Analysis of Mr. Mill's System of Logic Part 3

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 a.n.a.lysed 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 pa.s.s through the intermediate stage of a general proposition (to which cla.s.s 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 cla.s.s, 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 circ.u.mstances at all times, or of a whole cla.s.s. 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 cla.s.s 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 un.o.bserved 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 cla.s.sed 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 a.s.sumes, 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 a.s.sumes, 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 cla.s.s; 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 cla.s.s 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 circ.u.mstances, 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 cla.s.s of laws of number or of s.p.a.ce; for though these are certain and universal, no laws except those of s.p.a.ce 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 a.s.surance 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 cla.s.sed 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 a.s.semblage 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 causa, 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 a.s.semblage 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 G.o.d, 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 pa.s.sive 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 a.s.sume 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 p.r.o.neness 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 G.o.d, not _qua_ mind, or _qua_ volition, but _qua_ 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' eie 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 circ.u.mstance 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 cla.s.ses, 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.