What belongs to the individuals examined belongs to the whole class.The property of the ruminating belongs to the individuals examined, ox, sheep, goat, etc.Therefore, it belongs to all.
What belongs to the individuals examined belongs to the whole class.The property of the ruminating belongs to the individuals examined, ox, sheep, goat, etc.Therefore, it belongs to all.
What belongs to the individuals examined belongs to the whole class.
The property of the ruminating belongs to the individuals examined, ox, sheep, goat, etc.
Therefore, it belongs to all.
In answer to this, Hamilton repeated the traditional view, treating Whately's view merely as an instance ofthe prevailing ignorance of the history of Logic. He pointed out besides that Whately's Major was the postulate of a different kind of inference from that contemplated in Aristotle's Inductive Syllogism, Material as distinguished from Formal inference. This is undeniable if we take this syllogism purely as an argumentative syllogism. The "all" of the conclusion simply covers the individuals enumerated and admitted to be "all" in the Minor Premiss. If a disputant admits the cases produced to be all and can produce none to the contrary, he is bound to admit the conclusion. Now the inference contemplated by Whately was not inference from an admission to what it implies, but inference from a series of observations to all of a like kind, observed and unobserved.
It is not worth while discussing what historical justification Whately had for his view of Induction. It is at least arguable that the word had come to mean, if it did not mean with Aristotle himself, more than a mere summation of particulars in a general statement. Even Aristotle's respondent in the concession of his Minor admitted that the individuals enumerated constituted all in the truly general sense, not merely all observed but all beyond the range of observation. The point, however, is insignificant. What really signifies is that while Hamilton, after drawing the line between Formal Induction and Material, fell back and entrenched himself within that line, Mill caught up Whately's conception of Induction, pushed forward, and made it the basis of his System of Logic.
In Mill's definition, the mere summation of particulars,Inductio per enumerationem simplicem ubi non reperitur instantia contradictoria, is Induction improperly so called. The only process worthy of the name isMaterial Induction, inference to the unobserved. Here only is there an advance from the known to the unknown, a veritable "inductive hazard".
Starting then with this conception of inference to the unobserved as the only true inference, and with an empirical law—a generality extended from observed cases to unobserved—as the type of such inference, Mill saw his way to connecting a new Logic with the old. We must examine this junction carefully, and the brilliant and plausible arguments by which he supported it; we shall find that, biased by this desire to connect the new with the old, he gave a misleading dialectic setting to his propositions, and, in effect, confused the principles of Argumentative conclusion on the one hand and of Scientific Observation and Inference on the other. The conception of Inference which he adopted from Whately was too narrow on both sides for the uses to which he put it. Be it understood that in the central methods both of Syllogistic and of Science, Mill was substantially in accord with tradition; it is in his mode of junction, and the light thereby thrown upon the ends and aims of both, that he is most open to criticism.
As regards the relation between Deduction and Induction, Mill's chief proposition was the brilliant paradox that all inference is at bottom Inductive, that Deduction is only a partial and accidental stage in a process the whole of which may be called Induction. An opinion was abroad—fostered by the apparently exclusive devotion of Logic to Deduction—that all inference is essentially Deductive. Not so, answered Mill, meeting this extreme with another: all inference is essentially Inductive. He arrives at this through the conception that Induction is a generalisation fromobserved particulars, while Deduction is merely the extension of the generalisation to a new case, a new particular. The example that he used will make his meaning plain.
Take a common Syllogism:—
All men are mortal.Socrates is a man.Socrates is mortal.
All men are mortal.Socrates is a man.Socrates is mortal.
All men are mortal.
Socrates is a man.
Socrates is mortal.
"The proposition," Mill says, "that Socrates is mortal is evidently an inference. It is got at as a conclusion from something else. But do we in reality conclude it from the proposition, All men are mortal?" He answers that this cannot be, because if it is not true that Socrates is mortal it cannot be true that all men are mortal. It is clear that our belief in the mortality of Socrates must rest on the same ground as our belief in the mortality of men in general. He goes on to ask whence we derive our knowledge of the general truth, and answers: "Of course from observation. Now all which man can observe are individual cases.... A general truth is but an aggregate of particular truths. But a general proposition is not merely a compendious form for recording a number of particular facts.... It is also a process of inference. From instances which we have observed we feel warranted in concluding that what we have found true in those instances, holds in all similar ones, past, present, and future. We then record all that we have observed together with what we infer from our observations, in one concise expression." A general proposition is thus at once a summary of particular facts and a memorandum of our right to infer from them. And when we make a deduction we are, as it were,interpreting this memorandum. But it is upon the particular facts that the inference really rests, and Mill contends that we might if we chose infer to the particular conclusion at once without going through the form of a general inference. Thus Mills seeks to make good his point that all inference is essentially Inductive, and that it is only for convenience that the word Induction has been confined to the general induction, while the word Deduction is applied to the process of interpreting our memorandum.
Clear and consecutive as this argument is, it is fundamentally confusing. It confuses the nature of Syllogistic conclusion or Deduction, and at the same time gives a partial and incomplete account of the ground of Material inference.
The root of the first confusion lies in raising the question of the ground of material inference in connexion with the Syllogism. As regards the usefulness of the Syllogism, this is anIgnoratio Elenchi. That the Major and the conclusion rest upon the same ground as matters of belief is indisputable: but it is irrelevant. In so far as "Socrates is mortal" is an inference from facts, it is not the conclusion of a Syllogism. This is implicitly and with unconscious inconsistency recognised by Mill when he represents Deduction as the interpretation of a memorandum. To represent Deduction as the interpretation of a memorandum—a very happy way of putting it and quite in accordance with Roger Bacon's view—is really inconsistent with regarding Deduction as an occasional step in the process of Induction. If Deduction is the interpretation of a memorandum, it is no part of the process of inference from facts. The conditions of correct interpretation as laid down in Syllogism are one thing,and the methods of correct inference from the facts, the methods of science that he was in search of, are another.
Let us emphasise this view of Deduction as the interpretation of a memorandum. It corresponds exactly with the view that I have taken in discussing the utility of the Syllogism. Suppose we want to know whether a particular conclusion is consistent with our memorandum, what have we to look to? We have to put our memorandum into such a form that it is at once apparent whether or not it covers our particular case. The Syllogism aspires to be such a form. That is the end and aim of it. It does not enable us to judge whether the memorandum is a legitimate memorandum or not. It only makes clear that if the memorandum is legitimate, so is the conclusion. How to make clear and consistent memoranda of our beliefs in words is a sufficiently complete description of the main purpose of Deductive Logic.
Instead, then, of trying to present Deduction and Induction as parts of the same process, which he was led to do by his desire to connect the new and the old, Mill ought rather, in consistency as well as in the interests of clear system, to have drawn a line of separation between the two as having really different ends, the conditions of correct conclusion from accepted generalities on the one hand, and the conditions of correct inference from facts on the other. Whether the first should be called inference at all is a question of naming that ought to have been considered by itself. We may refuse to call it inference, but we only confuse ourselves and others if we do not acknowledge that in so doing we are breaking with traditional usage. Perhaps the best way in the interests of clearness is tocompromise with tradition by calling the one Formal Inference and the other Material Inference.
It is with the latter that the Physical Sciences are mainly concerned, and it was the conditions and methods of its correct performance that Mill desired to systematise in his Inductive Logic. We have next to see how his statement of the grounds of Material Inference was affected by his connexion of Deduction and Induction. Here also we shall find a reason for a clearer separation between the two departments of Logic.
In his antagonism to a supposed doctrine that all reasoning is from general to particular, Mill maintainedsimpliciterthat all reasoning is from particulars to particulars. Now this is true onlysecundum quid, and although in the course of his argument Mill introduced the necessary qualifications, the unqualified thesis was confusing. It is perfectly true that we may infer—we can hardly be said to reason—from observed particulars to unobserved. We may even infer, and infer correctly, from a single case. The village matron, called in to prescribe for a neighbour's sick child, infers that what cured her own child will cure the neighbour's, and prescribes accordingly. And she may be right. But it is also true that she may be wrong, and that no fallacy is more common than reasoning from particulars to particulars without the requisite precautions. This is the moral of one of the fables of Camerarius. Two donkeys were travelling in the same caravan, the one laden with salt, the other with hay. The one laden with salt stumbled in crossing a stream, his panniers dipped in the stream, the salt melted, and his burden was lightened. When they came to another stream, the donkey that was laden with hay dipped his panniersin the water, expecting a similar result. Mill's illustrations of correct inference from particulars to particulars were really irrelevant. What we are concerned with in considering the grounds of Inference, is the condition of correct inference, and no inference to an unobserved case is sound unless it is of a like kind with the observed case or cases on which it is founded, that is to say, unless we are entitled to make a general proposition. We need not go through the form of making a general proposition, but if a general proposition for all particulars of a certain description is not legitimate, no more is the particular inference. Mill, of course, did not deny this, he was only betrayed by the turn of his polemic into an unqualified form of statement that seemed to ignore it.
But this was not the worst defect of Mill's attempt at a junction of old and new through Whately's conception of Induction. A more serious defect was due to the insufficiency of this conception to represent all the modes of scientific inference. When a certain attribute has been found in a certain connexion in this, that, and the other, to the extent of all observed instances, we infer that it will be found in all, that the connexion that has obtained within the range of our actual experience has obtained beyond that range and will obtain in the future. Call this an observed uniformity of nature: we hold ourselves justified in expecting that the observed uniformities of nature will continue. Such an observed uniformity—that All animals have a nervous system, that All animals die, that Quinine cures ague—is also called an Empirical Law.
But while we are justified in extending an empirical law beyond the limits within which it has beenobserved to hold good, it is a mistake to suppose that the main work of science is the collection of empirical laws, and that the only scientific inference is the inference from the observed prevalence of an empirical law to its continuance. With science the collection of empirical laws is only a preliminary: "the goal of science," in Herschel's phrase, "is explanation". In giving such prominence to empirical laws in his theory, Mill confined Induction to a narrower scope than science ascribes to it. Science aims at reaching "the causes of things": it tries to penetrate behind observed uniformities to the explanation of them. In fact, as long as a science consists only of observed uniformities, as long as it is in the empirical stage, it is a science only by courtesy. Astronomy was in this stage before the discovery of the Law of Gravitation. Medicine is merely empirical as long as its practice rests upon such generalisations as that Quinine cures ague, without knowing why. It is true that this explanation may consist only in the discovery of a higher or deeper uniformity, a more recondite law of connexion: the point is that these deeper laws are not always open to observation, and that the method of reaching them is not merely observing and recording.
In the body of his Inductive Logic, Mill gave a sufficient account of the Method of Explanation as practised in scientific inquiry. It was only his mode of approaching the subject that was confusing, and made it appear as if the proper work of science were merely extending observed generalities, as when we conclude that all men will die because all men have died, or that all horned animals ruminate because all hitherto observed have had this attribute. A minor source of confusion incident to the same controversywas his refusing the title of Induction proper to a mere summary of particulars. He seemed thereby to cast a slight upon the mere summation of particulars. And yet, according to his theory, it was those particulars that were the basis of the Induction properly so called. That all men will die is an inference from the observation summed up in the proposition that all men have died. If we refuse the name of Induction to the general proposition of fact, what are we to call it? The truth is that the reason why the word Induction is applied indifferently to the general proposition of fact and the general proposition applicable to all time is that, once we are sure of the facts, the transition to the inference is so simple an affair that it has not been found necessary in practice to distinguish them by different names.
Our criticism of Mill would itself mislead if it were taken to mean that the methods of science which he formulated are not the methods of science or that his system of those methods is substantially incomplete. His Inductive Logic as a system of scientific method was a great achievement in organisation, a veritableNovum Organumof knowledge. What kept him substantially right was that the methods which he systematised were taken from the practice of men of science. Our criticism amounts only to this, that in correlating the new system with the old he went upon a wrong track. For more than two centuries Deduction had been opposed to Induction, thears disserendito thears inveniendi. In trying to reconcile them and bring them under one roof, Mill drew the bonds too tight. In stating the terms of the union between the two partners, he did not separate their spheres of work with sufficient distinctness.
Mill's theory of Deduction and Induction and the voluminous criticism to which in its turn it has been subjected have undoubtedly been of great service in clearing up the foundations of reasoning. But the moral of it is that if we are to make the methods of Science a part of Logic, and to name this department Induction, it is better to discard altogether the questions of General and Particular which are pertinent to Syllogism, and to recognise the new department simply as being concerned with a different kind of inference, inference from facts to what lies beyond them, inference from the observed to the unobserved.
That this is the general aim and proper work of Science is evident from its history. Get at the secrets of Nature by the study of Nature, penetrate to what is unknown and unexperienced by help of what is known and has been experienced, was the cry of the early reformers of Science. Thus only, in Roger Bacon's phrase, could certainty—assured, well grounded, rational belief—be reached. This doctrine, like every other, can be understood only by what it was intended to deny. The way of reaching certainty that Roger Bacon repudiated was argument, discussion, dialectic. This "concludes a question but does not make us feel certain, or acquiesce in the contemplation of truth that is not also found in Experience". Argument is not necessarily useless; the proposition combated is only that by it alone—by discussion that does not go beyond accepted theories or conceptions—rational belief about the unknown cannot be reached. The proposition affirmed is that to this end the conclusions of argument must be tested by experience.
Observation of facts then is a cardinal part of the method of Science. The facts on which our inferencesare based, by which our conclusions are tested, must be accurate. But in thus laying emphasis on the necessity of accurate observation, we must beware of rushing to the opposite extreme, and supposing that observation alone is enough. Observation, the accurate use of the senses (by which we must understand inner as well as outer sense), is not the whole work of Science. We may stare at facts every minute of our waking day without being a whit the wiser unless we exert our intellects to build upon them or under them. To make our examination fruitful, we must have conceptions, theories, speculations, to bring to the test. The comparison of these with the facts is the inductive verification of them. Science has to exercise its ingenuity both in making hypotheses and in contriving occasions for testing them by observation. These contrived occasions are its artificial experiments, which have come to be called experiments simply by contrast with conclusive observations for which Nature herself furnishes the occasion. The observations of Science are not passive observations. The word experiment simply means trial, and every experiment, natural or artificial, is the trial of a hypothesis. In the language of Leonardo da Vinci, "Theory is the general, Experiments are the soldiers".
Observation and Inference go hand in hand in the work of Science, but with a view to a methodical exposition of its methods, we may divide them broadly into Methods of Observation and Methods of Inference. There are errors specially incident to Observation, and errors specially incident to Inference. How to observe correctly and how to make correct inferences from our observations are the two objects of our study in Inductive Logic: we study the examples of Science becausethey have been successful in accomplishing those objects.
That all inference to the unobserved is founded on facts, on the data of experience, need not be postulated. It is enough to say that Inductive Logic is concerned with inference in so far as it is founded on the data of experience. But inasmuch as all the data of experience are not of equal value as bases of inference, it is well to begin with an analysis of them, if we wish to take a comprehensive survey of the various modes of inference and the conditions of their validity.
Footnote 1:Hamilton'sReid, p. 712.
Footnote 2:TheNovum Organumwas never completed. Of the nine heads of special aids to the intellect in the final interpretation he completed only the first, the list of Prerogative Instances.
Footnote 3:Sylva Sylvarum, CenturyI, 24.
Footnote 4:Sylva Sylvarum, CenturyI, 5.
If we examine any of the facts or particulars on which an inference to the unobserved is founded, we shall find that they are not isolated individuals or attributes, separate objects of perception or thought, but relations among things and their qualities, constituents, or ingredients.
Take the "particular" from which Mill's village matron inferred, the fact on which she based her expectation of a cure for her neighbour's child. It is a relation between things. We have the first child's ailment, the administration of the drug, and the recovery, a series of events in sequence. This observed sequence is the fact from which she is said to infer, the datum of experience. She expects this sequence to be repeated in the case of her neighbour's child.
Similarly we shall find that, in all cases where we infer, the facts are complex, are not mere isolated things, but relations among things—using the word thing in its widest sense—relations which we expect to find repeated, or believe to have occurred before, or to be occurring now beyond the range of our observation. These relations, which we may call coincidences or conjunctions, are the data of experience from which westart in our beliefs or inferences about the unexperienced.
The problem of Inductive Logic being to determine when or on what conditions such beliefs are rational, we may begin by distinguishing the data of coincidence or conjunction accordingly. There are certain coincidences that we expect to find repeated beyond the occasions on which we have observed them, and others that we do not expect to find repeated. If it is a sound basis of inference that we are in search of, it is evidently to these first, the coincidences that we are assured of finding again, that we must direct our study. Let us see whether they can be specified.
(1) If there is no causal connexion between A and B, using these as symbols for the members of a coincidence—the objects that are presented together—we do not expect the coincidence to be repeated. If A and B are connected as cause and effect, we expect the effect to recur in company with the cause. We expect that when the cause reappears in similar circumstances, the effect also will reappear.
You are hit,e.g., by a snowball, and the blow is followed by a feeling of pain. The sun, we shall say, was shining at the moment of the impact of the snowball on your body. The sunshine preceded your feeling of pain as well as the blow. But you do not expect the pain to recur next time that the sun shines. You do expect it to recur next time you are hit by a snowball.
The taking of food and a certain feeling of strength are causally connected. If we go without food, we are not surprised when faintness or weariness supervenes.
Suppose that when our village matron administered her remedy to her own child, a dog stood by thebedside and barked. The barking in that case would precede the cure. Now, if the matron were what we should call a superstitious person, and believed that this concomitant had a certain efficacy, that the dog's barking and the cure were causally connected, she would take the dog with her when she went to cure her neighbour's child. Otherwise she would not. She would say that the barking was an accidental, casual, fortuitous coincidence, and would build no expectation upon it.
These illustrations may serve to remind us of the familiar fact that the causal nexus is at least one of the things that we depend on in our inferences to the unobserved. To a simple sequence we attach no importance, but a causal sequence or consequence that has been observed is a mainstay of inference.
Whether the causal sequence holds or not as a matter of fact, we depend upon it if we believe in it as a matter of fact. But unless it does hold as a matter of fact, it is valueless as a guide to the unknown, and our belief is irrational. Clearly, therefore, if rational belief is what we aim at, it is of importance that we should make sure of cause and effect as matter of fact in the sequence of events.
One large department of Inductive Logic, the so-called Experimental Methods, is designed to help us in thus making sure,i.e., in ascertaining causal sequence as a matter of fact. It is assumed that by careful observation of the circumstances, we can distinguish between mere simple sequence and causal sequence or consequence, and methods are recommended of observing with the proper precautions against error.
Observe that these methods, though called Inductive, are not concerned with arriving at general propositions.The principle we go upon is simply this, that if it can be ascertained as matter of fact that a certain thing is related to another as cause and effect, we may count upon the same relation as holding in unobserved Nature, on the general ground that like causes produce like effects in like circumstances.
Observe, also, that I deliberately speak of the causal relation as a relation among phenomena. Whether this use of the words cause and effect is philosophically justifiable, is a question that will be raised and partly discussed later on. Here I simply follow the common usage, in accordance with which objects of perception,e.g., the administration of a drug and the recovery of a patient, are spoken of as cause and effect. Such observable sequences are causal sequences in the ordinary sense, and it is part of the work of Science to observe them. I do not deny that thetruecause, of the cause that science aims ultimately at discovering, is to be found in the latent constitution or composition of the things concerned. Only that, as we shall see more precisely, is a cause of another description. Meantime, let us take the word to cover what it undoubtedly covers in ordinary speech, the perceptible antecedent of a perceptible consequent.
Strictly speaking, as we shall find, Science has only one method of directly observing when events are in causal sequence. But there are various indirect methods, which shall be described in some sort of order.
For the practical purposes of life, a single ascertained causal sequence is of little value as a basis of inference, because we can infer only to its repetition in identical circumstances. Suppose our village matron had been able to ascertain as a matter of fact—a feat as we shallfind not to be achieved by direct observation—that the drug did cure her child, this knowledge by itself would have been practically valueless, because the only legitimate inference would have been that an exactly similar dose would have the same effect in exactly similar circumstances. But, as we shall find, though practically valueless, a single ascertained causal sequence is of supreme value in testing scientific speculations as to the underlying causes.
(2) We have next to see whether there are any other rational expectations based on observed facts. We may lay down as a principle the following:—
If a conjunction or coincidence has constantly been repeated within our experience, we expect it to recur and believe that it has recurred outside our experience.
How far such expectations are rational, and with what degrees of confidence they should be entertained, are the questions for the Logic of Inference, but we may first note that we do as a matter of habit found expectations on repeated coincidence, and indeed guide our daily life in this way. If we meet a man repeatedly in the street at a certain hour, we go out expecting to meet him: it is a shock to our expectations, a surprise, when we do not. If we are walking along a road and find poles set up at regular intervals, we continue our walk expecting to find a pole coincident with the end of each interval.
What Mill calls the uniformities of Nature, the uniformities expressed in general propositions, are from the point of view of the observer, examples of repeated coincidence. Birth, growth, decay, death, are not isolated or variable coincidences with organised being: all are born, all grow, all decay, and all die. These uniformities constitute the order of Nature: the coincidencesobserved are not occasional, occurring once in a way or only now and then; they turn up again and again. Trees are among the uniformities on the varied face of Nature: certain relations between the soil and the plant, between trunk, branches, and leaves are common to them. For us who observe, each particular tree that comes under our observation is a repetition of the coincidence. And so with animals: in each we find certain tissues, certain organs, conjoined on an invariable plan.
Technically these uniformities have been divided into uniformities of Sequence and uniformities of Coexistence. Thus the repeated alternation of day and night is a uniformity of Sequence: the invariable conjunction of inertia with weight is a uniformity of Coexistence. But the distinction is really immaterial to Logic. What Logic is concerned with is the observation of the facts and the validity of any inference based on them: and in these respects it makes no difference whether the uniformity that we observe and found upon is one of Sequence or of Coexistence.
It was exclusively to such inferences, inferences from observed facts of repeated coincidence, that Mill confined himself in his theory of Induction, though not in his exposition of the methods. These are the inferences for which we must postulate what he calls the Uniformity of Nature. Every induction, he says, following Whately, may be thrown into the form of a Syllogism, in which the principle of the Uniformity of Nature is the Major Premiss, standing to the inference in the relation in which the Major Premiss of a Syllogism stands to the conclusion. If we express this abstractly denominated principle in propositional form, and take it in connexion with Mill's other saying thatthe course of Nature is not a uniformity but uniformities, we shall find, I think, that this postulated Major Premiss amounts to an assumption that the observed Uniformities of Nature continue. Mill's Inductive Syllogism thus made explicit would be something like this:—
All the observed uniformities of Nature continue.That all men have died is an observed uniformity.Therefore, it continues;i.e., all men will die and did die before the beginning of record.
All the observed uniformities of Nature continue.That all men have died is an observed uniformity.Therefore, it continues;i.e., all men will die and did die before the beginning of record.
All the observed uniformities of Nature continue.
That all men have died is an observed uniformity.
Therefore, it continues;i.e., all men will die and did die before the beginning of record.
There is no doubt that this is a perfectly sound postulate. Like all ultimate postulates it is indemonstrable; Mill's derivation of it from Experience did not amount to a demonstration. It is simply an assumption on which we act. If any man cares to deny it, there is no argument that we can turn against him. We can only convict him of practical inconsistency, by showing that he acts upon this assumption himself every minute of his waking day. If we do not believe in the continuance of observed uniformities, why do we turn our eyes to the window expecting to find it in its accustomed order of place? Why do we not look for it in another wall? Why do we dip our pens in ink, and expect the application of them to white paper to be followed by a black mark?
The principle is sound, but is it our only postulate in inference to the unobserved, and does the continuance of empirical laws represent all that Science assumes in its inferences? Mill was not satisfied about this question. He pointed out a difficulty which a mere belief in empirical continuity does not solve. Why do we believe more confidently in some uniformities than in others? Why would a reported breach ofone be regarded with more incredulity than that of another? Suppose a traveller to return from a strange country and report that he had met men with heads growing beneath their shoulders, why would this be pronounced more incredible than a report that he had seen a grey crow? All crows hitherto observed have been black, and in all men hitherto observed the heads have been above the shoulders: if the mere continuity of observed uniformities is all that we go upon in our inferences, a breach of the one uniformity should be just as improbable as a breach of the other, neither more nor less. Mill admitted the difficulty, and remarked that whoever could solve it would have solved the problem of Induction. Now it seems to me that this particular difficulty may be solved, and yet leave another behind. It may be solved within the limits of the principle of emperical—meaning by that observational—continuity. The uniform blackness of the crow is an exception within a wider uniformity: the colour of animals is generally variable. Hence we are not so much surprised at the reported appearance of a grey crow: it is in accordance with the more general law. On the other hand, the uniform position of the head relative to other parts of the body is a uniformity as wide as the animal kingdom: it is a coincidence repeated as often as animals have been repeated, and merely on the principle that uniformities continue, it has an absolutely uncontradicted series in its favour.
But is this principle really all that we assume? Do we not also assume that behind the observed fact uniformity, there is a cause for it, a cause that does not appear on the surface of the observation, but must be sought outside of its range? And do not the variousdegrees of confidence with which we expect a repetition of the coincidence, depend upon the extent of our knowledge of the producing causes and the mode of their operation? At bottom our belief in the continuance of the observed uniformities rests on a belief in the continuance of the producing causes, and till we know what these are our belief has an inferior warrant: there is less reason for our confidence.
To go back to the illustrations with which we started. If we have met a man every day for months at a certain place at a certain hour, it is reasonable to expect to meet him there to-morrow, even if our knowledge does not go beyond the observed facts of repeated coincidence. But if we know also what brings him there, and that this cause continues, we have a stronger reason for our expectation. And so with the case of poles at regular intervals on a road. If we know why they are placed there, and the range of the purpose, we expect their recurrence more confidently within the limits of that purpose. This further knowledge is a warrant for stronger confidence, because if we know the producing causes, we are in a better position for knowing whether anything is likely to defeat the coincidence. A uniformity is said to be explained when its cause is known, and an inference from an explained uniformity is always more certain than an inference from a uniformity that is merely empirical in the sense of being simply observed.
Now, the special work of Science is to explain, in the sense of discovering the causes at work beneath what lies open to observation. In so doing it follows a certain method, and obeys certain conditions of satisfactory explanation. Its explanations are inferences from facts, inasmuch as it is conformity withobserved facts, with outward signs of underlying causal nexus, that is the justification of them. But they are not inferences from facts in the sense above described as empirical inference. In its explanations also Science postulates a principle that may be called the Uniformity of Nature. But this principle is not merely that observed uniformities continue. It may be expressed rather as an assumption that the underlying causes are uniform in their operation, that as they have acted beneath the recorded experiences of mankind, so they have acted before and will continue to act.
The foregoing considerations indicate a plan for a roughly systematic arrangement of the methods of Induction. Seeing that all inference from the data of experience presupposes causal connexion among the data from which we infer, all efforts at establishing sound bases of inference, or rational ground for expectation fall, broadly speaking, under two heads: (1) Methods of ascertaining causal connexion among phenomena as a matter of fact, that is, Methods of Observation; and (2) Methods of ascertaining what the causal connexion is, that is, Methods of Explanation.
These constitute the body of Inductive Logic. But there is a preliminary and a pendant. Without raising the question of causal connexion, we are liable to certain errors in ascertaining in what sequence and with what circumstances events really occurred. These tendencies to error deserve to be pointed out by way of warning, and this I shall attempt in a separate chapter on observation of facts of simple sequence. This is preliminary to the special methods of observing causal sequence. Then, by way of pendant, I shall consider two modes of empirical inference from data inwhich the causal connexion has not been ascertained or explained—Inference from approximate generalisations to particular cases, and Inference from Analogy.
Most of these methods in one form or another were included by Mill in his system of Inductive Logic, and the great merit of his work was that he did include them, though at some sacrifice of consistency with his introductory theory. With regard to the kind of empirical inference which that theory, following the lead of Whately, took as the type of all inference, Logic has really little to say. It was this probably that was in Mill's mind when he said that there is no Logic of Observation, ignoring the fact that the Experimental Methods are really methods of observation, as well as the Methods of Eliminating Chance by calculation of Probability. There is no method of observing uniformities except simply observing them. Nor indeed is there any "method" of inferring from them: we can only point out that in every particular inference from them we assume or postulate their continuance generally. As regards their observation, we may point out further that a special fallacy is incident to it, the fallacy of ignoring exceptions. If we are prepossessed or prejudiced in favour of a uniformity, we are apt to observe only the favourable instances, and to be blind to cases where the supposed invariable coincidence does not occur. Thus, as Bacon remarked among hisIdola, we are apt to remember when our dreams come true, and to forget when they do not. Suppose we take up the notion that a new moon on a Saturday is invariably followed by twenty days of unsettled weather, one or two or a few cases in which this notably holds good are apt to be borne in mind, while cases where the weather is neither conspicuously good norbad are apt to be overlooked. But when a warning has been given against this besetting fallacy, Logic has nothing further to say about empirical uniformities, except that we may infer from them with some degree of reasonable probability, and that if we want ground for a more certain inference we should try to explain them.
All beliefs as to simple matter of fact must rest ultimately on observation. But, of course, we believe many things to have happened that we have never seen. As Chaucer says:—
But God forbedë but men shouldë 'lieveWel morë thing than men han seen with eye.Man shall not weenen everything a lieBut if himself it seeth or elsë doth.
But God forbedë but men shouldë 'lieveWel morë thing than men han seen with eye.Man shall not weenen everything a lieBut if himself it seeth or elsë doth.
But God forbedë but men shouldë 'lieve
Wel morë thing than men han seen with eye.
Man shall not weenen everything a lie
But if himself it seeth or elsë doth.
For the great bulk of matters of fact that we believe we are necessarily dependent on the observations of others. And if we are to apply scientific method to the ascertainment of this, we must know what errors we are liable to in our recollections of what we have ourselves witnessed, and what errors are apt to arise in the tradition of what purports to be the evidence of eye-witnesses.
It is hard to convince anybody that he cannot trust implicitly to his memory of what he has himself seen.We are ready enough to believe that others may be deceived: but not our own senses. Seeing is believing. It is well, however, that we should realise that all observation is fallible, even our own.
Three great besetting fallacies or tendencies to error may be specified:—
1. Liability to have the attention fastened on special incidents, and so diverted from other parts of the occurrence.
2. Liability to confuse and transpose the sequence of events.
3. Liability to substitute inference for fact.
It is upon the first of these weaknesses in man as an observing machine that jugglers chiefly depend on working their marvels. Sleight of hand counts for much, but diverting the spectator's eyes for a good deal more. That is why they have music played and patter incessantly as they operate. Their patter is not purposeless: it is calculated to turn our eyes away from the movements of their nimble hands.
It must be borne in mind that in any field of vision there are many objects, and that in any rapid succession of incidents much more passes before the eyes than the memory can retain in its exact order. It is of course in moments of excitement and hurry, when our observation is distracted, that we are most subject to fallacious illusions of memory. Unconsciously we make a coherent picture of what we have seen, and very often it happens that the sequence of events is not what actually passed, but what we were prejudiced in favour of seeing. Hence the unlikelihood of finding exact agreement among the witnesses of any exciting occurrence, a quarrel, a railway accident, a collision at sea, the incidents of a battle.
"It commonly happens," says Mr. Kinglake,1"that incidents occurring in a battle are told by the most truthful bystanders with differences more or less wide." In the attack on the Great Redoubt in the Battle of the Alma, a young officer, Anstruther, rushed forward and planted the colours of the Royal Welsh—but where? Some distinctly remembered seeing him dig the butt-end of the flagstaff into the parapet: others as distinctly remembered seeing him fall several paces before he reached it. Similarly with the incidents of the death of the Prince Imperial near the Italezi Hills in the Zulu War. He was out as a volunteer with a reconnoitring party. They had off-saddled at a kraal and were resting, when a band of Zulus crept up through the long grass, and suddenly opened fire and made a rush forward. Our scouts at once took horse, as a reconnoitring party was bound to do, and scampered off, but the Prince was overtaken and killed. At the Court-Martial which ensued, the five troopers gave the most conflicting accounts of particulars which an unskilled investigator would think could not possibly have been mistaken by eye-witnesses of the same event. One said that the Prince had given the order to mount before the Zulus fired: another that he gave the order directly after: a third was positive that he never gave the order at all, but that it was given after the surprise by the officer in command. One said that he saw the Prince vault into the saddle as he gave the order: another that his horse bolted as he laid hold of the saddle, and that he ran alongside trying to get up.
The evidence before any Court of Inquiry into an exciting occurrence is almost certain to reveal similardiscrepancies. But what we find it hard to realise is that we ourselves can possibly be mistaken in what we have a distinct and positive recollection of having seen. It once happened to myself in a London street to see a drunken woman thrown under a cab by her husband. Two cabs were running along, a four-wheeler and a hansom: the woman staggered almost under the first, and was thrown under the second. As it happened the case never got beyond the police station to which the parties were conveyed after fierce opposition from some neighbours, who sympathised entirely with the man. The woman herself, when her wounds were dressed, acknowledged the justice of her punishment, and refused to charge her husband. I was all the more willing to acquiesce in this because I found that while I had the most distinct impression of having seen the four-wheeler run over the woman's body, and should have been obliged to swear accordingly, there could be no doubt that it was really the hansom that had done so. This was not only the evidence of the neighbours, which I suspected at the time of being a trick, but of the cabdriver, who had stopped at the moment to abide the results of the accident. I afterwards had the curiosity to ask an eminent police magistrate, Sir John Bridge, whether this illusion of memory on my part—which I can only account for by supposing that my eyes had been fixed on the sufferer and that I had unconsciously referred her injuries to the heavier vehicle—would have entirely discredited my testimony in his Court. His answer was that it would not; that he was constantly meeting with such errors, and that if he found a number of witnesses of the same occurrence exactly agreed in every particular, he would suspect that they had talked the matter overand agreed upon what they were to say. This was the opinion of an experienced judge, a skilled critic of the defects of personal observation. An Old Bailey counsel for the defence, who is equally acquainted with the weakness of human memory, takes advantage of the fact that it is not generally understood by a Jury, and makes the fallacious assumption that glaring discrepancies are irreconcilable with the good faith of the witnesses who differ.2
Next in value to personal observation, we must place the report, oral or written, of an eye-witness. This is the best evidence we can get if we have not witnessed an occurrence ourselves. Yet Courts of Law, which in consideration of the defects of personal observation require more than one witness to establish the truth, exclude hearsay evidence altogether in certain cases, and not without reason.