Chapter 35

THE DATA OF EXPERIENCE AS GROUNDS OF INFERENCE OR RATIONAL BELIEF.

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 we start 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 the bedside 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 the _true_ cause, 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 shall find 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 coincidences observed 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 that the 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.

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 of one 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 various degrees 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 with observed 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 in which 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 his _Idola_, 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 nor bad 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.