ANALOGY (Gr. avaXo-yLa, proportion)  , a term signifying, (t) in general, resemblance which falls short of absolute similarity or identity . Thus by analogy, the word " loud," originally applied to sounds, is used of garments which obtrude themselves on the attention; all metaphor is thus a kind of analogy . (2) Euclid used the term for proportionate equality; but in mathematics it is now obsolete except in the phrase, " Napier's Analogies " in spherical trigonometry (see NAPIER, JOHN) . (3) In grammar, it signifies similarity in the dominant characteristics of a language, derivation, orthography and so on . (4) In logic, it is used of arguments by inference from resemblances between known particulars to other particulars which are not observed . Under the name of " example " (srapadetyga) the process is explained by Aristotle (Prior Anal. ii . 4) as an ANALYSIS inference which differs from induction (q.v.) in having a particular, not a general, conclusion; i.e. if A is demonstrably like B in certain respects, if may be assumed to be like it in another, though the latter is not demonstrated . Kant and his followers state the distinction otherwise, i.e. induction argues from the possession of an attribute by many members of a class that all members of the class possess it, while analogy argues that, because A has some of B's qualities, it must have them all (cf . Sir Wm . Hamilton, Lectures on Logic, ii . 165-174, for a slight modification of this view) . J .

S .

Mill very properly rejects this artificial distinction, which is in practice no distinction at all; he regards induction and analogy as generically the same, though differing in the demonstrative validity of their evidence, i.e. induction proceeds on the basis of scientific, causal connexion, while analogy, in absence of proof, temporarily accepts a probable hypothesis . In this sense, analogy may obviously have a universal conclusion . This type of inference is of the greates value in physical science, which has frequently and quite legiti mately used such conclusions until a negative instance has disproved or further evidence confirmed them (for a list of typical cases see T . Fowler's edition of Bacon's Nov . Org . Aph. ii . 27 note) . The value of such inferences depends on the nature of the resemblances on which they are based and on that of the differences which they disregard . If the resemblances are small and unimportant and the differences great and fundamental, the argument is known as " False Analogy." The subject is dealt with in Francis Bacon's Novum Organum, especially ii . 27 (see T . H .

Fowler's notes) under the

head of Instantiae conformes sive proportionatae . Strictly the argument by analogy is based on similarity of relations between things, not on the similarity of things, though it is, in general; extended to cover the latter . See works on Logic, e.g . J . S . Mill, T . H . Fowler, W . S . Jevons . For Butler's Analogy-and its method see BUTLER, JosEPH . The term was used in a special sense by Kant in his phrase, "Analogies of Experience," the third and most important group in his classification of the a priori elements of knowledge .

By it he understood the fundamental

laws of pure natural science under the three heads, substantiality, causality, reciprocity (see F . Paulsen, I . Kant, Eng. trans . 1902, pp . 188 ff.) .