analogy, as regards science, however, is as a guide to con jecture and to experiment; and even a faint degree of anaiogical evidence may be of great service in this way, by directing further inquiries into that channel, and so conduct. ing to eventual probability, or even certainty.

It is well remarked by Stewart, that the tendency of cur 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, Oɛwpia; Latin, theoria; French, théorie; Italian, teoria; from Bewpew, to perceive, see, contemplate) denotes properly any philosophical explana tion of phenomena, any connected arrangement and state. ment 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 (Vпо-TiOnμ) 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, i

its nature, conjectural, and therefore uncertain; has its degrees 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 ucorrect. 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 or 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 that the central force of the solar system is one to prove 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 a supposition. Assuming that distant bodies attract each other with a power inversely as the square of the distance.

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it proceeds on that supposition, and arrives at the desired conclusion.

In what Cases admissible. Now this method is always allowable, and strictly, scientific, whenever it is possible to id est. verify our hypothesis, .., in every case in which it is pos sible to show that no law but the one assumed can lead to these same results; that no other hypothesis can accord with the facts.

In the case supposed, it would not be possible to prove that the same movements might not follow from some other law than the one supposed. It is not certain, therefore, that the moving force of the solar system is identical with gravitation, merely because the latter would, if extended so far, produce the same results. In many other cases it is practicable; indeed, in all cases where the inquiry is not to ascertain the cause, but, the cause being already known, to ascertain the law of its action.

Even in cases where the inquiry is not of this nature, hypothesis is of use in the suggestion of future investigations, and, as such, is frequently indispensable.

View of Mr. Mill. Nearly every thing which is now theory, was once hypothesis, says Mill. "The process of tracing regularity in any complicated, and, at first sight, con fused set of appearances, is necessarily tentative: we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena we learn what correc tions to make in our assumption. The simplest supposition which accords with any of the most obvious facts, is the best to begin with, because its consequences are the most easily traced. This rude hypothesis is then rudely corrected, and the operation repeated, until the deductive results are at last made to tally with the phenomena. Let any one watch the manner in which he himself unravels any complicated mass of evidence; let him observe how, for instance, he elicits the true history of any occurrence from

the involved statements of one or of many witnesses. He will find that he does not take all the items of evidence into his mind at once, and attempt to weave them together; the human faculties are not equal to such an undertaking; he extemporizes, from a few of the particulars, a first rude theory of the mode in which the facts took place, and then looks at the other statements, one by one, to try whether they can be reconciled with the provisional theory, or what corrections or additions it requires to make it square w.th them. In this way, which, as M. Comte remarks, has some resemblance to the methods of approximation of mathema ticians, we arrive by means of hypothesis at conclusions not hypothetical."

§ V.- DIFFERENT FORMS OF REASONING.

It remains to treat briefly of the different forms of reason ing, as founded in the laws of thought.

How far these Forms fall within the Province of Psychology. As there are different kinds or modes of reasoning, according to the difference of the subject-matter or material about which our reasoning is employed, so there are certain general forms into which all reasoning may be cast, and which, according to the laws of thought, it naturally assumes. To treat specifically of these forms, their nature, use, and value, is the business of logic; but, in so far as they depend upon the laws of thought, and are merely modes of mental activity as exercised in reasoning, they are to be considered, in connection with other phenomena of the mind, by the psychologist. Briefly to describe these forms, and then to consider their value, is all that I now propose. I begin with the proposition, as the starting point in every process of reasoning.

I. ANALYSIS OF THE PROPOSITION.

What constitutes a Proposition.-All reasoning deals