Analogy, (from Greek ana logon, “according to a ratio”), originally, a similarity in proportional relationships. It may be a similarity between two figures (e.g., triangles) that differ in scale or between two quantities, one of which, though unknown, can be calculated if its relation to the other is known to be similar to that in which two other known quantities stand. Thus, if 2:4::4:x, it can be seen that x = 8. Another form of analogy noted by the Greeks is that of inferring similarity of function, known as “educing the correlate.” Aristotle (Topics, i, 17) stated the formulas of these two kinds of analogy: “As A is to B, so C is to D”; and “As A is in B, so C is in D.”
Plato employed a functional analogy when he argued that the Idea of the Good makes knowledge possible in the intelligible world just as the Sun makes vision possible in the perceptual world. Here a relationship not yet understood is analogous to one already familiar.
In the European Middle Ages it was believed that the universe forms an ordered structure such that the macrocosmic pattern of the whole is reproduced in the microcosmic pattern of the parts so that it is possible to draw inferences by analogy from the one to the other. Thus, the law of nature conceived in the juridical sense, which prescribes the fitting order of human relationships, could be assimilated to the physical sense of law, which describes the order obtaining in the natural world. Because the natural world exhibits hierarchical degrees of subordination, it was argued, human relationships should also exhibit such subordination. Such parallels were held to constitute arguments and not merely allegorical illustrations; it was contended, for instance, that, as there were two luminaries to light the world and two authorities set over man (the papacy and the empire), then, as the Moon’s light is reflected from the Sun, so the imperial authority must be derived from the papal. Dante, in his De monarchia (c. 1313), while claiming that it is light and not authority that the empire derives from the papacy, nevertheless accepted the principles on which such arguments are built.
In scientific thinking, analogies or resemblances may be used to suggest hypotheses or the existence of some law or principle, especially if a comparison can be made between the functions of elements in two systems, as when observation of the moons of Jupiter suggested by analogy the modern conception of the solar system. The argument of Thomas Robert Malthus, the English economist, that populations tend to increase in numbers beyond the means of their subsistence suggested to Charles Darwin the evolutionary hypothesis of natural selection. The fruitfulness of such analogies depends on whether any testable consequences can be deduced from them, which is likely to depend on whether the resemblance is of a fundamental or a merely superficial kind. Functional resemblances are more likely to be fundamental than qualitative ones (such as colour). It would not be legitimate, for instance, to conclude from the model of the atomic nucleus as a miniature solar system that the process of nuclear fission is similar to that by which new planetary systems may be formed or disrupted.
In social and political discussion, analogies may elucidate some unfamiliar point in terms of what is more familiar. Thus, biological analogies may suggest that a community has an “organic” relationship. Such analogies are misleading, however, insofar as they overlook the fact that individual members of the community also have purposes, rights, and responsibilities of their own. In employing the method of analogy, it should always be possible to show that the resemblances noted bear relevantly on the point to be established, whereas the differences are irrelevant. In many cases it is difficult to be sure of this distinction, and arguments from analogy are therefore precarious unless supported by considerations that can be established independently.