VIII.4

The Pragmatic Justification of Induction



HANS REICHENBACH

Hans Reichenbach (1891-1953) was born in Germany, taught at the University of Berlin, and was Professor of Philosophy at the University of California, Los Angeles, from 1938 until his death.

Reichenbach agrees with Hume that neither a deductive nor an inductive demonstration for inductive inference is possible.  Nevertheless, we have good practical reasons for trusting induction.  Our situation is like that of a patient who will die unless he undergoes an operation.  The operation may, not succeed, but it's his only hope for continued life.  Likewise, the principle of induction is our only hope for guidance in life and in science.  Living by inductive principles is our best bet, for if there are laws of nature and we follow them, we will be able to predict and, to a degree, control the future.  If there are no such laws, it doesn't matter what we do, for nature will prove to be lawless and chaotic.

The nontautological character of induction has been known a long time; Bacon had already emphasized that it is just this character to which the importance of induction is due.  If inductive inference can teach us something new, in opposition to deductive inference, this is because it is not a tautology. This useful quality has, however, become the center of the epistemological difficulties of induction, It was David Hume who first attacked the principle from this side; he pointed out that the apparent constraint of the inductive inference, although submitted to by everybody, could not be justified.  We believe in induction; we cannot even get rid of the belief when we know the impossibility of a logical demonstration of the validity of inductive inference; but as logicians we must admit that this belief is a deception--such is the result of Hume's criticism,.  We may summarize his objections in two statements:

1. We have no logical demonstration for the validity of inductive inference.

2. There is no demonstration a posteriori for the inductive inference; any such demonstration would presuppose the very principle which it is to demonstrate.

These two pillars of Hume's criticism of the principle of induction have stood unshaken for two centuries, and I think they still stand as long as there is a scientific philosophy....

Inductive inference cannot be dispensed with because we need it for the purpose of action.  To deem the inductive assumption unworthy of the assent of a philosopher, to keep a distinguished reserve, and to meet with a condescending smile the attempts of other people to bridge the gap between experience and prediction is cheap self-deceit; at the very moment when the apostles of such a higher philosophy leave the field of theoretical discussion and pass to the simplest actions of daily life, they follow the inductive principle as surely as does every earth-bound mind.  In any' action there are various means to the realization of our aim;  we have to make a choice, and we decide in accordance with the inductive principle.  Although there is no means which will produce with certainty the desired effect, we do not leave the choice to chance but prefer the means indicated by the principle of induction.  If we sit at the wheel of a car and want to turn the car to

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the right, why do we turn the wheel to the right? There is no certainty that the car will follow the wheel; there are indeed cars which do not always so behave.  Such cases arc fortunately exceptions.  But if we should not regard the inductive prescription and consider the effect of a turn of the wheel as entirely unknown to us, we might turn it to the left as well.  I do not say this to suggest such an attempt; the effects of skeptical philosophy applied in motor traffic would be rather unpleasant.  But I should say a philosopher who is to put aside his principles any time he steers a motor-car is a bad philosopher.

It is no justification of inductive belief to show that it is a habit, It is a habit; but the question is whether it is a good habit, where "good" is to mean "useful for the purpose of actions directed to future events."  If a person tells me that Socrates is a man, and that all men are mortal, I have the habit of believing that Socrates is mortal. I know, however, that this is a good habit.  If anyone had the habit of believing in such a case that Socrates is not mortal, we could demonstrate to him that this was a bad habit.  The analogous question must be raised for inductive inference. If we should not be able to demonstrate that it is a good habit, we should either cease using it or admit frankly that our philosophy is a failure.
Science proceeds by induction and not by tautological transformations of reports. [Francis] Bacon is right about Aristotle; but the novum organon [i.e., induction as opposed to deduction] needs a justification as good as that of the organon. Hume's criticism was the heaviest blow against empiricism; if we do nor want to dupe our consciousness of this by means of the narcotic drug of aprioristic rationalism, or the soporific of skepticism, we must find a defense for the inductive inference which holds as well as does the formalistic justification of deductive logic.

§ 39. The Justification of the Principle of Induction

We shall now begin to give the justification of induction which Hume thought impossible.  In the pursuit of this inquiry, let us ask first what has been proved, strictly, by Hume's objections.

Hume started with the assumption that a justification of induction: inference is only given if we can show that inductive inference must lead to success.  In other words, Hume believed that any justified application of the inductive inference presupposes a demonstration that the conclusion is true.  It is this assumption on which Hume's criticism is based.  His two objections directly concern only the question of the truth of the conclusion; they prove that the truth of the conclusion cannot be demonstrated. The two objections, therefore, are valid only in so far as the Humean assumption is valid.  It is this question to which we must turn: Is it necessary, for the justification of inductive inference to show that its conclusion is true?

A rather simple analysis shows us that this assumption does not hold.  Of course, if we were able to prove the truth of the conclusion, inductive inference would be justified; but the converse does not hold: a justification of the inductive inference does not imply a proof of the truth of the conclusion.  The proof of the truth of the conclusion is only a sufficient condition for the justification of induction, not a necessary condition.

The inductive inference is a procedure which is to furnish us the best assumption concerning the future.  If we do nor know the truth about the future, there may be nonetheless a best assumption about it, i.e., a best assumption relative to what we know. We must ask whether such a characterization may be given to the principle of induction.  If this turns our to be possible, the principle of induction will be justified.

An example will show the logical structure of our reasoning. A man may be suffering from a grave disease; the physician tells us: "I do not know, whether an operation will save the man, but if there is any remedy, it is an operation."  In such a case the operation would be justified. Of course, it would be better to know that the operation will save the man; but, if we do not know this, the knowledge formulated in the statement of the physician is a sufficient justification. If we cannot realize the sufficient conditions of success, we shalat least realize the necessary conditions.  If we were able to show that the inductive inference is a necessary condition of success, it would be justified; such a proof would satisfy any demands which may be raised about the justification of induction.

Now obviously there is a great difference between,



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our example and induction. The reasoning of the physician presupposes inductions; his knowledge about an operation as the only possible means of saving a life is based on inductive generalizations, just as are all other statements of empirical character. But we wanted only to illustrate the logical structure of our reasoning. If we want to regard such a reasoning as a justification of the principle of induction, the character of induction as a necessary condition of success must be demonstrated in a way which does not presuppose induction. Such a proof, however, can be given.

If we want to construct this proof, we must begin with a determination of the aim of induction. It is usually said that we perform inductions with the aim of foreseeing the future. This determination is vague; let us replace it by a formulation more precise in character:

We choose this formulation because we found that we need probabilities and that a probability is to be defined as the limit of a frequency; thus our determination of the aim of induction is given in such a way that it enables us to apply probability methods. If we compare this determination of the aim of induction with determinations usually given, it turns out to be not a confinement to a narrow aim but an expansion. What we usually call "foreseeing the future" is included in our formulation as a special case; the case of knowing with certainty for every event A the event B following it would correspond in our formulation to a case where the limit of the frequency is of the numerical value 1. Hume thought of this case only. Thus our inquiry differs from that of Hume in so far as it conceives the aim of induction in a generalized form. But we do not omit any possible applications if we deter- mine the principle of induction as the means of obtaining the limit of a frequency. If we have limits of frequency, we have all we want, including the case considered by Hume; we have then the laws of nature in their most general form, including both statistical and so-called causal laws--the latter being nothing but a special case of statistical laws, corresponding to the numerical value 1 of the limit of the frequency. We are entitled, therefore, to consider the determination of the limit of a frequency as the aim of the inductive inference.

Now it is obvious that we have no guaranty that this aim is at all attainable. The world may be so disorderly that it is impossible for us to construct series with a: limit. Let us introduce the term "predictable" for a world which is sufficiently ordered to enable us to construct series with a limit. We must admit, then, that we do not know whether the world is predictable. . . .

These considerations lead, however, to a more precise formulation of the logical structure of the inductive inference. We must say that, if there is any method which leads to the limit of the frequency, the inductive principle will do the same; if there is a limit of the frequency, the inductive principle is a sufficient condition to find it. If we omit now the premise that there is a limit of the frequency, we cannot say that the inductive principle is the necessary condition of finding it because there are other methods using a correction c_n. There is a set of equivalent conditions such that the choice of one of the members of the set is necessary if we want to find the limit; and, if there is a limit, each of the members of the set is an appropriate method for finding it. We may say, therefore, that the applicability of the inductive principle is a necessary condition of the existence of a limit of the frequency.

The decision in favor of the inductive principle among the members of the set of equivalent means may be substantiated by pointing out its
quality of embodying the smallest risk; after all, this decision is not of a great relevance, as all these methods must lead to the same value of the limit if they are sufficiently continued. It must not be forgotten, however, that the method of clairvoyance is not, without further ado, a number of the set because we do not know whether the correction c_n occurring here is submitted to the condition of convergence to zero. This must be proved first, and it can only be proved by using the inductive principle, viz., a method known to be a member of the set: this is why clairvoyance, in spite of all occult pretensions, is to be submitted to the control of scientific methods, i.e., by the principle of induction. 

It is in the analysis expounded that we see the solution of Hume's problem. Hume demanded too much when he wanted for a justification of the inductive inference a proof that its conclusion is

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 true. What his objections demonstrate is only that such a proof cannot be given. We do not perform, however, an inductive inference with the pretension of obtaining a true statement. What we obtain is a wager; and it is the best wager we can lay because it corresponds to a procedure the applicability of which is the necessary condition of the possibility of predictions. To fulfill the conditions sufficient for the attainment of true predictions does not lie in our power; let us be glad that we are able to fulfill at least the conditions necessary for the realization of this intrinsic aim of science. . . .

. . . With this result the application of the sys- tem of scientific inductions finds a justification similar to, and even better than, that of the single induction: the system of scientific inductions is the best posit we know concerning the future.

We found that the posits of the highest level are always blind posits; thus the system of knowledge, as a whole, is a blind posit. Posits of the lower levels have appraised weights; but their serviceableness depends on the unknown weights of the posits of higher levels. The uncertainty of knowledge as a whole therefore penetrates to the simplest posits we can make-those concerning the events of daily life. Such a result seems unavoidable for any theory of prediction. We have no certainty as to foreseeing the future. We do not know whether the predictions of complicated theories, such as the quantum theory or the theory of albumen molecules, will turn out to be true; we do not even know whether the simplest posits con cerning our immediate future will be confirmed, whether they concern the sun's rising or the persistence of the conditions of our personal environment. There is no principle of philosophy to warrant the reliability of such predictions; that is our answer to all attempts made within the history of philosophy to procure for us such certainty, from Plato, through all varieties of theology, to Descartes and Kant. In spite of that, we do not renounce prediction; the arguments of skeptics like Hume cannot shake our resolution: at least to try predictions. We know with certainty that among all procedures for foreseeing the future, known to us as involving success if success is possible, the procedure of concatenated inductions is the best. We try it as our best posit in order to have our chance-if we do not succeed, well, then our trial was in vain.

Is this to say that we are to renounce any. belief in success? There is such a belief; everyone .. has it when he makes inductions; does our solution of the inductive problem oblige us to dissuade him from this firm belief?

This is not a philosophical but a social question. As philosophers we know that such a belief is not justifiable; as sociologists we may be glad that there is such a belief. Not everyone is likely to act according to a principle if he does not believe in success; thus belief may guide him when the postulates of logic turn out to be too weak to direct him.

Yet our admission of this belief is not the attitude of the skeptic who, not knowing a solution of his own, permits everyone to believe what he wants. We may admit the belief because we know that it will determine the same actions that logical analysis would determine. Though we cannot justify the belief, we can justify the logical structure of the inference to which it fortunately corresponds as far as the practical results are concerned. This happy coincidence is certainly to be explained by Darwin's idea of selection; those animals were to survive whose habits of belief corresponded to the most useful instrument for foreseeing the future. There is no reason to dissuade anybody from doing with belief something which he ought to do in the same way if he had no belief.

This remark does not merely apply to the belief in induction as such. There are other kinds of belief which have crystallized round the methods of expanding knowledge. Men of scientific research are not always of so clear an insight into philosophical problems as logical analysis would require: they have filled up the world of research work with mystic concepts; they talk of "instinctive presentiments," of "natural hypotheses," and one of the best among them told me once that he found his great theories because he was convinced of the harmony of nature. If we were to analyze the discoveries of these men, we would find that their way of proceeding corresponds in a surpris ingly high degree to the rules of the principle of induction, applied however to a domain of facts where average minds did not see their traces. In such cases, inductive operations are imbedded within a belief which as to its intension differs from the inductive principle, although its function within the system of 

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operations of knowledge amounts to the same. The mysticism of scientific discovery is nothing but a superstructure of images and wishes; the supporting structure below is determined by the inductive principle.

I do not say this with the intention to discredit the belief-to pull the superstructure down. On the contrary, it seems to be a psychological law that discoveries need a kind of mythology; just as the inductive inference may lead us in certain cases to the preference of methods different from it, it may lead us also to the psychological law that sometimes those men will be best in making inductions who believe they possess other guides. The philosopher should not be astonished at this.

This does not mean that I should advise him to share any of these kinds of belief. It is the philosopher's aim to know what he does; to understand thought operations and not merely to apply them instinctively, automatically. He wants to look through the superstructure and to discover the supporting structure. Belief in induction, belief in a uniformity of the world, belief in a mystic harmony between nature and reason-they belong, all of them, to the superstructure; the solid foundation below is the system of inductive operations. The difficulty of a logical justification of these operations misled philosophers to seek a justification of the superstructure, to attempt an ontological justification of inductive belief by looking for necessary qualities of the world which would insure the success of inductive inferences. All such attempts will fail-because we shall never be able to give a cogent proof of any material presumption concerning nature. The way toward an under- standing of the step from experience to prediction lies in the logical sphere; to find it we have to free ourselves from one deep-rooted prejudice: from the presupposition that the system of knowledge is to be a system of true propositions. If we cross out this assumption within the theory of knowledge, the difficulties dissolve, and with them dissolves the mystical mist lying above the research methods of science. We shall then interpret knowledge as a system of posits, or wagers; with this the question of justification assumes as its form the question whether scientific knowledge is our best wager. Logical analysis shows that this demonstration can be given, that the inductive procedure of science is distinguished from other methods of prediction as leading to the most favorable posits. Thus we wager on the predictions of science and wager on the predictions of practical wisdom: we wager on the sun's rising tomorrow, we wager that food will nourish us tomorrow, we wager that our feet will carry us tomorrow. Our stake is not low; all our personal existence, our life itself, is at stake. To confess ignorance in the face of the future is the tragic duty of all scientific philosophy; but, if we are excluded from knowing true predictions, we shall be glad that at least we know the road toward our best wagers.