ANALOGY is the name in logic for a mode of real or material inference, proceeding upon the resemblance between particulars: speaking generally, it is that process whereby, from the known agreement of two or more things in certain respects, we infer agreement in some other point known to be present in one or more, but not known to be present in the other or others. It was signalized already by Aristotle under the different name of Example (paradeigma, Gk.), the word Analogy (analogia, Gk.) having with him the special sense of mathematical proportion or resemblance (equality) of ratios. The earliest use of the name in its current logical sense is to be found apparently in Galen. While, in popular language, the word has come to be vaguely used as a synonym for resemblance, the logical authorities, though having generally the same kind of inference in view, are by no means agreed as to its exact nature and ground. It is chiefly to be distinguished from the related process of Induction, in their conception of which logicians are notoriously at variance. (See Induction.)

Aristotle, distinguishing Syllogism and Induction as passing the one from whole to part (any part), and the other from part (all the parts) to whole, notes under each a loose or rhetorical form—Enthymeme under Syllogism, and Paradigm, or Example, under Induction. Thus, to give him his own instance, it is an inference by way of example—if a war to come of Athens against Thebes is condemned because a past war of Thebes against Phocis is known to have been disastrous. Here the reasoning, which may be said to pass from part to part, is resolved by Aristotle as compounded of an imperfect induction and syllogism; the particular case of Thebes against Phocis started from being first inductively widened into war between neighbors generally, and the particular case of Athens against Thebes arrived at being then drawn out by regular syllogism from that major. Example, or, to speak of it by its later name, the inference from analogy, is thus presented by Aristotle as directly related to induction: it differs from an imperfect induction—what is now often called real or material induction from particulars incompletely enumerated—only in having its conclusion particular instead of general, and its datum singular instead of plural.

Kant and his followers, while maintaining a relation between induction and analogy, mark the difference otherwise than Aristotle. By induction, it is said, we seek to prove that some attribute belongs (or not) to all the members of a class, because it belongs (or not) to many of that class; by analogy, that all attributes of a thing belong (or not) to another thing, because of many of the attributes belong (or not) to this other. In this country Sir William Hamilton has adopted this view (Lectures on Logic, vol. ii. pp. 165-174) though he differs from Kant in understanding it only of the process called applied or modified induction,--not of the pure form of reasoning from all the parts of the whole, which, in the manner of Aristotle, he puts on a level with pure syllogistic deduction. The relation and difference of the two processes may be formulated in the short expressions: One in many, therefore one in all (Induction); Many in one, therefore all in one (Analogy). For instance, it would be an analogical inference—to conclude that a disease corresponding in many symptoms with those observed in typhus corresponds in all, or, in other words, is typhus; whereas it would be an induction—to infer that a particular symptom appearing in a number of typhus patients will appear in all.

The view of Kant and Hamilton does not reach below the surface of the matter, if it can be maintained at all. In the first of the examples just given the inference might well be good induction, all depending upon the kind of symptoms that are made the ground of the conclusion; on the other hand, the second must be a case of mere analogy, not to be called induction. Neither, again, is Aristotle’s view satisfactory, which practically makes the difference to depend upon the mere quantity of the conclusion, worked out as particular for analogy by appending to the induction involved a syllogism of application. Since the universal always carries with it the particular, and cannot be affirmed unless the particular can, the two processes become to all intents and purposes one and the same. If the particular or analogical conclusion is justifiable, it is because there was ground for a good induction (only not of the pure sort); if there was no ground for a good induction, then, upon Aristotle’s resolution, there can be no ground for the particular inference either. Should it be said, indeed, that the peculiarity of the case lies not so much in the conclusion, as in the start being made from one particular instance, whence the process gets its name Example, that undoubtedly will distinguish it from anything that can seriously be called induction; but then what becomes of the resolution that Aristotle makes of it? That resolution can be upheld only at the cost of the character of the inductive process.





The logician who has done most to elaborate the theory of real or material induction, John Stuart Mill, has also been able to give an interpretation of analogy, which, without in the least severing its connection with induction, leaves it as a process for which a distinct name is necessary. According to him, the two kinds of argument, while homogeneous in the type of their inference, which holds for all reasoning from experience,--namely, that things agreeing with one another in certain respects agree also in certain other respects,--yet differ in respect of their degree of evidence. In both the argument is from known points of agreement to unknown; but, whereas in induction the known points of agreement are supposed by due comparison of instances to be have been ascertained as the material ones for the case in hand or conclusion in view,--in other words, to be invariably connected by way of causation with the inferred properties,--it is otherwise in analogy, where it is only supposed that there is no incompatibility between the inferred properties and the common properties, or known points of resemblance, that are taken as the ground of inference. Thus, if by comparison of instances it had been ascertained, or otherwise it were known, that organic life is dependent on the bare possession of an atmosphere in planetary bodies rotating upon an axis, then it would be an induction to infer the presence of life upon any heavenly body, known or as yet undiscovered, in which these conditions should be detected. With our actual knowledge, confined to the case of the Earth, and only enabling us to say that the absence of an atmosphere must destroy life, the inference to such a plant as Mars, where the conditions stated seem to be present, is but analogical; while to the Moon, which seems to have no atmosphere, the inference has not even this amount of force, but there is rather ground for inductively concluding against the possibility of organic life. Upon this view it cases to be characteristic of analogy that the inference should be to a particular case only; for the inductive conclusion, when the evidence is of a kind to admit of such being drawn, may as well be particular; and, again, it may equally well happen that the analogical inference, where nothing stronger can be drawn, should have universal application. Notwithstanding, it will be found in general that, where the evidence, consisting of bare similarity of attributed in two or more particular instances, permits only of an analogical interference being made, the extension in thought takes place to particular cases only which have a special interest, and the mind hesitates to commit itself to a general law or rule. Mill, therefore, though he does not raise the point, is practically at one with Aristotle and all other who make example or analogy to consist in the passage from one or more particular cases to a particular new case bearing resemblance to the former. It is his peculiar merit to have determined the specific conditions under which the passage in thoughts, whether to a particular or a general, acquires the authority of an effective induction.

Analogy is so much resorted to in science in default of induction, either provisionally till induction can be made, or as its substitute where the appropriate evidence cannot be obtained, -- it is also much relied upon in practical life for the guidance of conduct, -- that it becomes a matter of great importance to determine its conditions. Whether in science or in the affairs of life, the abuse of the process, or what is technically called False Analogy, is one of the most besetting snares set for the human mind. It is obvious that, as the argument from analogy proceeds upon bare resemblance, its strength increases with the amount of similarity; so that, though no connection is, or can be inductively made out between any of the agreeing properties and the additional property which is the subject of inference, yet (in Mill’s words), "where the resemblance is very great, the ascertained difference very small, and our knowledge of the subject matter very extensive, the argument from analogy may approach in strength very near to a valid induction. If (he continues), after much observation of B, we find that it agrees with A in nine to one, that it will possesses any given derivative property of A" (Logic, b. iii., c. xx., §3). But it is equally obvious that against the resemblance the ascertainable differences should be told off. For bare analogy, the differences in the two (or more) cases must as little as the resemblances be known to have any connection, one way or the other, with the point in question; both alike must only not be known to be immaterial, else they should fall quite out of the reckoning. As regards the differences, however, this is what can least easily be discovered, or is, by the mind in its eagerness to bring things together, most easily overlooked; and, accordingly, the error of false analogy arises chiefly from neglecting so to consider them. Thus, id the inference is to the presence of organic life of the terrestrial type on other planetary bodies, any agreements, even when extending to the details of chemical constitution, are of small account in the positive sense, compared with the negative import of such facts as absence of atmosphere in the Moon, and excess of heat or cold in the inmost or outermost planets. To neglect such points in question us concerned in them, the analogy becomes false and positively misleading. Still greater is the danger when the things analogically brought together belong not at all to the same natural classes, but the resemblance is only in some internal relation of each to another thing of its own kind; as when, for example, under the name of motives particular states of mind (feelings, &c.) are supposed to determine the action of a man, as the motion of a body may be determined by a composition of forces. In such cases there may be nothing to prevent the drawing of a good analogy upon a strictly limited issue; nay there may even sometimes, in special circumstances, be ground for drawing an inductive conclusion; but generally the elements of differences are so numerous, and their import either so hard to appreciate, or, when, appreciable, so decisive in a sense opposite to the conclusion aimed at, that to leave them out of sight and argue without reference to them, as the mind is tempted to do, vitiates the whole proceeding. What is not sufficient for analogy may, however, be good, as metaphor, and metaphor is of no small use for expository purposes ; while (as Mill save), though it is not an argument, it my imply that an argument exists.

The sense just mentioned of a resemblance of relations suggests the question how far the common argument from analogy and mathematically determinate proportion, which was originally called by the name, are cognate processes. Undoubtedly the common argument, proceeding upon resemblance in the properties of things, can be made to assume roughly the guise of a proportion, -- e.g., Earth: Mars:: Me: Mars-dwellers, or Earth: Men=Mars: Mars dwellers, the fact of planetary nature, or other resembling attributes gone upon, being regarded as common exponent. Less easy is it to interpret a determinate proportion, with numerical equality of ratios, as analogy in the common sense; for here the very determinateness makes all the difference.

The name analogy is so suggestive to English readers of Bishop Butler’s famous treatise, that a word, in conclusion, seems called for on the nature and scope of the particular application of the process made by him. His work is entitled The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature, and consists in an attempt to convince deists that there are no difficulties urged against revelation, or the system of natural religion, which do not bear with equal force against the order of the nature as determined by Providence. The argument is a perfectly fair one within the limits assigned, and Butler must be allowed the credit of very well apprehending the logical conditions involved in it. In his introduction he understates rather than overstates the strength of his position; for, on the assumption that the system of nature and the system of religion must both spring from one causal source, his argument acquires rather an inductive character. Accordingly, it is interesting to see how, in connection with his sense of analogy, he practically raises, in his Introduction, the question which the general theory of inductive logic, as now understood, has first to consider, -- the question, namely, " whence it proceeds that likeness should beget that presumption opinion and full conviction which the human mind us formed to receive from it;" though he would not take it upon him to say "how far the extent, compass, and force of analogical reasoning can be formed into a system." (G. C. R.)






The above article was written by George Croom Robertson, M.A., Professor of Mental Philosophy and Logic at University College, London, 1867-92; first editor of Mind; his articles have been republished under the title of Philosophical Remains.