3. Reasoning from Analogy.
Meaning of the term Analogy.—This word, analogy, is used with great variety of meaning, and with much vagueness, therefore. It properly denotes any sort of resemblance, whether of relation or otherwise; and the argument from analogy is an argument from resemblance, an argument of an inductive nature, but not amounting to complete induction. A resembles B in certain respects; therefore it probably resembles it, also, in a certain other respect: such is the argument from analogy. A resembles B in such and such properties, but these are always found connected with a certain other property; therefore A resembles B also in regard to that property: such is the argument from induction. Every resemblance which can be pointed out between A and B creates a further and increased probability that the resemblance holds also in respect to the property which is the object of inquiry. If the two resembled each other in all their properties, there would be no longer any doubt as to this one, but a positive certainty, and the more resemblances in other respects so much the nearer we come to certainty respecting the one that happens to be in question.
Illustration of this Principle.—It was observed by Newton, that the diamond possessed a very high refractive power compared with its density. The same thing he knew to be true of combustible substances. Hence, he conjectured that the diamond was combustible. He conjectured the same thing, and for the same reason, of water, i. e., that it contains a combustible ingredient. In both instances, he guessed right—reasoning from analogy.
Further Illustration of Reasoning from Analogy.—Reasoning from analogy, I might infer that the moon is inhabited, thus: The earth is inhabited—land, sea, and air, are all occupied with life. But the moon resembles the earth in figure, relation to the sun, movement, opacity, etc.; moreover, it has volcanoes as the earth has; therefore, it is probably like the earth in this other respect, that of being inhabited. To make this out by induction, I must show that the moon not only resembles the earth in these several respects, but that these circumstances are in other cases observed to be connected with the one in question; thus, in other cases, bodies that are opaque, spherical, and moving in elliptical orbits, are known to be inhabited. The same thing is probably true then in all cases, and inasmuch as the moon has these marks, it is therefore inhabited.
Counter Probability.—On the other hand, the points of dissimilarity create a counter probability, as, e. g., the moon has no atmosphere, no clouds, and therefore no water; but air and water are, on our planet, essential to life; the presumption is, then, looking at these circumstances merely, that the moon is uninhabited. Nay, more: if life exists, then it must be under very different conditions from those under which it exists here. Evidently, then, the greater the resemblance in other respects between the two planets, the less probability that they differ in this respect (i. e., the mode of sustaining life), so that the resemblances already proved, become, themselves, presumptions against the supposition that the moon is inhabited.
Amount of Probability.—The analogy and diversity, when they come thus into competition and the arguments from the one conflict with those of the other, must be weighed against each other. The extent of the resemblance, compared with the extent of the difference, gives the amount of probability on one side or the other, so far as these elements are known. If any region lies unexplored, we can infer nothing with certainty or probability as to that. Suppose then, that so far as we have had the means of observing, the resemblances are to the differences as four to one; we conclude with a probability of four to one, that any given property of the one will be found to belong to the other. The chances are four out of five.
Value of Analogical Reasoning.—The chief value of analogy, as regards science, however, is as a guide to conjecture and to experiment; and even a faint degree of analogical evidence may be of great service in this way, by directing further inquiries into that channel, and so conducting to eventual probability, or even certainty.
It is well remarked by Stewart, that the tendency of our nature is so to reason from analogy, that we naturally confide in it, as we do in the evidence of testimony.
Liable to mislead.—It must be confessed, however, that it is a species of reasoning likely to mislead in many cases. Its chief value lies not in proving a position, but in rebutting objections; it is good, not for assault, but defence. As thus used it is a powerful weapon in the hands of a skilful master. Such it was in Butler's hands.