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. - Rea soning from analogy, I might infer that the moon is inbabited, 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 ele nents are known. If any region lies unexplored, we can infer nothing with certainty or probability as to that. Sup pose, 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 con jecture 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 ur 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.

§ IV. — USE OF HYPOTHESES AND THEORIES IN REASONING.

Theory, what. The terms hypothesis and theory are often used interchangeably and loosely. Confusion is the result. It is difficult to define them accurately.

Theory (from the Greek, Oɛopia; Latin, theoria; French, théorie; Italian, teoria; from Oɛwpɛw, to perceive, see, contemplate denotes properly any philosophical explanation of phenomena, any connected arrangement and statement of facts according to their bearing on some real or imaginary law.) The facts, the phenomena, once known, proved, rest on independent evidence. Theory takes survey of them as such, with special reference to the law which governs and connects them, whether that law be also known or merely conjectured.

Hypothesis, what.- ·Hypothesis (vπо-т0ημ) denotes a gratuitous supposition or conjecture, in the absence of all positive knowledge as to what the law is that governs and connects the observed phenomena, or as to the cause which will account for them.

Theory may or may not be Hypothesis.- Hypothesis is, in

its nature, conjectural, and therefore uncertain; has its de grees of probability - no certainty. The moment the thing supposed is proved true, or verified, if it ever is, it ceases to be hypothesis. Theory, however, is not necessarily a matter of uncertainty. After the law or the cause is ascertained, fully known, and no longer a hypothesis at all, there may be still a theory about it; a survey of the facts and phenomena, as they stand affected by that law, or as accounted for by that cause. The motion of the planets in elliptical orbits, was originally matter of conjecture, of hypothesis. It is still matter of theory.

Probability of Hypothesis. - The probability of a hypothesis is in proportion to the number of facts or phenomena, in the given case, which it will satisfactorily explain, in other words, account for. Of several hypotheses, that is the most probable which will account for the greatest number of the given phenomena - those which, if the hypothesis be true, ought to fall under it as their law. If it accounts for all the phenomena in the case, it is generally regarded as having established its claim to certainty. So Whewell maintains. This, however, is not exactly the case. The hypothesis can be verified only by showing that the facts or phenomena in the case cannot possibly be accounted for on any other supposition, or result from any other cause; not simply that they can be accounted for, or can result from this. This is well stated by Mill in his System of Philosophy. The hypothesis of the undulating movement of a subtle and all-pervading ether will account for many of the known phenomena of light; but it has never been shown, and in the nature of the case never can be, probably, that no other hypothesis possible or supposable will also account for them.

Use of Hypotheses. As to the use of hypotheses in science, Reid's remarks are altogether too sweeping, and quite mucorrect. It is not true that hypotheses lead to no valuable result in philosophy. Almost all discoveries were at first hypotheses, suppositions, lucky guesses, if you please to call

them so. The Copernican theory that the earth revolves on its axis was a mere hypothesis at the outset. Kepler's theory of the elliptical orbits of the planets was such; he made and abandoned nineteen false ones before he hit the right. This discovery led to another that planets describe equal areas in equal times. Newton never framed hypotheses, if we may believe him. But his own grand discovery of the law of gravity as the central force of the system, depends for one of its steps of evidence on his previous discovery that the force of attraction varies as the inverse square of the dis tance, and this was suggested by him at first as a mere hypothesis; he was able to verify it only by calling in the aid of Kepler's discovery of equal areas in equal times, which latter, as already stated, was itself the result of hypothesis. Had it not been for one hypothesis of Newton, verified by the results of another hypothesis of Kepler, Newton could never have made his own discovery.

A hypothesis, it must be remembered, is any supposition, with or without evidence, made in order to deduce from it conclusions agreeable to known facts. If we succeed in doing this, we verify our hypothesis (unless, indeed, it can be shown that some other hypothesis will equally well suit these facts), and our hypothesis, when verified, ceases to be longer a hypothesis, takes its place as known truth, and in turn serves to explain those facts which would, on the supposition of its truth, follow from it as a cause. It is simply a short-hand process of arriving at conclusions in science. Suppose the problem to be the one already named

to prove that the central force of the solar system is one and the same with gravity. Now it may not be easy, or even possible in some cases, to establish the first step or premiss in such a chain of reasoning. The inductions leading to it may not be forthcoming. Hypothesis steps in and supplies. the deficiency, by substituting in place of the induction at supposition. Assuming that distant bodies attract each other with a power inversely as the square of the distance,