Analysis of Mr. Mill's System of Logic Part 4

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 a.n.a.lysis or resolution of this complex uniformity into the simpler uniformities which make it up. We must first mentally a.n.a.lyse the facts, not making this a.n.a.lysis minuter than is needed for our object at the time, but at the same time not regarding (as did the Greeks their verbal cla.s.sifications) a mental decomposition of facts as ultimate. When we have thus succeeded in looking at any two successive chaotic ma.s.ses (for such nature keeps at each instant presenting to us) as so many distinct antecedents and consequents, we must a.n.a.lyse the facts themselves, and try, by varying the circ.u.mstances, 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 circ.u.mstances. 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 circ.u.mstances, 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 circ.u.mstances; 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.[1]

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 circ.u.mstance in common, the circ.u.mstance in which alone all the circ.u.mstances 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 circ.u.mstance in common, save one, and that one occurs only in the former, that one circ.u.mstance 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 circ.u.mstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circ.u.mstance, the circ.u.mstance 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 circ.u.mstance, 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 quant.i.ty; and then, if we know the absolute quant.i.ties 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 quant.i.ty 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 a.s.sume the reduction of an argument to formulae, 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 a.n.a.logous 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 princ.i.p.al topic of logic.

FOOTNOTE:

[1] 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 reb.u.t.ted; 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 circ.u.mstance, 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 circ.u.mstance 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 circ.u.mstance.

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 cla.s.s 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 cla.s.s 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 _a 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_.[2] 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 cla.s.s 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:

[2] These, and other ill.u.s.trations in chap. xiii., cannot be usefully represented in an abridged form.

CHAPTER XIV.

THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE. HYPOTHESES.

The constant tendency of science, operating by the Deductive Method, is to resolve all laws, even those which once seemed ultimate and not derivative, into others still more general. But no process of _resolving_ will ever reduce the number of ultimate laws below the number of those varieties of our feelings which are distinguishable in quality, and not merely in quant.i.ty or degree. The _ideal_ limit of the explanation of natural phenomena is to show that each of these ultimate facts has (since the differences in the different cases of it affect our sensations as differences in degree only, and not in quality) only one sort of cause or mode of production; and that all the seemingly different modes of production or causes of it are resolvable into one.

But _practically_ this limit is never attained. Thus, though various laws of Causes of Motion have been resolved into others (e.g. the fall of bodies to the earth, and the motions of the planets, into the one law of mutual attraction), many causes of it remain still unresolved and distinct.

Hypotheses are made for the sake of this resolving and explaining of laws. When we do not _know_ of any more general laws into which to resolve an uniformity, we then (either on no or on insufficient evidence) _suppose_ some, imagining either causes (as, e.g. Descartes did the Vortices), or the laws of their operation (as did Newton respecting the planetary central force); but we never feign both cause and law. The use of a hypothesis is to enable us to apply the Deductive Method before the laws of the causes have been ascertained by Induction.

In those cases where a false law could not have led to a true result (as was the case with Newton's hypothesis as to the law of the Attractive force) the third part of the process in the Deductive Method, viz.

Verification, which shows that the results deduced are true, amounts to a complete induction, and one conforming to the canon of the Method of Difference. But this is the case only when either the cause is known to be one given agent (and only its law is unknown), or to be one of several given agents.