Book III

INDUCTION.

CHAPTER I.

PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.

As all knowledge not intuitive comes exclusively from inductions, induction is the main topic of Logic; and yet neither have metaphysicians analysed this operation with a view to practice, nor, on the other hand, have discoverers in physics cared to generalise the methods they employed.

Inferences are equally inductive, whether, as in science, which needs its conclusions for record, not for instant use, they pass through the intermediate stage of a general proposition (to which class Dr. Whewell, without sanction from facts, or from the usage of Reid and Stewart, the founders of modern English metaphysical terminology, limits the term induction), or are drawn direct from particulars to a supposed parallel case. Neither does it make any difference in the character of the induction, whether the process be experiment or ratiocination, and whether the object be to infer a general proposition or an individual fact. That, in the latter case, the difficulty of the practical enquiries, e.g. of a judge or an advocate, lies chiefly in selecting from among all approved general propositions those inductions which suit his case (just as, even in deductive sciences, the ascertaining of the inductions is easy, their combination to solve a problem hard) is not to the point: the legitimacy of the inductions so selected must at all events be tried by the same test as a new general truth in science. Induction, then, may be treated here as though it were the operation of discovering and proving general propositions; but this is so only because the evidence which justifies an inference respecting one unknown case, would justify a like inference about a whole class, and is really only another form of the same process: because, in short, the logic of science is the universal logic applicable to all human enquiries.

CHAPTER II.

INDUCTIONS IMPROPERLY SO CALLED.

Induction is the process by which what is true at certain times, or of certain individuals, is inferred to be true in like circumstances at all times, or of a whole class. There must be an inference from the known to the unknown, and not merely from a less to a more general expression. Consequently, there is no valid induction, 1, in those cases laid down in the common works on Logic as the only perfect instances of induction, viz. where what we affirm of the class has already been ascertained to be true of each individual in it, and in which the seemingly general proposition in the conclusion is simply a number of singular propositions written in an abridged form; or, 2, when, as often in mathematics, the conclusion, though really general, is a mere summing up of the different propositions from which it is drawn (whether actually ascertained, or, as in the case of the uncalculated terms of an arithmetical series, when once its law is known, readily to be understood); or, 3, when the several parts of a complex phenomenon, which are only capable of being observed separately, have been pieced together by one conception, and made, as it were, one fact represented in a single proposition.

Dr. Whewell sets out this last operation, which he terms the colligation of facts, as induction, and even as the type of induction generally. But, though induction is always colligation, or (as we may, with equal accuracy, characterise such a general expression obtained by abstraction simply connecting observed facts by means of common characters) description, colligation, or description, as such, though a necessary preparation for induction, is not induction. Induction explains and predicts (and, as an incident of these powers, describes). Different explanations collected by real induction from supposed parallel cases (e.g. the Newtonian and the Impact doctrines as to the motions of the heavenly bodies), or different predictions, i.e. different determinations of the conditions under which similar facts may be expected again to occur (e.g. the stating that the position of one planet or satellite so as to overshadow another, and, on the other hand, that the impending over mankind of some great calamity, is the condition of an eclipse), cannot be true together. But, for a colligation to be correct, it is enough that it enables the mind to represent to itself as a whole all the separate facts ascertained at a given time, so that successive tentative descriptions of a phenomenon, got by guessing till a guess is found which tallies with the facts, may, though conflicting (e.g. the theories respecting the motions of the heavenly bodies), be all correct so far as they go. Induction is proof, the inferring something unobserved from something observed; and to provide a proper test of proof is the special purpose of inductive logic. But colligation simply sums up the facts observed, as seen under a new point of view. Dr. Whewell contends that, besides the sum of the facts, colligation introduces, as a principle of connection, a conception of the mind not existing in the facts. But, in fact, it is only because this conception is a copy of something in the facts, although our senses are too weak to recognise it directly, that the facts are rightly classed under the conception. The conception is often even got by abstraction from the facts which it colligates; but also when it is a hypothesis, borrowed from strange phenomena, it still is accepted as true only because found actually, and as a fact, whatever the origin of the knowledge of the fact, to fit and to describe as a whole the separate observations. Thus, though Kepler's consequent inference that, because the orbit of a planet is an ellipse, the planet would continue to revolve in that same ellipse, was an induction, his previous application of the conception of an ellipse, abstracted from other phenomena, to sum up his direct observations of the successive positions occupied by the different planets, and thus to describe their orbits, was no induction. It altered only the predicate, changing--The successive places of, e.g. Mars, are A, B, C, and so forth, into--The successive places of, e.g. Mars, are points in an ellipse: whereas induction always widens the subject.

CHAPTER III.

THE GROUND OF INDUCTION.

Induction is generalisation from experience. It assumes, that whatever is true in any one case, is true in all cases of a certain description, whether past, present, or future (and not merely in future cases, as is wrongly implied in the statement by Reid's and Stewart's school, that the principle of induction is 'our intuitive conviction that the future will resemble the past'). It assumes, in short, that the course of nature is uniform, that is, that all things take place according to general laws. But this general axiom of induction, though by it were discovered the obscure laws of nature, is no explanation of the inductive process, but is itself an induction (not, as some think, an intuitive principle which experience verifies only), and is arrived at after many separate phenomena have been first observed to take place according to general laws. It does not, then, prove all other inductions. But it is a condition of their proof. For any induction can be turned into a syllogism by supplying a major premiss, viz. What is true of this, that, &c. is true of the whole class; and the process by which we arrive at this immediate major may be itself represented by another syllogism or train of syllogisms, the major of the ultimate syllogism, and which therefore is the warrant for the immediate major, being this axiom, viz. that there is uniformity, at all events, in the class of phenomena to which the induction relates, and a uniformity which, if not foreknown, may now be known.

But though the course of nature is uniform, it is also infinitely various. Hence there is no certainty in the induction in use with the ancients, and all non-scientific men, and which Bacon attacked, viz. 'Inductio per enumerationem simplicem, ubi non reperitur instantia contradictoria'--unless, as in a few cases, we must have known of the contradictory instances if existing. The scientific theory of induction alone can show why a general law of nature may sometimes, as when the chemist first discovers the existence and properties of a before unknown substance, be inferred from a single instance, and sometimes (e.g. the blackness of all crows) not from a million.

CHAPTER IV.

LAWS OF NATURE.

The uniformity of the course of nature is a complex fact made up of all the separate uniformities in respect to single phenomena. Each of these separate uniformities, if it be not a mere case of and result from others, is a law of nature; for, though law is used for any general proposition expressing a uniformity, law of nature is restricted to cases where it has been thought that a separate act of creative will is necessary to account for the uniformity. Laws of nature, in the aggregate, are the fewest general propositions from which all the uniformities in the universe might be deducted. Science is ever tending to resolve one law into a higher. Thus, Kepler's three propositions, since having been resolved by Newton into, and shown to be cases of the three laws of motion, may be indeed called laws, but not laws of nature.

Since every correct inductive generalisation is either a law of nature, or a result from one, the problem of inductive logic is to unravel the web of nature, tracing each thread separately, with the view, 1, of ascertaining what are the several laws of nature, and, 2, of following them into their results. But it is impossible to frame a scientific method of induction, or test of inductions, unless, unlike Descartes, we start with the hypothesis that some trustworthy inductions have been already ascertained by man's involuntary observation. These spontaneous generalisations must be revised; and the same principle which common sense has employed to revise them, correcting the narrower by the wider (for, in the end, experience must be its own test), serves also, only made more precise, as the real type of scientific induction. As preliminary to the employment of this test, nature must be surveyed, that we may discover which are respectively the invariable and the variable inductions at which man has already arrived unscientifically. Then, by connecting these different ascertained inductions with one another through ratiocination, they become mutually confirmative, the strongest being made still stronger when bound up with the weaker, and the weakest at least as strong as the weakest of those from which they are deduced (as in the case of the Torricellian experiment) while those leading deductively to incompatible consequences become each other's test, showing that one must be given up (e.g. the old farmers' bad induction that seed never throve if not sown during the increase of the moon). It is because a survey of the uniformities ascertained to exist in nature makes it clear that there are certain and universal uniformities serving as premisses whence crowds of lower inductions may be deduced, and so be raised to the same degree of certainty, that a logic of induction is possible.

CHAPTER V.

THE LAW OF UNIVERSAL CAUSATION.

Phenomena in nature stand to each other in two relations, that of simultaneity, and that of succession. On a knowledge of the truths respecting the succession of facts depends our power of predicting and influencing the future. The object, therefore, must be to find some law of succession not liable to be defeated or suspended by any change of circumstances, by being tested by, and deduced from which law, all other uniformities of succession may be raised to equal certainty. Such a law is not to be found in the class of laws of number or of space; for though these are certain and universal, no laws except those of space and number can be deduced from them by themselves (however important elements they may be in the ascertainment of uniformities of succession). But causation is such a law; and of this, moreover, all cases of succession whatever are examples.

This Law of Causation implies no particular theory as to the ultimate production of effects by efficient causes, but simply implies the existence of an invariable order of succession (on our assurance of which the validity of the canons of inductive logic depends) found by observation, or, when not yet observed, believed, to obtain between an invariable antecedent, i.e. the physical cause, and an invariable consequent, the effect. This sequence is generally between a consequent and the sum of several antecedents. The cause is really the sum total of the conditions, positive and negative; the negative being stated as one condition, the same always, viz. the absence of counteracting causes (since one cause generally counteracts another by the same law whereby it produces its own effects, and, therefore, the particular mode in which it counteracts another may be classed under the positive causes). But it is usual, even with men of science, to reserve the name cause for an antecedent event which completes the assemblage of conditions, and begins to exist immediately before the effect (e.g. in the case of death from a fall, the slipping of the foot, and not the weight of the body), and to style the permanent facts or states, which, though existing immediately before, have also existed long previously, the conditions. But indeed, popularly, any condition which the hearer is least likely to be aware of, or which needs to be dwelt upon with reference to the particular occasion, will be selected as the cause, even a negative condition (e.g. the sentinel's absence from his post, as the cause of a surprise), though from a mere negation no consequence can really proceed. On the other hand, the object which is popularly regarded as standing in the relation of patient, and as being the mere theatre of the effect, is never styled cause, being included in the phrase describing the effect, viz. as the object, of which the effect is a state. But really these so-called patients are themselves agents, and their properties are positive conditions of the effect. Thus, the death of a man who has taken prussic acid is as directly the effect of the organic properties of the man, i.e. the patient, as of the poison, i.e. the agent.

To be a cause, it is not enough that the sequence has been invariable. Otherwise, night might be called the cause of day; whereas it is not even a condition of it. Such relations of succession or coexistence, as the succession of day and night (which Dr. Whewell contrasts as laws of phenomena* with *causes, though, indeed, the latter also are laws of phenomena, only more universal ones), result from the coexistence of real causes. The causes themselves are followed by their effects, not only invariably, but also necessarily, i.e. unconditionally, or subject to none but negative conditions. This is material to the notion of a cause. But another question is not material, viz. whether causes must precede, or may, at times, be simultaneous with (they certainly are never preceded by) their effects. In some, though not in all cases, the causes do invariably continue together with their effects, in accordance with the schools' dogma, Cessante causâ, cessat et effectus; and the hypothesis that, in such cases, the effects are produced afresh at each instant by their cause, is only a verbal explanation. But the question does not affect the theory of causation, which remains intact, even if (in order to take in cases of simultaneity of cause and effect) we have to define a cause, as the assemblage of phenomena, which occurring, some other phenomenon invariably and unconditionally commences, or has its origin.

There exist certain original natural agents, called permanent causes (some being objects, e.g. the earth, air, and sun; others, cycles of events, e.g. the rotation of the earth), which together make up nature. All other phenomena are immediate or remote effects of these causes. Consequently, as the state of the universe at one instant is the consequence of its state at the previous instant, a person (but only if of more than human powers of calculation, and subject also to the possibility of the order being changed by a new volition of a supreme power) might predict the whole future order of the universe, if he knew the original distribution of all the permanent causes, with the laws of the succession between each of them and its different mutually independent effects. But, in fact, the distribution of these permanent causes, with the reason for the proportions in which they coexist, has not been reduced to a law; and this is why the sequences or coexistences among the effects of several of them together cannot rank as laws of nature, though they are invariable while the causes coexist. For this same reason (since the proximate causes are traceable ultimately to permanent causes) there are no original and independent uniformities of coexistence between effects of different (proximate) causes, though there may be such between different effects of the same cause.

Some, and particularly Reid, have regarded man's voluntary agency as the true type of causation and the exclusive source of the idea. The facts of inanimate nature, they argue, exhibit only antecedence and sequence, while in volition (and this would distinguish it from physical causes) we are conscious, prior to experience, of power to produce effects: volition, therefore, whether of men or of God, must be, they contend, an efficient cause, and the only one, of all phenomena. But, in fact, they bring no positive evidence to show that we could have known, apart from experience, that the effect, e.g. the motion of the limbs, would follow from the volition, or that a volition is more than a physical cause. In lieu of positive evidence, they appeal to the supposed conceivableness of the direct action of will on matter, and inconceivableness of the direct action of matter on matter. But there is no inherent law, to this effect, of the conceptive faculty: it is only because our voluntary acts are, from the first, the most direct and familiar to us of all cases of causation, that men, as is seen from the structure of languages (e.g. their active and passive voices, and impersonations of inanimate objects), get the habit of borrowing them to explain other phenomena by a sort of original Fetichism. Even Reid allows that there is a tendency to assume volition where it does not exist, and that the belief in it has its sphere gradually limited, in proportion as fixed laws of succession among external objects are discovered.

This proneness to require the appearance of some necessary and natural connection between the cause and its effect, i.e. some reason per se why the one should produce the other, has infected most theories of causation. But the selection of the particular agency which is to make the connection between the physical antecedent and its consequent seem conceivable, has perpetually varied, since it depends on a person's special habits of thought. Thus, the Greeks, Thales, Anaximenes, and Pythagoras, thought respectively that water, air, or number is such an agency explaining the production of physical effects. Many moderns, again, have been unable to conceive the production of effects by volition itself, without some intervening agency to connect it with them. This medium, Leibnitz thought, was some per se efficient physical antecedent; while the Cartesians imagined for the purpose the theory of Occasional Causes, that is, supposed that God, not quâ mind, or quâ volition, but quâ omnipotent, intervenes to connect the volition and the motion: so far is the mind from being forced to think the action of mind on matter more natural than that of matter on matter. Those who believe volition to be an efficient cause are guilty of exactly the same error as the Greeks, or Leibnitz or Descartes; that is, of requiring an explanation of physical sequences by something [Greek: aneu hou to aition ouk an pot' eiê aition]. But they are guilty of another error also, in inferring that volition, even if it is an efficient cause of so peculiar a phenomenon as nervous action, must therefore be the efficient cause of all other phenomena, though having scarcely a single circumstance in common with them.

CHAPTER VI.

THE COMPOSITION OF CAUSES.

An effect is almost always the result of the concurrence of several causes. When all have their full effect, precisely as if they had operated successively, the joint effect (and it is not inconsistent to give the name of joint effect even to the mutual obliteration of the separate ones) may be deduced from the laws which govern the causes when acting separately. Sciences in which, as in mechanics, this principle, viz. the composition of causes, prevails, are deductive and demonstrative. Phenomena, in effect, do generally follow this principle. But in some classes, e.g. chemical, vital, and mental phenomena, the laws of the elements when called on to work together, cease and give place to others, so that the joint effect is not the sum of the separate effects. Yet even here the more general principle is exemplified. For the new heteropathic laws, besides that they never supersede all the old laws (thus, The weight of a chemical compound is equal to the sum of the weight of the elements), have been often found, especially in the case of vital and mental phenomena, to enter unaltered into composition with one another, so that complex facts may thus be deducible from comparatively simple laws. It is even possible that, as has been already partly effected by Dalton's law of definite proportions, and the law of isomorphism, chemistry itself, which is now the least deductive of sciences, may be made deductive, through the laws of the combinations being ascertained to be, though not compounded of the laws of the separate agencies, yet derived from them according to a fixed principle.

The proposition, that effects are proportional to their causes, is sometimes laid down as an independent axiom of causation: it is really only a particular case of the composition of causes; and it fails at the same point as the latter principle, viz. when an addition does not become compounded with the original cause, but the two together generate a new phenomenon.

CHAPTER VII.

OBSERVATION AND EXPERIMENT.

Since the whole of the present facts are the infallible result of the whole of the past, so that if the prior state of the entire universe could recur it would be followed by the present, the process of ascertaining the relations of cause and effect is an analysis or resolution of this complex uniformity into the simpler uniformities which make it up. We must first mentally analyse the facts, not making this analysis minuter than is needed for our object at the time, but at the same time not regarding (as did the Greeks their verbal classifications) a mental decomposition of facts as ultimate. When we have thus succeeded in looking at any two successive chaotic masses (for such nature keeps at each instant presenting to us) as so many distinct antecedents and consequents, we must analyse the facts themselves, and try, by varying the circumstances, to discover which of the antecedents and consequents (for many are always present together) are related to each other.

Experiment and observation are the two instruments for thus varying the circumstances. When the enquiry is, What are the effects of a given cause? experiment is far the superior, since it enables us not merely to produce many more and more opportune variations than nature, which is not arranged on the plan of facilitating our studies, offers spontaneously, but, what is a greater advantage, though one less attended to, also to insulate the phenomenon by placing it among known circumstances, which can be then infinitely varied by introducing a succession of well-defined new ones.

Observation cannot ascertain the effects of a given cause, because it cannot, except in the simplest cases, discover what are the concomitant circumstances; and therefore sciences in which experiment cannot be used, either at all, as in astronomy, or commonly, as in mental and social science, must be mainly deductive, not inductive. When, however, the object is to discover causes by means of their effects, observation alone is primarily available, since new effects could be artificially produced only through their causes, and these are, in the supposed case, unknown. But even then observation by itself cannot directly discover causes, as appears from the case of zoology, which yet contains many recognised uniformities. We have, indeed, ascertained a real uniformity when we observe some one antecedent to be invariably found along with the effects presented by nature. But it is only by reversing the process, and experimentally producing the effects by means of that antecedent, that we can prove it to be unconditional, i.e. the cause.

CHAPTER VIII. AND NOTE TO CHAPTER IX.

THE FOUR METHODS OF EXPERIMENTAL ENQUIRY.

Five canons may be laid down as the principles of experimental enquiry. The first is that of the Method of Agreement, viz.: If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the circumstances agree is the cause or the effect of the given phenomenon. The second canon is that of the Method of Difference, viz.: If an instance in which the phenomenon occurs and an instance in which it does not occur have every circumstance in common, save one, and that one occurs only in the former, that one circumstance is the effect, or the cause, or a necessary part of the cause, of the phenomenon.

These two are the simplest modes of singling out from the facts which precede or follow a phenomenon, those with which it is connected by an invariable law. Both are methods of elimination, their basis being, for the method of agreement, that whatever can be eliminated is not, and for that of difference, that whatever cannot be eliminated is connected with the given phenomenon by a law. It is only, however, by the method of difference, which is a method of artificial experiment (and by experiment we can introduce into the pre-existing facts a change perfectly definite), that we can, at least by direct experience, arrive with certainty at causes. The method of agreement is chiefly useful as preliminary to and suggestive of applications of the method of difference, or as an inferior resource in its stead, when, as in the case of many spontaneous operations of nature, we have no power of producing the phenomenon.

When we have power to produce the phenomenon, but only by the agency, not of a single antecedent, but of a combination, the method of agreement can be improved (though it is even then inferior to the direct method of difference) by a double process being used, each proof being independent and corroborative of the other. This may be called the Indirect Method of Difference, or the Joint Method of Agreement and Difference, and its canon will be: If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or a necessary part of the cause, of the phenomenon.

The fourth canon is that of the Method of Residues, viz.: Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. This method is a modification of the method of difference, from which it differs in obtaining, of the two required instances, only the positive instance, by observation or experiment, but the negative, by deduction. Its certainty, therefore, in any given case, is conditional on the previous inductions having been obtained by the method of difference, and on there being in reality no remaining antecedents besides those given as such.

The fifth canon is that of the Method of Concomitant Variations, viz.: Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or* (since they may be effects of a common cause) *is connected with it through some fact of causation. Through this method alone can we find the laws of the permanent causes. For, though those of the permanent causes whose influence is local may be escaped from by changing the scene of the observation or experiment, many can neither be excluded nor even kept isolated from each other; and, therefore, in such cases, the method of difference, which requires a negative instance, and that of agreement, which requires the different instances to agree only in one circumstance, in order to prove causation, are (together with the methods which are merely forms of these) equally inapplicable. But, though many permanent antecedents insist on being always present, and never present alone, yet we have the resource of making or finding instances in which (the accompanying antecedents remaining unchanged) their influence is varied and modified. This method can be used most effectually when the variations of the cause are variations of quantity; and then, if we know the absolute quantities of the cause and the effect, we may affirm generally that, at least within our limits of observation, the variations of the cause will be attended by similar variations of the effect; it being a corollary from the principle of the composition of causes, that more of the cause is followed by more of the effect. This method is employed usually when the method of difference is impossible; but it is also of use to determine according to what law the quantity or different relations of an effect ascertained by the method of difference follow those of the cause.

These four methods are the only possible modes of experimental enquiry. Dr. Whewell attacks them, first, on the ground (and the canon of ratiocination was attacked on the same) that they assume the reduction of an argument to formulæ, which (with the procuring the evidence) is itself the chief difficulty. And this is in truth the case: but, to reduce an argument to a particular form, we must first know what the form is; and in showing us this, Inductive Logic does a service the value of which is tested by the number of faulty inductions in vogue. Dr. Whewell next implies a complaint that no discoveries have ever been made by these four methods. But, as the analogous argument against the syllogism was invalidated by applying equally as against all reasoning, which must be reducible to syllogism, so this also falls by its own generality, since, if true against these methods, it must be true against all observation and experiment, since these must ever proceed by one of the four. And, moreover, even if the four methods were not methods of discovery, as they are, they would yet be subjects for logic, as being, at all events, the sole methods of Proof, which (unless Dr. Whewell be correct in his view that inductions are simply conceptions consistent with the facts they colligate) is the principal topic of logic.

FOOTNOTE:

Chap. IX. consists of 'Miscellaneous Examples of the Four Methods,' which cannot be well represented in an abridged form.

CHAPTER X.

PLURALITY OF CAUSES, AND INTERMIXTURE OF EFFECTS.

The difficulty in tracing the laws of nature arises chiefly from the Intermixture of Effects, and from the Plurality of Causes. The possibility of the latter in any given case--that is, the possibility that the same effect may have been produced by different causes--makes the Method of Agreement (when applied to positive instances) inconclusive, if the instances are few; for that Method involves a tacit supposition, that the same effect in different instances, which have one common antecedent, must follow in all from the same cause, viz. from their common antecedent. When the instances are varied and very many (how many, it is for the Theory of Probability to consider), the supposition, that the presence in all of the common antecedent may be simply a coincidence, is rebutted; and this is the sole reason why mere number of instances, differing only in immaterial points, is of any value. As applied, indeed, to negative instances, i.e. to those resembling each other in the absence of a certain circumstance, the Method of Agreement is not vitiated by Plurality of Causes. But the negative premiss cannot generally be worked unless an affirmative be joined with it: and then the Method is the Joint Method of Agreement and Difference. Thus, to find the cause of Transparency, we do not enquire in what circumstance the numberless non-transparent objects agree; but we enquire, first, in what the few transparent ones agree; and then, whether all the opaque do not agree in the absence of this circumstance.

Not only may there be Plurality of Causes, the whole of the effect being produced now by one, now by another antecedent; but there may also be Intermixture of Effects, through the interference of different causes with each other, so that part of the total effect is due to one, and part to another cause. This latter contingency, which, more than all else, complicates, the study of nature, does not affect the enquiry into those (the exceptional) cases, where, as in chemistry, the total effect is something quite different to the separate effects, and governed by different laws. There the great problem is to discover, not the properties, but the cause of the new phenomenon, i.e. the particular conjunction of agents whence it results; which could indeed never be ascertained by specific enquiry, were it not for the peculiarity, not of all these cases (e.g. not of mental phenomena), but of many, viz. that the heterogeneous effects of combined causes often reproduce, i.e. are transformed into their causes (as, e.g. water into its components, hydrogen and oxygen). The great difficulty is not there to discover the properties of the new phenomenon itself, for these can be found by experiment like the simple effects of any other cause; since, in this class of cases the effects of the separate causes give place to a new effect, and thereby cease to need consideration as separate effects. But in the far larger class of cases, viz. when the total effect is the exact sum of the separate effects of all the causes (the case of the Composition of Causes), at no point may it be overlooked that the effect is not simple but complex, the result of various separate causes, all of which are always tending to produce the whole of their several natural effects; having, it may be, their effects modified, disturbed, or even prevented by each other, but always preserving their action, since laws of causation cannot have exceptions.

These complex effects must be investigated by deducing the law of the effect from the laws of the separate causes on the combination of which it depends. No inductive method is conclusive in such cases (e.g. in physiology, or à fortiori, in politics and history), whether it be the method of simple observation, which compares instances, whether positive or negative, to see if they agree in the presence or the absence of one common antecedent, or the empirical method, which proceeds by directly trying different combinations (either made or found) of causes, and watching what is the effect. Both are inconclusive; the former, because an effect may be due to the concurrence of many causes, and the latter, because we can rarely know what all the coexisting causes are; and still more rarely whether a certain portion (if not all) of the total effect is not due to these other causes, and not to the combination of causes which we are observing.

CHAPTER XI.

THE DEDUCTIVE METHOD.

The deductive method is the main source of our knowledge of complex phenomena, and the sole source of all the theories through which vast and complicated facts have been embraced under a few simple laws. It consists of processes of Induction, Ratiocination, and Verification. First, by one of the four inductive methods, the simple laws (whence may be deduced the complex) of each separate cause which shares in producing the effect, must be first ascertained. This is difficult, when the causes or rather tendencies cannot be observed singly. Such is the case in physiology, since the different agencies which make up an organized body cannot be separated without destroying the phenomenon; consequently there our sole resource is to produce experimentally, or find (as in the case of diseases), pathological instances in which only one organ at a time is affected. Secondly, when the laws of the causes have been found, we calculate the effect of any given combination of them by ratiocination, which may have (though not necessarily) among its premisses the theorems of the sciences of number and geometry. Lastly, as it might happen that some of the many concurring agencies have been unknown or overlooked, the conclusions of ratiocination must be verified; that is, it must be explained why they do not, or shown that they do, accord with observed cases of at least equal complexity, and (which is the most effectual test) that the empirical laws and uniformities, if any, arrived at by direct observation, can be deduced from and so accounted for by them, as, e.g. Kepler's laws of the celestial motions by Newton's theory.

CHAPTERS XII. AND XIII.

THE EXPLANATION AND EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.

The aim, in the deductive method, is either to discover the law of the effect, or to account for it by explaining it, that is, by pointing out some more general phenomenon (though often less familiar to us) of which this is a case and a partial exemplification, or some laws of causation which produce it by their joint or successive action. This explanation may be made, either--1. By resolving the laws of the complex effect into its elements, which consist as well of the separate laws of the causes which share in producing it, as also of their collocation, i.e. the fact that these separate laws have been so combined; or--2. By resolving the law which connects two links, not proximate, in a chain of causation, into the laws which connect each link with the intermediate links; or--3. By the subsumption or gathering up of several laws under one which amounts to the sum of them all, and which is the recognition of the same sequence in different sets of instances. In the first two of the processes, laws are resolved into others, which both extend to more cases, i.e. are more general, and also, as being laws of nature, of which the complex laws are but results, are more certain, i.e. more unconditional and more universally true. In the third process, laws are resolved into others which are indeed more general, but not more certain, since they are in fact the same laws, and therefore, subject to the same exceptions.

Liebig's researches, e.g. into the Contagious Influence of Chemical Action, and his Theory of Respiration, are among the finest examples, since Newton's exposition of the law of gravitation, of the use of the deductive method for explanation. But the method is as available for explaining mental as physical facts. It is destined to predominate in philosophy. Before Bacon's time deductions were accepted as sufficient, when neither had the premisses been established by proper canons of experimental enquiry, nor the results tested by verification by specific experience. He therefore changed the method of the sciences from deductive to experimental. But, now that the principles of deduction are better understood, it is rapidly reverting from experimental to deductive. Only it must not be supposed that the inductive part of the process is yet complete. Probably, few of the great generalisations fitted to be the premisses for future deductions will be found among truths now known. Some, doubtless, are yet unthought of; others known only as laws of some limited class of facts, as electricity once was. They will probably appear first in the shape of hypotheses, needing to be tested by canons of legitimate induction.

FOOTNOTE:

These, and other illustrations in chap. xiii., cannot be usefully represented in an abridged form.