Analogy

ANALOGY. Originally the general term analogy appears to have been used in the sense of "proportion," and so confined to quantitative relationships. Thus, for instance, the relation between three and four would be described as analogous to that between nine and i 2 ; or, more generally, the relation between x and y would be described as analogous to that between nx and ny. An alogy in this sense could obviously serve as a basis for reliable inferences. In the solution of equations of many kinds it is usually possible to determine (that is, to infer) the value of an unknown quantity when its relation to a known quantity is given. Hence the early vogue of the expression "inference (or reasoning) from analogy." In mathematics, however, the term analogy has been displaced by the term proportion, except in the expression "Napier's Analogies" still used in spherical geometry.

Side by side with this quantitative application of the term an alogy we find, already in Aristotle, a qualitative use of it. In its quantitative sense of "proportion," analogy designated similarity or identity of quantitative relationship between two pairs of terms ; in its qualitative use the term analogy indicates similarity in any kind of (non-quantitative) relationship between two sets of terms. In this wider sense the term is very common, and the thought which it expresses is applied very extensively, especially in popular modes of thought and of expression. This is evident from the frequent use of metaphor, which is but one example of analogy. For instance, the metaphorical use of the term "sweet" in the phrase "a sweet melody" is an abridgment of the analogy that "this melody affects the ear in the same pleasing way as sweet things affect the palate." Similarly the expression "Mother Country" implies the analogy that "the relation of a country to its colonies is like that of a mother to her children." Another familiar group of analogies may be seen in the way in which peo ple inflect new terms (or terms which are new to them) on the model of the known inflections of other terms—e.g., "looped" is to "loop" as "looked" is to "look." Or, again, the names of certain organs of animals are often based on analogies—the so-called "wings" of butterflies are structurally very different from the wings of birds, but their function in relation to the butterfly (viz., in enabling it to fly) is essentially like that of the wings of birds, and so these otherwise different organs of butterflies and of birds are called "analogous organs." Similarly, all kinds of new inventions are frequently given names based on analogy—"air ships," e.g., are machines which do in the air what ships do in the water. And so on.

As appears already from the case of metaphors, from the case of "analogous organs" in biology, and analogous constructions in grammar, the similarity of relationships between pairs or sets of terms is apt to appear as a similarity between the terms or things themselves. And so the term "analogy" has come to be extended to similarities generally, excepting that close similarity which exists between members of the same recognized class of objects in respect of those qualities which are regarded as characteristic of that class. Thus, e.g., one would not think of potatoes as being "analogous" to one another—they are too much like one another for that. Similarly with apples. But, as is evident from their French and German names, potatoes are regarded as "analogous" to apples.

The Psychology of Analogy.

Psychologically or education ally the importance of analogy lies in the fact that it is a very com mon form of apperception (q.v.), a way of assimilating new and strange objects to older and more familiar ones—a way of profit ing from past experience for the proper apprehension and treat ment of new situations. Any new thing or occurrence is apt to appear familiar, and so to become acceptable, as soon as it can be linked up in some way with the general store of our already acquired ideas and beliefs. The only safeguard against the evils of so-called "reasoning from analogy," or "analogical argument," is a correct insight into the real nature and function of analogy considered from a logical point of view.

The Logic of Analogy.

As was pointed out above quantita tive analogy is a basis of valid inferences. Qualitative analogy (the only type with which we are now concerned) is also frequently made the ground of inference. In fact some thinkers regard ana logical reasoning as one of the fundamental types of inference together with deductive and inductive inference. Some, on the other hand, regard it as a species of deductive inference, and others as a variety of inductive inference. But at all events analogy is commonly accepted as a legitimate ground of inference when due care is taken. Now it is true that, as a matter of fact, people commonly do draw inferences from analogy. The real question, however, is whether such inferences can be regarded as conclusive or cogent. In other words, can reasoning from analogy ever be regarded as more than tentative, as equivalent to proof ? This question must be answered in the negative for the following rea sons. Reasoning from analogy usually assumes the following form: A certain phenomenon or a certain class of phenomena, say S, resembles a certain other phenomenon or class of phe nomena, say Z, in some assignable respect, say M. Now Z is known to be P as well as M. It is accordingly inferred that S which resembles Z in respect of M also resembles it in respect of P; in other words, S is P. Now, strictly speaking, this conclusion could only be justified if it could be shown that M and P are connected by some law, either directly or indirectly. For unless M and P are so connected, the presence of M, in S or in anything else, may be entirely irrelevant to the question of the presence of P. That is why it is usually insisted that analogies or similarities must be weighed, not merely counted. For instance, the fact that light and sound resemble each other in respect of being transmitted through considerable distances is in itself no evidence that they also resemble each other in respect of having the same medium, or in respect of polarization, or even in respect of an undulatory form of transmission. If there is any connection between trans missibility and any of these other phenomena, it must be estab lished independently. Now the question whether there is any con nection betwen ICI and P, and if so, what it is, can only be decided by the usual methods of induction, not by mere analogy. The analogy may suggest hypotheses for inductive investigation ; but it cannot prove anything. Analogy, in brief, is probably the most fruitful source of suggestions, of hypotheses, that is, of tentative inferences, but it is not a type of proof at all. If an analogical inference is proved at all it is proved by inductive methods; if it is not proved or verified by inductive methods, it is not proved at all, and remains a mere suggestion, which may indeed be true, but is not yet established. In so far as an analogical suggestion proves fruitful it results in the inductive establishment of a connection between M and P, and so leads to the deductive application of this law of their connection to cases like S, etc. In other words, the analogy may eventually lead to both inductive and deductive proofs; but the analogy itself is neither inductive nor deductive, nor is it a proof at all ; it is only an auxiliary to all these.

Of the value of analogy as an auxiliary to inductive investiga tion there can be no reasonable doubt. The history of science affords abundant evidence of this. A few illustrations may be adduced here. Descartes' perception of the analogy between alge braic and geometrical relationships has led to many important discoveries in modern mathematics. The observation of Jupiter and the Medicean satellites or moons led by analogy to the sug gestion of the modern conception of the solar system. Newton's perception of the analogy between a falling apple and the moon led to the establishment of celestial gravitation. But analogy as such never goes beyond helpful suggestion—the actual results must be borne out by scientific methods. That is why in the more advanced sciences analogy plays a relatively unimportant part. The finished results are supported by inductive evidence; the analogies by which they may have been first suggested are no part of the evidence, and are of interest only as incidents in the mental history of the discoverer, in the history of the builder rather than in the structure of the building. On the other hand, in the less developed sciences analogy may play a prominent role. Much of so-called biological sociology consists in the exploita tion of analogies between the structures and functions of animals and those of societies. The reason for the conspicuous part played by analogy in the less developed sciences, or stages of a science, is this : The first problem to be attacked in the history of a science is that of classification—the most helpful (intellectual) grouping of the phenomena to be investigated. Now some phenomena are obviously similar or obviously different (though not always really so) . Others are not so, and it may require a keen eye for analogies to bring together things that really belong together but not ob viously. In this way analogy may be an early stage in the recog nition of a new and somewhat complex class of facts. The history of terms like "boycott" or "Hobson's choice" furnishes popular illustrations of this process. Franklin's study of lightning, and his careful enumeration of the analogies between lightning and elec tricity, may 'serve as a scientific illustration of the help that may be rendered by analogy in the classificatory stage, as well as in the later stages, of a science. It should be noted, however, that Franklin did not stop at the analogies between lightning and electricity, but proceeded to test the suggestion experimentally by means of his famous kite. In comparatively simple cases the tran sition from analogy to a new class concept is easy. After con sidering a few cases analogous to that of Captain Boycott, or to that of Hobson, one may readily get at the idea of social ostra cism, or of apparent without real choice, respectively. But in more complex instances there is the danger that some important feature may be overlooked in the general description or definition of the type as such. Hence probably the legal tendency to cite cases and follow precedents rather than formulate general laws or principles—flexible analogies being regarded as safer than rigid formulae in certain types of legal and similar problems.

BIBLIOGRAPHY.-B. Bosanquet, Logic; J. S. Mill, System of Logic Bibliography.-B. Bosanquet, Logic; J. S. Mill, System of Logic (1874, etc.) ; C. Sigwart, Logic; A. Wolf, Essentials of Scientific Method; see APPERCEPTION, and SCIENTIFIC METHOD. (A. Wo.)