The Elements of Inductive Logic: Designed Mainly for the Use of Students in ...

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Preface To The First Edition

The object of the following work is to serve as an introduction to that branch of scientific method which is known as Induction. It is designed mainly for the use of those who have not time or opportxmity to consult larger works, or who require some preliminary knowledge before they can profitably enter upon the study of them. ,

To the works of Mr. Mill, Dr. Whewell, and Sir John Herschel, the Author must,\once for all, express his obligations. *He has, however,' if he may be allowed to repeat the language already employed in the Preface to his Manual of Deductive Logic, * endeavoured, on all disputed points, to reason out his own conclusions, feeling assured that no manual, however elementary, can be of real service to the student, unless it express what may be called the " reasoned opinions " of its author.'

The analysis of Induction presents far more difficulties than that of Deduction, and requires to be illustrated

VI PREFACE TO THE FIRST EDITION.

by far more numerous and intricate examples. But, on the other hand, it is more interesting both to the teacher and to the student; and, being a comparatively recent study, is less hampered by conventionalities of treatment. Since the time of Bacon, it has always, with more or less of success, claimed a place in liberal education, and many, to whom the technical terms and subtle distinctions of the older logic are justly repulsive, have experienced a peculiar delight in attempting to discover and test the grounds on which the results of modem science mainly rest.

The study of Deductive Logic can be of littie service unless it be supplemented by, at least, some knowledge of the principles of Induction, which supplies its premisses. Many of the objections directed against the study of Logic are due to the narrow conceptions which are entertained of its province, and might be easily met by showing that the study, when we include both its parts, has a much wider range than is popularly assigned to it.

Though the present work is mainly intended for students in the Universities, it is hoped that it will be found to present some interest for the general reader, and that it may be useful to students of medicine and the physical

Preface To The First Edition. Vu

sciences, as well as to some of the more advanced scholars in our Public Schools.

The number of scientific examples adduced throughout the work renders it necessary, perhaps, that the Author should state emphatically that the work is intended as an introduction, not to science, but to scienHfic method. Its object is not to give a rdsum6 of the sciences, physical or social, a task to which the Author would be wholly incompetent, but to show the grounds on which our scientific knowledge rests, the methods by which it has been built up, and the defects from which it must be free. Notwithstanding its frequent incursions into the domain of science, the purport of the work must be regarded as strictly logical.

The examples have, as a rule, been selected from the physical rather than the social sciences, as being usually less open to dispute, and lying within a smaller compass. Wherever it has been possible, they have been given in the exact words of the author from whom they are taken.

Some of the more complicated cases of inductive reasoning, such as those which deal with Progressive Causes or Intermixture of Effects, have, if alluded to

at all, been only briefly noticed. Any detailed examination of these more intricate questions seemed to lie viii PREFACE TO THE FIRST EDITION.

without the scope of the treatise. The student who has leisure to pursue the subject will find ample information in the pages of Mr. Mill's Lcgtc,

It only remains for the Author to express his grateful acknowledgments to those who have assisted him in the execution of the work. These are, in the first place, due to Dr. Liddell, Dean of Christ Church, through whose hands the sheets have passed, and who, in addition to revising the proofs, has, from time to time, offered many very valuable suggestions. They are due also, in no small degree, to Sir John Herschel and Professor Bartholomew Price, who most kindly undertook to revise the scientific examples; to Professors Rolleston and Clifton, who have frequently allowed the Author to consult them on questions connected with the subjects of their respective chaurs, and to the Rev. G. W. Kitchin, the Organising Secretary of the Clarendon Press Series. The Author must, however, be regarded as alone responsible for any errors which may occur either in the theoretical portion of the work or in the examples.

Lincoln Colleqe, Oct. 30, 1869.

Preface To The Second Edition

Some misprints, and some inaccuracies or ambiguities of expression, which occurred in the former edition, have been corrected in the present one. A few alterations also have been made which cannot, perhaps, be referred to either of these heads, and one or two examples have been added.

The discussion of the questions raised by some of the Author's reviewers (as, for instance, in the Scoisman, the Saturday Review^ and the Academy) would occupy more space than could be conveniently devoted to them in a work which is intended to be mainly educational. The Author, therefore, feels, at least for the present, compelled to waive their consideration. When, however, any adverse criticism has seemed to him to be justified, he has either modified the passage criticised, or has attempted to re-state it in such a manner as to prevent future misunderstanding.

The Author has here, as in his recent edition of the

X PREFACE TO THE SECOND EDITION,

Deductive Logic^ to thank Professor Park, of Belfast, for several suggestions, some of which he has gladly adopted. He can only regret that the plan and object of the work prevent him from availing himself of them to as full an extent as he could otherwise have desired.

Lincoln College, Sept, 35, 1871.

Preface To The Third Edition

Since the publication of my second edition, there has appeared an important work on Scientific Method, entitled * The Principles of Science,' by Professor Stanley Jevons, of Owens College, Manchester. To this I have made occasional references in the foot-notes to my present edition. • But, as I differ entirely from Professor Jevons on the fundamental question of the validity of our induetive inferences, I think it desirable to offer a few remarks on this point in the present place, rather than to introduce controversial matter into the body of the work.

Mr. JevOns over and over again asserts the uncertainty, or the mere probability, of all inductive inferences. Thus, for instance, in his chapter on the Philosophy of Inductive Iirference, he says: — *I have no objection to use the words cause and causation, provided they are never allowed to lead us to imagine that our knowledge of nature can attain to certainty V And again: *We can never recur too often to the truth that our knowledge of xii PREFACE TO THE THIRD EDITION.

the laws and future events of the external world is only probable^/ Once more: 'By induction we gain no certain knowledge ; but by observation, and the inverse use of deductive reasoning, we estimate the probability that an event which has occurred was preceded by conditions of specified character, or that such conditions will be followed by the event '/

At the same time, I am quite unable to reconcile with these passages other passages, such as those in which Mr. Jevons says : * We know that a penny thrown into the air will certainly fall upon a flat side, so that either the head or tail will be uppermost *,' or, * I can be certain that nitric acid will not dissolve gold, provided I know that the substances employed really correspond to those on which I tried the experiment previously ^/

But, waiving the question of inconsistency, I maintain as against Mr. Jevons that many of our inductive inferences have all the certainty of which human knowledge is capable. Is the law of gravitation one whit less certain than the conclusion of the 47th Proposition of the First Book of Euclid ? Or is the proposition that animal and

* Id. p. 2 28. Mr. Jevons, however, curiously enough is not certain about the truth of the Law of Gravitation. See below. * Id. p. 270.

• ••

PREFACE TO THE THIRD EDITION. XUl

vegetable life cannot exist without moisture one whit less certain than the truths of the multiplication table ? Both these physical generalisations are established by the Method of Difference, and, as ac/ual Laws of Nature, admit, I conceive, of no doubt. But it may be asked if they will always continue to be Laws of Nature? I reply that, unless the constitution of the Universe shall be changed to an extent which I cannot now even conceive, they will so continue, and that no reasonable man has any practical doubt as to their continuance. And why ? Because they are confirmed by the whole of our own experiences, which in both these cases is of enormous extent and variety, by the experience of our ancestors, and by all that we can ascertain of the past history of nature, while their reversal would involve the reversal of almost all the other laws with which we are acquainted. Still, it must be confessed that all oiu- inferences from the present to the future are, in one sense, hypothetical, the hypothesis being that the circumstances on which the laws themselves depend will continue to be the same as now, that is, in the present case, that the constitution of nature, in its most general features, will remain unchanged ; or, to put it in still another form, that ^e same causes will continue to produce the same effects. What xiv PREFACE TO THE THIRD EDITION.

would happen if this expectation were ever frustrated, it is absolutely impossible for us to say, so completely is it assumed in all our plans and reasonings.

We may say, then, that there are many inductions as to the ac/ual constitution of nature which we may accept with certainty, while, with respect even to the distant future, we may accept them with equal certainty, on the hypothesis that the general course of nature will not be radically changed. And if the general course of nature were changed, might not the change affect our faculties as well as the objects of our knowledge ; and, in that case, are we certain that we should still regard things that are equal to the same thing as equal to one another, or assume that a thing cannot both be and not be in the same place at the same time ? There is, in fact, no limit to the possibility of scepticism with regard to the persistency either of the laws of external nature or of the laws of mind. But all our reasonings depend on the hypothesis that the most general laws of matter and the most general laws of tnind will continue to be what they are, and of the truth of this hypothesis no reasonable man entertains any practical doubt ^.

• Thus Mr. Jevons, who, when he begins to theorise, has doubts as to the truth of the law of gravitation, has no doubt, when he throws a penny up into the air, jhat it will fall on a flat side.

Preface To The Third Edition. XV

There is, then, I contend, no special uncertainty attaching to the truths arrived at by induction. They are, indeed, Hke all other truths, relative to the present constitution of nature and the present constitution of the human mind, but this is a limitation to which all our knowledge alike is subject, and which it is vain for us to attempt to transcend. Syllogistic reasoning implies a particular constitution of the mind, as much as inductive reasoning implies a particular constitution of nature. Both mind and nature might, of course, be radically changed by an omnipotent power, but what the consequences of that change might be it is utterly impossible for us to say.

The uniformity of nature, the trustworthiness of our own faculties — these are the ultimate generalisations which lie at the root of all our beliefs, and are the conditions of all our reasonings. It is, of course, always possible to insinuate doubts as to either, but, however curious and entertaining such doubts may be, they have no practical influence even dn those who originate them. Even Mr. Jevons himself, we have seen, when not under the dominion of his theory, speaks of some of the results of induction as certain, and we can hardly conceive men of science commonly speaking of the most firmly

XVi PREFACE TO THE THIRD EDITION.

established generalisations of mechanics, optics, or chemistry, simply as conclusions possessing a high degree of probability.

Still, Mr. Jevons, appearing not in the character of a physicist, but of a logician, tells us that * the law of gravitation itself is only probably true ^.' It would be interesting to learn what is the exact amount of this * probability,' or, if it be meant that we can only be certain that the force of gravity is acting here and now, it would be an interesting enquiry to ascertain what is the exact value of the * probability' that it is at this moment acting in Manchester as well as in Oxford, or that it will be acting at this time to-morrow as well as to-day.

But, if the conclusions of Induction are thus uncertain, where, according to Mr. Jevons, are we to find certainty? 'Certainty belongs only to the deductive process and to the teachings of direct intuition®.' Does it then belong to the conclusions of deduction ? Apparently not, for, at the very beginning of the work^ we are told that *in its ultimate origin or foundation, all knowledge is inductive,' and Mr. Jevons is, of course, too practised a logician to suppose that the conclusion

PREFACE TO THE THIRD EDITION. xvii

can be more certain than the premisses. The conclusions of geometry, therefore, partake of the same 'uncertainty' as the results of the physical sciences, and the region of 'certainty' is confined to our direcJt intuitions and to the rules of syllogism (supposing, that is, a difference to be intended between the 'deductive process' and deductive results). We venture to suggest that this small residuum of ' certainty ' would soon yield to solvents as powerfiil as those which Mr. Jevons has applied to the results of induction (and apparently also of deduction); and that, therefore, its inherent 'uncertainty' is no special characteristic of that method, but one which it shares with all our so-called knowledge.

The fact is that in all reasoning, whether inductive or deductive, we make, and must make, assumptions which may theoretically be questioned, but of the truth of which no man, in practice, entertains the slightest doubt. Thus, in syllogistic reasoning, we assume at every step the trustworthiness of memory; we assume, moreover, the validity of the premisses, which, as Mr. Jevons acknowledges, must ultimately be guaranteed either by induction or durect observation; lastly, we assume the validity of the primary axioms of reasoning,

XVIU PREFACE TO THE THIRD EDITION.

which, according to different theories, are either obtained by induction or assumed to be necessary laws of the human mind. In this sense, all reasoning and all science is hypothetical, and the assumption of the Uniformity of Nature does not render inductive reasoning hypothetical in any special sense of the term. For, if the Laws of the Uniformity of Nature and of Universal Causation admit of exceptions or are liable to ultimate frustration, so, for aught we know, may the axioms of syllogistic reasoning or the inductions by which we have established the trustworthiness of our faculties. And, if the conceptions of uniformity and causation be purely relative to man, so, for aught we know, may be the so-called laws of thought themselves ^®. Induction would only be hypothetical in a special sense, if we had any reasonable ground for doubting the truth of the hjrpotheses" on which it rests.

^ According to the view of the nature and ultimate origin of human knowledge, accepted both by Mr. Jevons and myself, it is, in fact, no paradox but a mere truism to say that the fundamental axioms of reasoning are themselves only particular uniformities of nature, arrived at by the same evidence and depending for their justification on the same grounds as those ultimate generalisations on causation to which we give the special names of the Law of Universal Causation and the Law of the Uniformity of Nature.

^ I need hardly say that I am not here using the word * hypothesis ' in the sense of an unverified assumption. Reasoning, both inductive and

Preface To The Third Edition. XIX

But, as 'in its ultimate origin or foundation, all knowledge ' (including, of course, that of the laws which govern the syllogistic process itself) *is inductive,' Professor Jevons must either employ the word 'certain' in a variety of senses, or he must be prepared with the philosophers of the New Academy to maintain the uncertainty of all knowledge whatsoever.

Such, as it appears to me, are the inconsistences and paradoxes into which a very able writer has been led by a tendency to over-refinement, and, still more perhaps, by a desire to apply the ideas and formulae of mathematics to the explanation of logical problems.

I must further express my dissidence from Mr. Jevons' statement that all inductive inference is preceded by hypotheses", from his theory that Induction is simply the Inverse Method of Deduction, and, above all, from what appears to me to be the exceedingly misleading

deductive, is found on analysis to depend, in the last resort, on certain assumptions or hypotheses, but then the truth of these assumptions or hypotheses is guaranteed by the whole experience of the human race, past and present, and beyond this guarantee we conceive that there is no other attainable. In other words, all truth is relative to our faculties of knowing, and this condition it is in vain for us to attempt to transcend. " See chap, i, pp. 1 1, 12, of this work.

b 2

XX PREFACE TO THE THIRD EDITION.

parallel drawn between Nature and a ballot-box. 'Events/ says Mr. Jevons, *come out like balls from the vast ballot-box of Nature"/ Now the balls were placed in the ballot-box by human hands; the number and character of them may have been due merely to caprice or chance; moreover, they are all isolated entities having no connection with each other. Would it be possible to find a stronger contrast to the works of nature? If natural phenomena did indeed admit only of the same kind of study as the drawing of balls from a ballot-box, Mr. Jevons* conception of Induction would undoubtedly be the true one, and we should agree with him that 'no finite number of particular verifications of a supposed law will render that law certain.' But, just because we believe that the operations of Nature are conducted with an uniformity for which we seek in vain amongst the contrivances of men, do we regard ourselves as capable, in many cases, of predicting the one class of events with certainty, while the other affords only matter for more or less probable conjecture.

Intimately connected with Mr. Jevons* depreciation of the value of the inductive inference is his statement

Preface To The Third Edition, XXI

that Induction is simply the inverse method of Deduction. If Induction simply consists in framing hypotheses, deducing consequences from the hypotheses, and then comparing these consequences with individual facts for the purpose of verifying them by specific experience", I grant that the procedure must, in most cases, be very untrustworthy. In my first Appended Note to my Section on Hypothesis, I have examined this account of Induction, which is virtually identical with that of Dr. Whewell. In opposition to it, I maintain the following theses, which are explained and defended in the course of my work: i. That our inductions are not always preceded by hypotheses (and it might be added that even where they are, the hypothesis itself must rest originally on some basis of fact, that is to say, on some induction or other, however imperfect; for a hypothesis must always be suggested by something of which we have had experience); 2. That the mere verification of our hypotheses by specific experience is not sufficient to constitute a valid induction, unless the instances conform to the requirements of one of the inductive methods, or (as in the case of the fundamental laws of

XXli PREFACE TO THE THIRD EDITION.

inductive reasoning) be coextensive with the whole experience of mankind. Induction, I maintain, may or may not employ hypothesis, but what is essential to it is the inference from the particular to the general, from the known to the unknown, and the nature of this inference it is impossible to represent adequately by reference to the forms of deduction.

Mr. Jevons* statement that 'induction is really the reverse process of deduction* I am wholly unable to reconcile with the following statements which occur in the very same page*^: *In its ultimate origin or founda-, tion all knowledge is inductive,* and *only when we possess such knowledge, in the form of general propositions and natural laws, can we usefully apply the reverse process of deduction to ascertain the exact information required at any moment.' When we compare these statements, the circle seems complete. A precedes B, and B precedes A. A depends for its validity on B, and B depends for its validity on A. No wonder that human reasoning affords us no 'certain' results!

In offering these criticisms on some fundamental points of difference between Mr. Jevons and myself,

Preface To The Third Edition. Xxiu

I am far from denying the utility of many portions of his work, especially the chapters on the Methods of Measurement and on Hypothesis.

In the present Edition of this work, I have occasionally availed myself of the * Inductive Logic' of Mr. Bain, a work which, though it does not, in my opinion, supersede Mr. Mill's Logic, supplies on some points a valuable complement to it.

In this, as in the last edition, I have to acknowledge the kindness of Professor Park of Belfast, whose corrections and suggestions have enabled me to make both my works more accurate and serviceable than they would otherwise have been.

Lincoln College, Feb. 24, 1876.

*:,.* It may be useful to the reader to be informed that the new matter introduced in the present edition occurs chiefly on pp. 7-9, 53, 218, 219 (Uniformities of Coexistence), pp. 200-202 (the Historical Method), xxiv PREFACE TO THE THIRD EDITION.

pp. 217, 218 (the distinction between Inductio per Enumerationem Simplicem and the Method of Agreement), pp. 241-243 (the constant alternation in practice of the inductive and deductive processes), and pp. 292, 293 (the Argument from Universal Consent). Several minor alterations and additions have also been made.

Contents

CHAP. PAGE

^\. The Nature of Inductive Inference 3

§ I. Observation and Experiment . . . • 3^

CHAPTER I. On the Nature of Inductive Inference

i

TWO bodies of unequal weight (say a guinea and a feather). are placed at the same height under the exhausted receiver of an air-pump. When released, they are observed to reach the bottom of the vessel at the same instant of time, or, in other words, to fall in equal times. From this fact, it is inferred that a repetition of the experiment either with these two bodies or with any other bodies would be attended with the same result, and that, if it were not for the resistance of the atmosphere and other hnpeding circumstances, all bodies, whatever their weight, would fall through equal vertical spaces in equal times. Now, that these two bodies in this particular experiment fall to the bottom of the receiver in equal times is merely a fact of observation, but that they would do so if we repeated the experiment, or that the next two bodies we selected, or any bodies, or all bodies, would do so, is an inference, and is an inference of that particular character which is called an Inductive Inference or an Induction \

^ The student must throughout bear in mind the ambiguous use of the words Induction, Inference, &c., as signifying both the result and

B 2

What assumptions underlie this inference, and on what grounds does it rest ?

My object in placing the two bodies under the receiver was obviously to answer a question which I had previously addressed to myself: viz. whether, when subject to the action of gravity ^ only, they would fall in equal or in unequal times. By exhausting the air in the receiver, I am able to isolate the phenomenon^ and thus, by removing all circumstances affecting the bodies, except the action of gravity, to watch the eflfect of this cause operating alone. But in trying this experiment, in isolating the phenomenon, and asking what will be the effect of the action of gravity operating alone, I am evidently assuming that the effect, whatever it may be, will be entirely due to the cause or causes which are then and \ there in action; in other words, I am assuming that nothing can happen without a cause, that no change can take place without being preceded or attended by circumstances which, if we were fully acquainted with them, would fully account for that change. This assumption (which may be called the Law of Universal Causation) is universally admitted by mankind, or at least by the

the process by which the result is arrived at. See Deductive Logic, Preface, and Part III. ch. i. note I.

* When I employ the expression * action of gravity * or * force of gravity,* I must not be understood as adopting any particular theory on the nature of the phenomenon which we call * gravitation.* I use these terms simply because they are short and recognised phrases for expressing the fact that all terrestrial bodies, when left entirely free, fell in the direction of the earth's centre.

INDUCTIVE INFEREkc^', y *; V

reflecting portion of mankind, though the groHtpds q^ /^

which it is admitted have been variously statea f/^me /> J

justifying it by an appeal to the continuous and. un^o^ tradicted experience not only of the individual himself/ "/f» but of the human race, others by an appeal to the nedes- ^/ sities of thought

Thus far, however, we have only ascertained that the fact of these two particular bodies, in this particular instance, falling to the ground in equal times is due to the action of gravity, unimpeded by any other circumstances. But why should I infer that they, if the experiment were repeated, or any other two bodies, if exposed to the same circumstances, would behave in the same way ? It is not enough to feel assured that nothing can happen without a cause, and that the only cause operating in this particular instance is the action of gravity ; I must also feel assured that the same cause will ' invariably be followed by the same eifect, or, to speak more accurately, that the same cause or combination of causes, will, if unimpeded by the action of any other cause or combination of causes, be invariably followed by the same effect or combination of effects, or, to state the same proposition in somewhat different language, that, whenever the ^ same antecedents, and none others, are introduced, the same consequents will invariably follow. This assump-

' The expression ' will * is used for the sake of brevity. The argument, however, is not simply from the present to the future, but from cases within the range of our experience to all cases, past, present, or future, without that range. See p. 31, note 37.

tion (or law) is, like the former, universally admitted by mankind, or the reflecting portion of mankind, though the grounds on which it is admitted have been variously stated, some, as in the case of the former law, referring it to experience, others to certain necessities of thought arising from the original constitution of the human mind. This law may be called /he Lcojo of the Uniformify of Nature *.

The argument, then, in the case which we have selected as our instance, may be represented as follows : —

I observe that these two bodies (though of unequal weight) reach the bottom of the receiver at the same moment.

This fact must be due to some cause or combination of causes (Law of Universal Causation). The only cause operating in this instance is the action of gravity. .-. The fact that these two bodies reach the bottom of the receiver at the same moment is due to the action of gravity, operating alone.

But, whenever the same cause or combination of causes is in operation, and that only, the same effect will invariably follow (Law of Uniformity of Nature).

^ It is, perhaps, necessary thus early to warn the student that the converse of the Law of the Uniformity of Nature does not hold true. Though the same cause, that is, the same antecedent or combination of antecedents, is never followed by different effects, the same effect may be doe to different causes. We can, thus, always argue from the cause to the effect, but we cannot alwajrs argue from the effect to the cause.

INDUCTIVE INFERENCE. J

.•. Whenever these two bodies, or any other two or more bodies (even though of unequal weight), are subject to the action of gravity only, they will reach the bottom of the receiver at the same moment, or, in other words, will fall in equal times.