The logical status of induction has long been a philosophical issue. As expressed by Whitehead, "The theory of induction is the despair of philosophy--and yet all of our activities are based upon it."63 In recent years, however, it has increasingly been realized that these philosophical difficulties are the result of an attempt to equate the results of induction to those of deduction, whereas, in fact, their status is quite different. The deductive process is complete in itself, and if sound reasoning is applied to valid premises, this process arrives at conclusions that are physically certain. The product of induction, on the other hand, is a  probability. Induction is therefore an incomplete process, and the inductive conclusions must be verified. Thus the equivalent of deduction is not induction alone, but induction plus verification. Like the sound deductive conclusions, the verified inductive conclusions are physically certain.

Beyond Space and Time
05 Levels of Existence
DB Larson's picture
Submitted by DB Larson --- not chap 5, but ch 4

There are many different kinds of inductive processes, and they arrive at answers which have widely different degrees of a priori probability of being valid. The basic process is simple enumeration, in which it is assumed that, where all known units of entity A have property x,  all units of entity A have property x. If only a few units of this entity A have been observed, the probability that the conclusion is valid is low, but if the number of observed units is immense, as is often the case, the probability is so great that it is equivalent to physical certainty without any further verification. A somewhat less reliable form of  extrapolation that does require verification reaches this same conclusion that all units of entity A have property x from the observed facts that (1) some units of this entity have property x, and (2) no such units are definitely known to be without this property. A process that arrives at a still lower degree of probability is analogy, in which it is reasoned that since entity A has property x, some entity B that resembles A in certain respects also has property x. A process that is widely utilized in the initial analysis of a mass of observational data is the method of concomitant variations, in which a connection between x and y is inferred from the fact that the analysis shows that factors which cause a change in x also cause a change of a related nature in y. Regardless of whether the inductive conclusions are reached by one of these common methods, or in some other way, these conclusions become physically certain, and acquire the status of scientific knowledge, if, and only if, they are verified.

successes have come in those instances where there were enough empirical facts available to permit arriving at conclusions by induction. The merit of the inductive process is that it is not, like invention, a shot in the dark; it produces a result which has a distinct probability, often a very high probability, of being correct.