If opaque revolving body will alternately | acted, the effect will continue. produce day and night; but since the they exist and are not counteracted sun no longer does shine on such to-morrow, the sun will rise toa body, the derivative uniformity, morrow. the succession of day and night on the given planet, is no longer true. Those derivative uniformities, therefore, which are not laws of causation, are (except in the rare case of their depending on one cause alone, not on a combination of causes) always more or less contingent on collocations; and are hence subject to the characteristic infirmity of empirical laws, that of being admissible only where the collocations are known by experience to be such as are requisite for the truth of the law, that is, only within the conditions of time and place confirmed by actual observation. Since the causes, namely, the sun and the earth, the one in the state of giving out light, the other in a state of rotation, will exist until something destroys them, all depends on the probabilities of their destruction, or of their counteraction. We know by observation (omitting the inferential proofs of an existence for thousands of ages anterior) that these phenomena have continued for (say) five thousand years. Within that time there has existed no cause sufficient to diminish them appreciably, nor which has counteracted their effect in any appreciable degree. The chance, therefore, that the sun may not rise to-morrow amounts to the chance that some cause, which has not manifested itself in the smallest degree during five thousand years, will exist to-morrow in such intensity as to destroy the sun or the earth, the sun's light or the earth's rotation, or to produce an immense disturbance in the effect resulting from those causes. § 2. This principle, when stated in general terms, seems clear and indisputable; yet many of the ordinary judgments of mankind, the propriety of which is not questioned, have at least the semblance of being inconsistent with it. On what grounds, it may be asked, do we expect that the sun will rise to-morrow? To-morrow is beyond the limits of time comprehended in our observations. They Now, if such a cause will exist tohave extended over some thousands morrow, or at any future time, some of years past, but they do not in-cause, proximate or remote, of that clude the future. Yet we infer with confidence that the sun will rise tomorrow; and nobody doubts that we are entitled to do so. Let us consider what is the warrant for this confidence. cause must exist now, and must have existed during the whole of the five thousand years. If, therefore, the sun do not rise to-morrow, it will be because some cause has existed, the effects of which, though during five In the example in question, we thousand years they have not amounted know the causes on which the deri- to a perceptible quantity, will in one vative uniformity depends. They are, day become overwhelming. Since the sun giving out light, the earth in this cause has not been recognised a state of rotation and intercepting during such an interval of time by light. The induction which shows observers stationed on our earth, it these to be the real causes, and not must, if it be a single agent, be either merely prior effects of a common one whose effects develop themselves cause, being complete, the only cir- gradually and very slowly, or one cumstances which could defeat the which existed in regions beyond our derivative law are such as would observation, and is now on the point destroy or counteract one or other of arriving in our part of the universe. of the combined causes. While the Now all causes which we have expecauses exist, and are not counter-rience of act according to laws in compatible with the supposition that within the limits of whose influence their effects, after accumulating so we have not come during five thousand slowly as to be imperceptible for five years, but which in twenty thousand thousand years, should start into im- more may be producing effects upon mensity in a single day. No mathe- us of the most extraordinary kind. matical law of proportion between an Or the fact which is capable of preeffect and the quantity or relations of venting sunrise may be, not the cumuits cause could produce such contra-lative effect of one cause, but some dictory results. The sudden develop-new combination of causes; and the ment of an effect of which there was chances favourable to that combinano previous trace always arises from tion, though they have not produced the coming together of several distinct it once in five thousand years, may causes not previously conjoined; but produce it once in twenty thousand. So if such sudden conjunction is destined that the inductions which authorise us to take place, the causes, or their to expect future events grow weaker causes, must have existed during the and weaker the farther we look into entire five thousand years; and their the future, and at length become innot having once come together during appreciable. that period shows how rare that par- We have considered the probabiliticular combination is. We have, ties of the sun's rising to-morrow, therefore, the warrant of a rigid in-as derived from the real laws, that is, duction for considering it probable, in a degree undistinguishable from certainty that the known conditions requisite for the sun's rising will exist to-morrow. on from the laws of the causes on which that uniformity is dependent. Let us now consider how the matter would have stood if the uniformity had been known only as an empirical law; if we had not been aware that the sun's § 3. But this extension of deriva- light and the earth's rotation (or the tive laws, not causative, beyond the sun's motion) were the causes limits of observation, can only be to which the periodical occurrence of adjacent cases. If instead of to-mor- daylight depends. We could have row, we had said this day twenty extended this empirical law to cases thousand years, the inductions would adjacent in time, though not so great have been anything but conclusive. a distance of time as we can now. That a cause which, in opposition to Having evidence that the effects had very powerful causes, produced no remained unaltered, and been puncperceptible effect during five thousand tually conjoined for five thousand years, should produce a very con- years, we could infer that the unsiderable one by the end of twenty known causes on which the conjuncthousand, has nothing in it which is tion is dependent had existed undinot in conformity with our experience minished and uncounteracted during of causes. We know many agents, the same period. The same concluthe effect of which in a short period sions, therefore, would follow as in the does not amount to a perceptible preceding case; except that we should quantity, but by accumulating for a only know that during five thousand much longer period becomes con-years nothing had occurred to defeat siderable. Besides, looking at the immense multitude of the heavenly bodies, their vast distances, and the rapidity of the motion of such of them as are known to move, it is a supposition not at all contradictory to experience that some body may be in motion towards us, or we towards it, perceptibly this particular effect; while, when we know the causes, we have the additional assurance that during that interval no such change has been noticeable in the causes themselves as by any degree of multiplication or length of continuance could defeat the effect. there is no uniformity in the collocations of primeval causes. When, therefore, an empirical law is extended beyond the local limits within which it has been found true by observation, the cases to which it is thus extended must be such as are presumably within the influence of the same individual agents. If we discover a new planet within the known bouron of the solar system, (or even bey of those bounds, but indicating its othe nection with the system by revolving round the sun,) we may conclude, with great probability, that it revolves on its axis. For all the known planets do so; and this uniformity points to some common cause antecedent to the first records of astronomical ob servation: and though the nature of this cause can only be matter of conjecture, yet if it be, as is not unlikely, and as Laplace's theory supposes, not merely the same kind of cause, but the same individual cause, (such as an impulse given to all the bodies at once,) that cause, acting at the extreme points of the space occupied by the sun and planets, is likely, unless defeated by some counteracting cause, to have acted at every intermediate point, and probably somewhat beyond; and therefore acted, in all probability, upon the supposed newly-discovered planet. To this must be added, that when | number of places, is no guarantee for we know the causes, we may be able its existence in any other place, since to judge whether there exists any known cause capable of counteracting them; while as long as they are unknown, we cannot be sure but that if we did know them, we could predict their destruction from causes actually in existence. A bedridden savage, who had never seen the cataract of Niagara, but who lived within hearing of it, might imagine that the sound he heard would endure for ever; but if he knew it to be the effect of a rush of waters over a barrier of rock which is progressively wearing away, he would know that within a number of ages which may be calculated it will be heard no more. In proportion, therefore, to our ignorance of the causes on which the empirical law depends, we can be less assured that it will continue to hold good; and the farther we look into futurity, the less improbable is it that some one of the causes whose co-existence gives rise to the derivative uniformity may be destroyed or counteracted. With every prolongation of time the chances multiply of such an event, that is to say, its non-occurrence hitherto becomes a less guarantee of its not occurring within the given time. If, then, it is only to cases which in point of time are adjacent (or nearly adjacent) to those which we have actually observed that any derivative law, not of causation, can be extended with When, therefore, effects which are an assurance equivalent to certainty, always found conjoined can be traced much more is this true of a merely with any probability to an identical empirical law. Happily, for the pur-(and not merely a similar) origin, we poses of life it is to such cases alone that we can almost ever have occasion to extend them. In respect of place, it might seem that a merely empirical law could not be extended even to adjacent cases; that we could have no assurance of its being true in any place where it has not been specially observed. The past duration of a cause is a guarantee for its future existence, unless something occurs to destroy it; but the existence of a cause in one or any may with the same probability extend the empirical law of their conjunction to all places within the extreme local boundaries within which the fact has been observed; subject to the possibility of counteracting causes in some portion of the field. Still more confidently may we do so when the law is not merely empirical; when the phenomena which we find conjoined are effects of ascertained causes, from the laws of which the conjunction of their effects is deducible. In that case, we may both extend the derivative uniformity over a larger space, and with less abatement for the chance of counteracting causes. The first, because, instead of the local boundaries of our observation of the fact itself, we may include the extreme boundaries of the ascertained influence of its causes. Thus the succession of day and night, we know, holds true of all the bodies of the solar system the ept the sun itself; but we know caus only because we are acquainted if sin the causes: if we were not, we tould not extend the proposition beyond the orbits of the earth and moon, at both extremities of which we have the evidence of observation for its truth. With respect to the probability of counteracting causes, it has been seen that this calls for a greater abatement of confidence, in proportion to our ignorance of the causes on which the phenomena depend. On both accounts, therefore, a derivative law which we know how to resolve is susceptible of a greater extension to cases adjacent in place than a merely empirical law. CHAPTER XX. OF ANALOGY. THE word Analogy, as the name of a mode of reasoning, is generally taken for some kind of argument supposed to be of an inductive nature, but not amounting to a complete induction. There is no word, however, which is used more loosely, or in a greater variety of senses, then Analogy. It sometimes stands for arguments which may be examples of the most rigorous Induction. Archbishop Whately, for instance, following Ferguson and other writers, defines Analogy conformably to its primitive acceptation, that which was given to it by mathematicians, Resemblance of Relations. In this sense, when a country which has sent out colonies is termed the mother country, the expression is analogical, signifying that the colonies of a country stand in the same relation to her in which children stand to their parents. And if any inference be drawn from this resemblance of relations, as, for instance, that obedience or affection is due from colonies to the mother country, this is called reasoning by analogy. Or if it be argued that a nation is most beneficially governed by an assembly elected by the people, from the admitted fact that other associations for a common purpose, such as jointstock companies, are best managed by a committee chosen by the parties interested; this, too, is an argument from analogy in the preceding sense, because its foundation is, not that a nation is like a joint-stock company, or Parliament like a board of directors, but that Parliament stands in the same relation to the nation in which a board of directors stands to a joint-stock company. Now, in an argument of this nature, there is no inherent inferiority of conclusiveness. Like other arguments from resemblance, it may amount to nothing, or it may be a perfect and conclusive induction. The circumstance in which the two cases resemble may be capable of being shown to be the material circumstance; to be that on which all the consequences necessary to be taken into account in the particular discussion depend. In the example last given, the resemblance is one of relation; the fundamentum relationis being the management by a few persons of affairs in which a much greater number are interested along with them. Now, some may contend that this circumstance, which is common to the two cases, and the various consequences which follow from it, have the chief share in determining all the effects which make up what we term good or bad administration. If they can establish this, their argument has the force of a rigorous induction; if they cannot, they are said to have failed in proving the analogy between the two cases; a mode of speech which implies that when the analogy can be proved, the argument founded on it cannot be resisted. known to be connected with m; they must not be properties known to be unconnected with it. If, either by processes of elimination, or by deduction from previous knowledge of the laws of the properties in question, it can be concluded that they have nothing to do with m, the argument of analogy is put out of court. The supposition must be that m is an effect really dependent on some property of A, but we know not on which. We cannot point out any of the properties of A which is the cause of m, or united with it by any law. After rejecting all which we know to have nothing to do with it, there remain several between which we are unable to decide of which remaining properties B possesses one or more. This accordingly we consider as affording grounds, of more or less strength, for concluding by analogy that B possesses the attribute m. § 2. It is on the whole more usual, however, to extend the name of analogical evidence to arguments from any sort of resemblance, provided they do not amount to a complete induction without peculiarly distinguishing resemblance of relations. Analogical reasoning, in this sense, may be reduced to the following formula:-Two things resemble each other in one or more respects; a certain proposition is true of the one, therefore it is true of the other. But we have nothing here by which to discriminate analogy from induction, since this type will serve for all reasoning from experience. In the strictest induction, equally with the faintest analogy, we conclude because A resembles B in one or more properties, that it does so in a certain other property. The difference is, that in the case of a complete induction it has been previously shown, by due comparison of instances, that there is an invariable conjunction between the former property or properties and the latter property; but in what is called analogical reasoning, no such conjunction has been made out. There have been no opportunities of putting in practice the Method of Difference, or even the Method of Agreement; but we conelude (and that is all which the argu-perties dependent on that ultimate ment of analogy amounts to) that a fact m, known to be true of A, is more likely to be true of B if B agrees with A in some of its properties, (even though no connection is known to exist between m and those properties,) than if no resemblance at all could be traced between B and any other thing known to possess the attribute m. To this argument it is of course requisite that the properties common to A with B shall be merely not There can be no doubt that every such resemblance which can be pointed out between B and A affords some degree of probability, beyond what would otherwise exist, in favour of the conclusion drawn from it. If B resembled A in all its ultimate properties, its possessing the attribute m would be a certainty, not a probability; and every resemblance which can be shown to exist between them places it by so much the nearer to that point. If the resemblance be in an ultimate property, there will be resemblance in all the derivative pro. property, and of these m may be one. If the resemblance be in a derivative property, there is reason to expect resemblance in the ultimate property on which it depends, and in the other derivative properties dependent on the same ultimate property. Every resemblance which can be shown to exist affords ground for expecting an indefinite number of other resemblances: the particular resemblance sought will, therefore, be oftener found among things thus known to |