[26] I am happy to be able to quote the following excellent pa.s.sage from Mr. Baden Powell"s _Essay on the Inductive Philosophy_, in confirmation, both in regard to history and to doctrine, of the statement made in the text. Speaking of the "conviction of the universal and permanent uniformity of nature," Mr. Powell says (pp. 98-100),
"We may remark that this idea, in its proper extent, is by no means one of popular acceptance or natural growth. Just so far as the daily experience of every one goes, so far indeed he comes to embrace a certain persuasion of this kind, but merely to this limited extent, that what is going on around him at present, in his own narrow sphere of observation, will go on in like manner in future. The peasant believes that the sun which rose to-day will rise again to-morrow; that the seed put into the ground will be followed in due time by the harvest this year as it was last year, and the like; but has no notion of such inferences in subjects beyond his immediate observation. And it should be observed that each cla.s.s of persons, in admitting this belief within the limited range of his own experience, though he doubt or deny it in everything beyond, is, in fact, bearing unconscious testimony to its universal truth. Nor, again, is it only among the _most_ ignorant that this limitation is put upon the truth. There is a very general propensity to believe that everything beyond common experience, or especially ascertained laws of nature, is left to the dominion of chance or fate or arbitrary intervention; and even to object to any attempted explanation by physical causes, if conjecturally thrown out for an apparently unaccountable phenomenon.
"The precise doctrine of the _generalization_ of this idea of the uniformity of nature, so far from being obvious, natural, or intuitive, is utterly beyond the attainment of the many. In all the extent of its universality it is characteristic of the philosopher. It is clearly the result of philosophic cultivation and training, and by no means the spontaneous offspring of any primary principle naturally inherent in the mind, as some seem to believe. It is no mere vague persuasion taken up without examination, as a common prepossession to which we are always accustomed; on the contrary, all common prejudices and a.s.sociations are against it. It is pre-eminently _an acquired idea_. It is not attained without deep study and reflection. The best informed philosopher is the man who most firmly believes it, even in opposition to received notions; its acceptance depends on the extent and profoundness of his inductive studies."
[27] Supra, book iii. ch. iii. 1.
[28] It deserves remark, that these early generalizations did not, like scientific inductions, presuppose causation. What they did presuppose, was _uniformity_ in physical facts. But the observers were as ready to presume uniformity in the coexistences of facts as in the sequences. On the other hand, they never thought of a.s.suming that this uniformity was a principle pervading all nature: their generalizations did not imply that there was uniformity in everything, but only that as much uniformity as existed within their observation, existed also beyond it.
The induction, Fire burns, does not require for its validity that all nature should observe uniform laws, but only that there should be uniformity in one particular cla.s.s of natural phenomena: the effects of fire on the senses and on combustible substances. And uniformity to this extent was not a.s.sumed, anterior to the experience, but proved by the experience. The same observed instances which proved the narrower truth, proved as much of the wider one as corresponded to it. It is from losing sight of this fact, and considering the law of causation in its full extent as necessarily presupposed in the very earliest generalizations, that persons have been led into the belief that the law of causation is known _ priori_, and is not itself a conclusion from experience.
[29] Book ii. chap. iii.
[30] One of the most rising thinkers of the new generation in France, M.
Taine (who has given, in the Revue des Deux Mondes, the most masterly a.n.a.lysis, at least in one point of view, ever made of the present work), though he rejects, on this and similar points of psychology, the intuition theory in its ordinary form, nevertheless a.s.signs to the law of causation, and to some other of the most universal laws, that certainty beyond the bounds of human experience, which I have not been able to accord to them. He does this on the faith of our faculty of abstraction, in which he seems to recognise an independent source of evidence, not indeed disclosing truths not contained in our experience, but affording an a.s.surance which experience cannot give, of the universality of those which it does contain. By abstraction M. Taine seems to think that we are able, not merely to a.n.a.lyse that part of nature which we see, and exhibit apart the elements which pervade it, but to distinguish such of them as are elements of the system of nature considered as a whole, not incidents belonging to our limited terrestrial experience. I am not sure that I fully enter into M. Taine"s meaning; but I confess I do not see how any mere abstract conception, elicited by our minds from our experience, can be evidence of an objective fact in universal Nature, beyond what the experience itself bears witness of; or how, in the process of interpreting in general language the testimony of experience, the limitations of the testimony itself can be cast off.
[31] Book i. chap. vii.
[32] In some cases, a Kind is sufficiently identified by some one remarkable property: but most commonly several are required; each property considered singly, being a joint property of that and of other Kinds. The colour and brightness of the diamond are common to it with the paste from which false diamonds are made; its octohedral form is common to it with alum, and magnetic iron ore; but the colour and brightness and the form together, identify its Kind; that is, are a mark to us that it is combustible; that when burnt it produces carbonic acid; that it cannot be cut with any known substance; together with many other ascertained properties, and the fact that there exist an indefinite number still unascertained.
[33] This doctrine of course a.s.sumes that the allotropic forms of what is chemically the same substance are so many different Kinds; and such, in the sense in which the word Kind is used in this treatise, they really are.
[34] Mr. De Morgan, in his _Formal Logic_, makes the just remark, that from two such premises as Most A are B, and Most A are C, we may infer with certainty that some B are C. But this is the utmost limit of the conclusions which can be drawn from two approximate generalizations, when the precise degree of their approximation to universality is unknown or undefined.
[35] _Rationale of Judicial Evidence_, vol. iii. p. 224.
[36] Supra, vol. i. p. 115.
[37] Supra, book i. ch. v. 1, and book ii. ch. v. 5.
[38] The axiom, "Equals subtracted from equals leave equal differences,"
may be demonstrated from the two axioms in the text. If A = _a_ and B = _b_, A - B = _a - b_. For if not, let A - B = _a - b + c_. Then since B = _b_, adding equals to equals, A = _a + c_. But A = _a_. Therefore _a = a + c_, which is impossible.
This proposition having been demonstrated, we may, by means of it, demonstrate the following: "If equals be added to unequals, the sums are unequal." If A = _a_ and B not = _b_, A + B is not = _a + b_. For suppose it be so. Then, since A = _a_ and A + B = _a + b_, subtracting equals from equals, B = _b_; which is contrary to the hypothesis.
So again, it may be proved that two things, one of which is equal and the other unequal to a third thing, are unequal to one another. If A = _a_ and A not = B, neither is _a_ = B. For suppose it to be equal. Then since A = _a_ and _a_ = B, and since things equal to the same thing are equal to one another, A = B: which is contrary to the hypothesis.
[39] Geometers have usually preferred to define parallel lines by the property of being in the same plane and never meeting. This, however, has rendered it necessary for them to a.s.sume, as an additional axiom, some other property of parallel lines; and the unsatisfactory manner in which properties for that purpose have been selected by Euclid and others has always been deemed the opprobrium of elementary geometry.
Even as a verbal definition, equidistance is a fitter property to characterize parallels by, since it is the attribute really involved in the signification of the name. If to be in the same plane and never to meet were all that is meant by being parallel, we should feel no incongruity in speaking of a curve as parallel to its asymptote. The meaning of parallel lines is, lines which pursue exactly the same direction, and which, therefore, neither draw nearer nor go farther from one another; a conception suggested at once by the contemplation of nature. That the lines will never meet is of course included in the more comprehensive proposition that they are everywhere equally distant. And that any straight lines which are in the same plane and not equidistant will certainly meet, may be demonstrated in the most rigorous manner from the fundamental property of straight lines a.s.sumed in the text, viz. that if they set out from the same point, they diverge more and more without limit.
[40] _Philosophie Positive_, iii. 414-416.
[41] See the two remarkable notes (A) and (F), appended to his _Inquiry into the Relation of Cause and Effect_.
[42] Supra, pp. 119, 120.
[43] A writer to whom I have several times referred, gives as the definition of an impossibility, that which there exists in the world no cause adequate to produce. This definition does not take in such impossibilities as these--that two and two should make five; that two straight lines should inclose a s.p.a.ce; or that anything should begin to exist without a cause. I can think of no definition of impossibility comprehensive enough to include all its varieties, except the one which I have given: viz. An impossibility is that, the truth of which would conflict with a complete induction, that is, with the most conclusive evidence which we possess of universal truth.
As to the reputed impossibilities which rest on no other grounds than our ignorance of any cause capable of producing the supposed effects; very few of them are certainly impossible, or permanently incredible.
The facts of travelling seventy miles an hour, painless surgical operations, and conversing by instantaneous signals between London and New York, held a high place, not many years ago, among such impossibilities.
[44] Not, however, as might at first sight appear, 999 times as much. A complete a.n.a.lysis of the cases shows that (always a.s.suming the veracity of the witness to be 9/10) in 10,000 drawings, the drawing of No. 79 will occur nine times, and be announced incorrectly once; the credibility therefore of the announcement of No. 79 is 9/10; while the drawing of a white ball will occur nine times, and be announced incorrectly 999 times. The credibility therefore of the announcement of white is 9/1008, and the ratio of the two 1008:10; the one announcement being thus only about a hundred times more credible than the other, instead of 999 times.
BOOK IV.
OF OPERATIONS SUBSIDIARY TO INDUCTION.
"Clear and distinct ideas are terms which, though familiar and frequent in men"s mouths, I have reason to think every one who uses does not perfectly understand. And possibly it is but here and there one who gives himself the trouble to consider them so far as to know what he himself or others precisely mean by them; I have, therefore, in most places, chose to put determinate or determined, instead of clear and distinct, as more likely to direct men"s thoughts to my meaning in this matter."--LOCKE"S _Essay on the Human Understanding_; Epistle to the Reader.
"Il ne peut y avoir qu"une mthode parfaite, qui est la _mthode naturelle_; on nomme ainsi un arrangement dans lequel les tres du mme genre seraient plus voisins entre eux que ceux de tous les autres genres; les genres du mme ordre, plus que ceux de tous les autres ordres; et ainsi de suite. Cette mthode est l"idal auquel l"histoire naturelle doit tendre; car il est vident que si l"on y parvenait, l"on aurait l"expression exacte et complte de la nature entire."--CUVIER, _Rgne Animal_, Introduction.
"Deux grandes notions philosophiques dominent la thorie fondamentale de la mthode naturelle proprement dite, savoir la formation des groupes naturels, et ensuite leur succession hirarchique."--COMTE, _Cours de Philosophie Positive_, 42me leon.
CHAPTER I.
OF OBSERVATION AND DESCRIPTION.
1. The inquiry which occupied us in the two preceding books, has conducted us to what appears a satisfactory solution of the princ.i.p.al problem of Logic, according to the conception I have formed of the science. We have found, that the mental process with which Logic is conversant, the operation of ascertaining truths by means of evidence, is always, even when appearances point to a different theory of it, a process of induction. And we have particularized the various modes of induction, and obtained a clear view of the principles to which it must conform, in order to lead to results which can be relied on.
The consideration of Induction, however, does not end with the direct rules for its performance. Something must be said of those other operations of the mind, which are either necessarily presupposed in all induction, or are instrumental to the more difficult and complicated inductive processes. The present book will be devoted to the consideration of these subsidiary operations: among which our attention must first be given to those, which are indispensable preliminaries to all induction whatsoever.
Induction being merely the extension to a cla.s.s of cases, of something which has been observed to be true in certain individual instances of the cla.s.s; the first place among the operations subsidiary to induction, is claimed by Observation. This is not, however, the place to lay down rules for making good observers; nor is it within the competence of Logic to do so, but of the art of intellectual Education. Our business with observation is only in its connexion with the appropriate problem of logic, the estimation of evidence. We have to consider, not how or what to observe, but under what conditions observation is to be relied on; what is needful, in order that the fact, supposed to be observed, may safely be received as true.
2. The answer to this question is very simple, at least in its first aspect. The sole condition is, that what is supposed to have been observed shall really have been observed; that it be an observation, not an inference. For in almost every act of our perceiving faculties, observation and inference are intimately blended. What we are said to observe is usually a compound result, of which one-tenth may be observation, and the remaining nine-tenths inference.
I affirm, for example, that I hear a man"s voice. This would pa.s.s, in common language, for a direct perception. All, however, which is really perception, is that I hear a sound. That the sound is a voice, and that voice the voice of a man, are not perceptions but inferences. I affirm, again, that I saw my brother at a certain hour this morning. If any proposition concerning a matter of fact would commonly be said to be known by the direct testimony of the senses, this surely would be so.
The truth, however, is far otherwise. I only saw a certain coloured surface; or rather I had the kind of visual sensations which are usually produced by a coloured surface; and from these as marks, known to be such by previous experience, I concluded that I saw my brother. I might have had sensations precisely similar, when my brother was not there. I might have seen some other person so nearly resembling him in appearance, as, at the distance, and with the degree of attention which I bestowed, to be mistaken for him. I might have been asleep, and have dreamed that I saw him; or in a state of nervous disorder, which brought his image before me in a waking hallucination. In all these modes, many have been led to believe that they saw persons well known to them, who were dead or far distant. If any of these suppositions had been true, the affirmation that I saw my brother would have been erroneous; but whatever was matter of direct perception, namely the visual sensations, would have been real. The inference only would have been ill grounded; I should have ascribed those sensations to a wrong cause.
Innumerable instances might be given, and a.n.a.lysed in the same manner, of what are vulgarly called errors of sense. There are none of them properly errors of sense; they are erroneous inferences from sense. When I look at a candle through a multiplying gla.s.s, I see what seems a dozen candles instead of one: and if the real circ.u.mstances of the case were skilfully disguised, I might suppose that there were really that number; there would be what is called an optical deception. In the kaleidoscope there really is that deception: when I look through the instrument, instead of what is actually there, namely a casual arrangement of coloured fragments, the appearance presented is that of the same combination several times repeated in symmetrical arrangement round a point. The delusion is of course effected by giving me the same sensations which I should have had if such a symmetrical combination had really been presented to me. If I cross two of my fingers, and bring any small object, a marble for instance, into contact with both, at points not usually touched simultaneously by one object, I can hardly, if my eyes are shut, help believing that there are two marbles instead of one.
But it is not my touch in this case, nor my sight in the other, which is deceived; the deception, whether durable or only momentary, is in my judgment. From my senses I have only the sensations, and those are genuine. Being accustomed to have those or similar sensations when, and only when, a certain arrangement of outward objects is present to my organs, I have the habit of instantly, when I experience the sensations, inferring the existence of that state of outward things. This habit has become so powerful, that the inference, performed with the speed and certainty of an instinct, is confounded with intuitive perceptions. When it is correct, I am unconscious that it ever needed proof; even when I know it to be incorrect, I cannot without considerable effort abstain from making it. In order to be aware that it is not made by instinct but by an acquired habit, I am obliged to reflect on the slow process through which I learnt to judge by the eye of many things which I now appear to perceive directly by sight; and on the reverse operation performed by persons learning to draw, who with difficulty and labour divest themselves of their acquired perceptions, and learn afresh to see things as they appear to the eye.
It would be easy to prolong these ill.u.s.trations, were there any need to expatiate on a topic so copiously exemplified in various popular works.
From the examples already given, it is seen sufficiently, that the individual facts from which we collect our inductive generalizations are scarcely ever obtained by observation alone. Observation extends only to the sensations by which we recognise objects; but the propositions which we make use of, either in science or in common life, relate mostly to the objects themselves. In every act of what is called observation, there is at least one inference--from the sensations to the presence of the object; from the marks or diagnostics, to the entire phenomenon. And hence, among other consequences, follows the seeming paradox, that a general proposition collected from particulars is often more certainly true than any one of the particular propositions from which, by an act of induction, it was inferred. For, each of those particular (or rather singular) propositions involved an inference, from the impression on the senses to the fact which caused that impression: and this inference may have been erroneous in any one of the instances, but cannot well have been erroneous in all of them, provided their number was sufficient to eliminate chance. The conclusion, therefore, that is, the general proposition, may deserve more complete reliance than it would be safe to repose in any one of the inductive premises.
The logic of observation, then, consists solely in a correct discrimination between that, in a result of observation, which has really been perceived, and that which is an inference from the perception. Whatever portion is inference, is amenable to the rules of induction already treated of, and requires no further notice here: the question for us in this place is, when all which is inference is taken away, what remains. There remains, in the first place, the mind"s own feelings or states of consciousness, namely, its outward feelings or sensations, and its inward feelings--its thoughts, emotions, and volitions. Whether anything else remains, or all else is inference from this; whether the mind is capable of directly perceiving or apprehending anything except states of its own consciousness--is a problem of metaphysics not to be discussed in this place. But after excluding all questions on which metaphysicians differ, it remains true, that for most purposes the discrimination we are called upon practically to exercise is that between sensations or other feelings, of our own or of other people, and inferences drawn from them. And on the theory of Observation this is all which seems necessary to be said for the purposes of the present work.
3. If, in the simplest observation, or in what pa.s.ses for such, there is a large part which is not observation but something else; so in the simplest description of an observation, there is, and must always be, much more a.s.serted than is contained in the perception itself. We cannot describe a fact, without implying more than the fact. The perception is only of one individual thing; but to describe it is to affirm a connexion between it and every other thing which is either denoted or connoted by any of the terms used. To begin with an example, than which none can be conceived more elementary: I have a sensation of sight, and I endeavour to describe it by saying that I see something white. In saying this, I do not solely affirm my sensation; I also cla.s.s it. I a.s.sert a resemblance between the thing I see, and all things which I and others are accustomed to call white. I a.s.sert that it resembles them in the circ.u.mstance in which they all resemble one another, in that which is the ground of their being called by the name. This is not merely one way of describing an observation, but the only way. If I would either register my observation for my own future use, or make it known for the benefit of others, I must a.s.sert a resemblance between the fact which I have observed and something else. It is inherent in a description, to be the statement of a resemblance, or resemblances.
We thus see that it is impossible to express in words any result of observation, without performing an act possessing what Dr. Whewell considers to be characteristic of Induction. There is always something introduced which was not included in the observation itself; some conception common to the phenomenon with other phenomena to which it is compared. An observation cannot be spoken of in language at all without declaring more than that one observation; without a.s.similating it to other phenomena already observed and cla.s.sified. But this identification of an object--this recognition of it as possessing certain known characteristics--has never been confounded with Induction. It is an operation which precedes all induction, and supplies it with its materials. It is a perception of resemblances, obtained by comparison.