REQUIREMENTS OF A TRUE ANALOGY.
It has been remarked that the certitude of an induction by simple enumeration depends upon the number of uncontradicted instances. In analogy the case is different as the process emphasizes the weight of the points of resemblance rather than the number. In substance the requirements of a logical analogy are three.
First. The points of resemblance must be representative and not exceptional. For example: The argument that Mars is inhabited because it has two moons is of little worth, since we have no proof that moonshine is essential to life; this point of resemblance is not representative. On the other hand, if the basis of argument is the fact that Mars has an atmosphere, the conclusion carries some weight; as air seems to be essential to life.
Second. The points of resemblance must outweigh the points of difference. That is, the ratio of probability must always be in favor of the resembling instances. Since it is not a matter of numbers but of weight, a numerical proportion like this would be misleading: Resemblances: Differences = 10:6. It is obvious that the six differences might more than outweigh the ten resemblances. The safer way, if it were possible, would be to attach a value to each point of resemblance or difference, and then express the proportion in terms of the sums of these values.
Third. There must be no difference which is absolutely incompatible with the affirmation which we wish to prove. For example, the fact that the moon has no atmosphere renders nugatory any attempt to prove the habitability of the moon.
13. INDUCTION BY ANALYSIS.
This, the third form of inductive research, is by far the most important. Simple enumeration, because it depends upon the number of observed instances, consumes much time; while we have already noted how easy it isfor analogy to lead to error. At the best, the conclusion of these methods must be subjected to analytic investigation, if we are seeking universal validity. Induction by analysis is superior to the other forms because it secures a higher degree of probability and is a positive time saver.
Defined. We have learned that analysis is the process of separating a whole into its related parts. We thus define induction by analysis as the process of separating a whole into its parts with a view of deriving a generalization relative to the nature and causal connection of these parts.
ILLUSTRATIONS:
(1) Concerning the generalization that “all birds have wings,” it becomes possible to observe in detail the nature of the wings and advance the hypothesis that these wings are designed for aërial navigation. This hypothesis may then be strengthened by observing that the entire structure of the bird is adapted to flying.