data about a sample of that group or population; or we predict the occurrence of a future event on the basis of observations of similar past events; or we attribute a property to a nonobserved thing on the grounds that all observed things of the same kind have that property; or we draw conclusions about causes of an illness based on observations of symptoms. Inductive inference is used in almost all fields, including education, psychology, physics, chemistry, biology, and sociology. Consequently, because the role of induction is so central in our processes of reasoning, the study of inductive inference is one of the major areas of concern in efforts to create computer models of human reasoning in Artificial Intelligence.

The development of inductive logic owes a great deal to 19th-century British philosopher John Stuart Mill, who studied different methods of reasoning and experimental inquiry in his work A System of Logic (1843). Mill was chiefly interested in studying and classifying the different types of reasoning in which we start with observations of events and go on to infer the causes of those events. In A Treatise on Induction and Probability (1960), 20th-century Finnish philosopher Georg Henrik von Wright expounded the theoretical foundations of Mill’s methods of inquiry.

Philosophers have struggled with the question of what justification we have to take for granted induction’s common assumptions: that the future will follow the same patterns as the past; that a whole population will behave roughly like a randomly chosen sample; that the laws of nature governing causes and effects are uniform; or that we can presume that a sufficiently large number of observed objects gives us grounds to attribute something to another object we have not yet observed. In short, what is the justification for induction itself? This question of justification, known as the problem of induction, was first raised by 18th-century Scottish philosopher David Hume in his An Enquiry Concerning Human Understanding (1748). While it is tempting to try to justify induction by pointing out that inductive reasoning is commonly used in both everyday life and science, and its conclusions are, by and large, proven to be correct, this justification is itself an induction and therefore it raises the same problem: Nothing guarantees that simply because induction has worked in the past it will continue to work in the future. The problem of induction raises important questions for the philosopher and logician whose concern it is to provide a basis of assessment of the correctness and the value of methods of reasoning.