A Treatise on Induction and Probability

Georg Henrik Von Wright

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781317831013
• Edition: 1
• Topic: Filosofía
• Subtopic: Historia y teoría filosóficas

First published in 2000. This present book is primarily a treatise on induction. As such its aim is to examine, in the light of standards of logical correctness, various types of argument which can be grouped under the common heading of induction.

Chapter One
Induction and Its Problems

1. On the Division of Knowledge. Anticipation and Induction

OF human knowledge there are two main branches which may be called formal and material knowledge respectively. Their difference can be superficially described by saying that formal truth is tautologous and formal falsehood (self-)contradictory, whereas material truth consists in agreement and material falsehood in disagreement with facts. Formal truth is also called necessary, logical or analytic; material truth contingent, empirical or synthetic.

The possession of material knowledge may summarily be said to depend upon three basic faculties of our cognitive life, viz., memory, observation, and anticipation. We remember facts which have been, observe (or experience) facts which are, and anticipate facts to come. Whether and to what extent these three faculties can be sharply separated and defined independently of one another, is a problem which we shall not discuss here.

Of anticipation we can distinguish two types, according to whether the anticipatory activity is dependent upon information afforded by observation and memory, or not. Anticipation of the first kind we shall call anticipation from experience, or induction. Whether and in what sense of the above word 'dependent' non-inductive anticipation actually occurs, is another problem which we pass over.

Of anticipation from experience there are again two sub-types.

The first sub-type may, as a first approximation, be described as follows: From the information that something has been the case under certain conditions and that the conditions are repeated we anticipate that the same thing will be the case again. Anticipation of this kind which occurs in animals as well as in men, we shall call induction of the first order.

Induction of the first order can be studied from several points of view. Here we mention four:

First, it can be studied from an ethological or behaviouristic point of view, as the acquisition of habits or characteristic responses to stimuli. This study, being part of the psychology of learning, may, at least in the simplest cases, successfully employ the pattern of conditioned reflexes, roughly in the sense of Pavlov and Watson.

Secondly, it can be studied from a neurological point of view, as the acquisition of certain functional and possibly also structural units by the nervous system, which are causally responsible for the functional units of molar behaviour or habits.

Thirdly, it can (sometimes) be studied from a phenomenological or introspective point of view, as expectation, belief, and related states of consciousness, arising in the mind under certain conditions.

Fourthly, it can be studied from a logical point of view, as a sort of inference or argument. From the propositions that something has been the case under certain conditions and that the conditions are repeated we infer, as we say, the proposition that the same thing will be the case again. The conclusion of such an argument we shall call a prediction.

The second sub-type of anticipation from experience might, as a first approximation, be described as follows: From the information that something has been the case under certain conditions we anticipate that, if the same conditions are repeated, then the same thing will be the case again. Anticipation of this description, which seems to be characteristically human, we shall call induction of the second order.

Induction of the second order can also be studied under the behaviouristic aspect of habit, the neurological aspect of interconnexions in the nervous system, and the phenomenological aspect of expectation, though this study seems to be of a much more subtle and complicated nature than in the case of induction of the first order. Whether, from the points of view of psychology and nervous physiology, the two sub-types of anticipatory activity are fundamentally different, or whether the second cannot somehow be reduced to the first, is a debatable question.

Finally, induction of the second order can be studied under the logical aspect of inference. From the proposition that something has been the case under certain conditions we infer, as we say, the proposition that, if the same conditions are repeated, then the same thing will be the case again. The conclusion of such an argument we shall call a theory.

Of theories we can distinguish two basic types, according to whether the inductive conclusion is intended unrestrictedly to apply to all cases in which the conditions are fulfilled, or to a restricted number of such cases only. Theories with numerically unrestricted range of application we shall call laws (Laws of Nature).

(It is clear that our use of the words 'theory' and 'law' cannot pretend to be co-extensive with all actual uses of them in ordinary language or scientific discourse.)

Given a theory and a proposition to the effect that, in a particular case, certain conditions are fulfilled, a prediction can be deduced. It may be regarded as one of the chief purposes of making theories, to provide thereby a basis for the deduction of predictions.

In this book the study of induction will be mainly confined to the logical aspect of inference.-It should be stressed that, in ordinary life as well as in science, conscious inference by no means always accompanies anticipatory activity. The logic, therefore, of making predictions and theories is not so much a study of actual intellectual procedures as of certain 'rationalized counterparts' of them. This fact, however, does not diminish the importance of logical study for a true understanding of one of the principal aspects of human cognition.

2. On the Division of Science. The ‘savoir pour prévoir’

Science, or the methodical search for and attainment of knowledge, is sometimes divided into formal and material science, according to whether its aim lies in one or the other of the two main branches of human knowledge which we distinguished at the beginning of the previous section.

Material science may be further subdivided into theoretical and descriptive science. The distinguishing feature of theoretical science is the anticipation of facts from experience. Descriptive science is the systematic recording of facts.

Without claiming to be exhaustive, the above divisions exhibit certain types of scientific activity of which the actual sciences are a mixture. Any one of the actual sciences has, as a rule, a formal as well as a material, and a theoretical as well as a descriptive component. Purely formal, purely theoretical, and purely descriptive science thus represent borderline cases of a three-dimensional scale for the typological arrangement of actual sciences.

Formal science is sometimes called deductive. The anticipation of truth from experience is but another word for induction. Theoretical material science may therefore be called inductive.

The aim of science has frequently been characterized-by the words savoir pour prévoir or some equivalent phrase-as being to provide a basis for (successful) predictions. It is plain from the above that, strictly speaking, this applies only to that form of material science, which is here called theoretical. The characterization mentioned is not immediately applicable to formal science. Nor is it valid for descriptive material science, except in the normative sense of setting up an ideal. To what extent such a normative claim is justifiable will not be discussed here.

The above characterization of the aim of science is thus an exaggeration; The emphasis which has been laid on it is, however, illustrative of the important position which induction holds in the realm of scientific activity.

3. Induction and Discovery

Any act of anticipation from experience may be said to have been preceded by an act of discovery. From the failure to distinguish sharply between anticipation and discovery misunderstandings and disputes have arisen.

Discovery, as a preliminary phase of induction, consists in the detection of a feature common to a set of particular data. Anticipation, on the other hand, is the extension of this feature to unexamined cases.

Sometimes the process of discovery is altogether trivial. Such is, e.g., the case when, from the fact that some ravens are black, we anticipate the blackness of all ravens. When such 'primitive' instances of inductive inference are regarded from the point of view of logic, one is apt wholly to ignore the component of discovery, all the emphasis being laid upon the aspect of anticipation.

In more 'advanced' cases the opposite tendency becomes visible. Consider, e.g., the well-known law for the refraction of light $\frac{\sin \alpha }{\sin \beta }=c$. Before Snell, pairs of corresponding angles α and β had been recorded in tables. Snell detected a feature common to all such recorded correspondences. His law, however, embodies much more than the discovery of this feature; it also provides a rule which makes the prediction of new pairs of corresponding angles possible. Here the anticipation follows as a trivial matter of course, the discovery having once been made.

An example frequently mentioned in the literature on induction,¹ is Kepler's series of conjectures as to the orbit of Mars. Observation had informed Kepler of the position of the planet at various points in its path, and from this information the orbit itself was to be 'induced'. After having tried and rejected, so we are told, no less than nineteen assumptions as to the true orbit, he finally discovered the law which agreed with the observations. But, as Mill rightly pointed out in his polemic against Whewell concerning the nature of induction,² the mere discovery that the observed positions of Mars were correctly represented by points on an imaginary ellipse, did not constitute an inductive inference. It became an induction only when combined with the assumption that Mars would continue to revolve in that same ellipse, and that the positions of the planet during the time which intervened between two observations must have coincided with the intermediate points of the curve. This, however, is obscured in saying, as we usually do, that Kepler discovered the form of Mars' orbit.¹ Laws of Nature, strictly speaking, are not discovered, but established through a process of inference on the basis of discoveries made.

The making of discoveries in science is a worthy object of systematic study. It can be pursued from several points of view.

An important aspect of discovery is the phenomenological, by which we shall understand the scientists' own records of how their discoveries have come into being as a result of mental activity and effort. Valuable contributions to the phenomenology of discovery have been made by great men of science like Helmholtz and Mach, Claude Bernard and Poincaré, Faraday and Darwin.

In addition to this aspect of discovery from within, so to speak, there is also the psychological and sociological aspect from without. What are the main features of the discoverer's intelligence? What are his habits of working? What influence upon his ingenuity is to be attributed to factors of heredity, social environment, education, etc.?²

Finally it may be asked, whether discovery can or cannot be studied from the point of view of logic. We need not attempt to answer the question here. We shall only draw attention to two traditional mistakes which have originated from a confusion of the logical aspect of anticipation with that of discovery.

The first mistake may be schematically described as follows:

The possibility of a Logic of Induction, studying the inferential mechanism of inductive reasoning, is thought to imply the possibility of a Logic of Discovery, providing rules or precepts for the invention of truths in science. This mistake has deep roots in the history of philosophy. It underlies the famous Lullyan Ars magna which was also supposed to be an ars inventiva veritatum. It is, in particular, connected with the universal reaction in the sixteenth and seventeenth centuries against Aristotelian logic as being 'useless.' Descartes, Pascal, and the authors of the so-called Port Royal Logic are typical representatives of the view that logic ought to be somehow 'inventive.' In much the same spirit Zabarella, Galileo, and Leibniz expressed their opinions on induction and methodology. But by far the most important example of the confusion in question is found in the writings of Francis Bacon, who was strongly convinced that his contributions to the logical study of inductive inference were to make scientific discovery as independent of 'the acuteness and strength of wits' as had the invention of the compass made the drawing of exact circles independent of 'the steadiness and practice of the hand.'

One hundred years ago, William Whewell expressed in several works on induction the opinion that discoveries are, as he put it, 'happy guesses' or 'leaps which are out of the reach of method.' At the same time, Claude Bernard stressed similar views in polemics against Bacon.

As a criticism of the confusion of the logical study of scientific arguments with the invention of scientific truths, the attitude of Whewell and Claude Bernard towards discovery is fundamentally sound. If over-emphasized, however, it easily becomes unjustly discouraging to the systematic study of discovery as a psychological phenomenon. 'Il ne faut pas exagérer le mystère, ni faire de l'invention un miracle,' as Picard¹ rightly says. And if carried to the extreme, it promotes a new confusion as regards the relation of induction...