The rationalistic theory of induction and its justification had been sketched in the previous chapters. Now, we turn to discuss the empiricist theory of induction, and its solution to the problems involved from a logical point of view. By empiricism is meant the assertion that experience is the source of all human knowledge and the refusal of any a priori knowledge independently of sensible experience. Inductive inference faces, as has already been noted, three main problems; (1) why should we suppose a cause of (b), excluding absolute chance for its occurrence? (2) if there is a cause of (b), why should we suppose that (a) is its cause being concomitant with it, and not supposing that (b) is connected with (c) by relative chance? (3) If we could make sure, by inductive process, that (a) is the cause of (b), on what ground can we generalise the conclusion that all a's would be causes of b's? Formal logic solved the first and third questions by appealing to certain a priori principles on rationalistic lines, and solved the second problem by supposing another a priori principle denying the systematic repetition of relative chance.

    Since empiricism refuses any a priori principles and any rationalistic interpretation of causality, it was mainly concerned with giving different answers to the first and third questions, giving the second question a minor importance. We may make the empiricist theory clear if we distinguish three attitudes: certainty attitude, probability attitude, and psychological attitude.

    J.S. Mill, one of the greatest British empiricists, may be a representative of this attitude because he held the view that inductive conclusions are certainly true. His views on induction may be clarified if we summarise his positions on the first and third questions, then on the second question, already referred to.

    Certainty attitude holds that inductive inference has two notions as its ground, namely, causality and uniformity in nature, these are first premises. Like causes have like effects. It agrees also with formal logic in regarding inductive inference as a syllogism, the minor premise of which expresses particular instances, and its major premise expresses those two beliefs in causality and uniformity. It will be found for example that the extension of iron is, in all cases, concomitant with the occurrence of heat, and it is then concluded that when a phenomenon occurs under certain conditions, it occurs all the time in these conditions.

    Further, empiricism differs from rationalism in considering causality. For whereas the latter takes causality as a priori principle, the former reduces it to sensible experience, that is why Mill maintains that our belief in causality is the outcome of widespread inductions in the physical world. We derive our concept of cause from induction, but once so derived, this concept becomes our basis of any subsequent inductive generalization.

    Empiricism differs also from rationalism in detecting the meaning of cause; the rationalistic meaning of cause involves a necessary relation between certain phenomena, such as that when a phenomenon produces another, then the first is the cause, the second the effect. Whereas empiricism means by causal principle that every event has a cause in nature, but there is here no necessity [or production] since these go beyond experience. Causality means, for Mill, nothing more than a certain succession between two events. But not every temporal succession is causal; causal succession requires that succession should be uniform.

    We may now compare rationalistic conception of cause to empiricist one. First, succession between cause and effect is temporal in the latter, whereas it is ontological in the former. Secondly, rationalism takes causal relation as uniform concomitance between two events, resulting from the existence of a cause and its production by necessity of the effect, this being deduced from its cause. But empiricism refuses causal relation to be uniform concomitance and holds it to be a relation of another kind, namely, the observation and not deduction of temporal succession.

    Our comments on certainty attitude concerning induction are as follows. First, the author differs from both rationalistic and empiricist answers to the second question, namely, whether induction needs causality as a necessary postulate. Both schools, though different, answer that question in the positive, while the author will say no, owing to what will be maintained in the sequel. Secondly, we agree with certainty attitude that causal principle is itself reached by induction, and thus hold that induction needs no a priori postulates. But the impasse of empiricism in our view, is that it holds that induction is grounded upon causality postulate while it holds at the same time that causal principle is itself an inductive generalisation.

    If we reach causality by induction, why need we any a priori postulate to vindicate induction? Finally, when we say that induction is the basis of our idea of causality without any a priori postulate, we understand causality in the rationalistic sense as expressing a relation between cause and effect; otherwise, we cannot argue that causality is a result of empirical generalization. For the principal condition on which induction depends is, in our view, to conceive causality in the rationalistic sense, and if this is not the case, inductive inference would be incapable of reaching any generalization whatsoever, even in the probabilistic level.

    It is now possible to state the empiricist answer to the second problem of induction, which was central to formal logic as we have seen. For empiricism maintains our belief in the uniformity of nature, that is, if two certain events succeed each other under certain circumstances, we believe succession to occur in the future. It is meant of course, not that the belief is maintained if these two events happened once or twice, but that those events should have occurred countless times; and then we reach the same rationalistic position that relative chance cannot recur uniformly, with the difference that the latter position depends on a priori statement while empiricism rests on inductive inference in reaching uniformity.

    J.S. Mill has given us in his inductive logic four methods to discover the causal relation between any two phenomena. These methods are concerned with the second problem of induction, rejecting relative chance in nature.

    These methods are stated as follows: (1) The method of agreement: If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon"[3]. For example, if the phenomenon to the explained (b), is preceded or succeeded in the first instance by the circumstances (a), (c), (d), in the second by (e), (f), (a), and in the third by (x), (a), (y), then the only circumstance in common (a) it is cause of (b).

    If we wish to discuss this method deeply, we may discover clearly that it deals in fact with the problem of the probability of relative chance. In the first instance of the phenomenon (b), we find that (b) succeeds (a), but there is still the probability that (b) is caused by (a), or by (c), or (d), where as we find in the other instances that the probability is greater in the connection of (a) and (b) than otherwise.

    Thus the role of this first method is confined to facing the second problem of induction, and enables us to minimize relative chance.

    (2) The method of difference: "If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon"[4]

    Such method, like the first, is designed for solving the second problem and decreasing the probability of relative chance. For when we encounter the first instance of the phenomenon (a), and try a variety of circumstances, we cannot ascribe causality to only one of those circumstances; so that we cannot say A is the cause. And when we come to another circumstance, we get the same result. So we tend to make [A and a] causally related, and no relative chance involved.

    (3) Method of concomitant variations: "Whatever phenomenon varies in any manner, wherever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation"[5].. If we have two phenomena, and studied one of them in various circumstances, then we find that it occurs in different degrees, and when in studying the other phenomenon we find that the variations happened to it correspond to those happened to the former phenomenon, then there is causal relation between the two phenomena.

    This method, we notice, is nothing but a complex form of the method of agreement, for the third method involves a circumstance in common among various instances. Yet, the third method adds that such common circumstance has different degrees.

    (4) Method of residues: "Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents".

    This method, it is said, enabled astronomers to discover, theoretically, the planet "Neptune". For they held the theory of gravitation to be true, and observed some diversion in the orbit of the planet, "Uranus", contrary to what gravitational theory prescribes. Such difference between theory and fact needed an explanation, so Liverier put forward the hypothesis that such diversion in the orbit of Uranus is due to interference of some yet unknown planet. Later, it was discovered and called Neptune.

    Although this method is badly formulated, we may put it aright with application to the discovery of Neptune; this may be put as follows. When astronomers observed the diversion of Uranus from its normal orbit according to gravitational theory, they provided two alternatives to explain this: either to suppose the existence of a new planet which causes such diversion if the theory of gravitation is true, or that no new planet and then the theory is defective. Astronomers preferred the former, on the ground that very many other phenomena have confirmed the theory of gravitation, and then we tend to rule put the supposition that the diversion of Uranus' orbit happened by chance.

    We may conclude that Mill's four methods are intended to consider the second of the three problems of induction, in opposition to relative chance. Formal logic put forward the principle "chance cannot occur permanently and consistently", while Mill provided his four canons to oppose complete chance. Nevertheless, Mill had not succeeded in rejecting chance occurrence of phenomena in all respects, [x] since he made probable other circumstances to produce the effect other than the assigned cause.

    This is the second attitude of the empiricistic theory of induction. Such attitude suggests that inductive generalisation needs certain assumption and postulates which can be confirmed independently of induction itself; but it maintains also that such confirmation is not possible on rationalistic lines since it rejects any a priori principles, not is it possible in accordance with certainty attitude which believed such postulates to be considered as results of previous inductions. And since those postulates cannot possibly be confirmed, inductive conclusions cannot be certain, but only probable: any more observation or experiment helps to increase probability of the conclusion.

    It may be useful to quote from Professor Zaki Naguib, a proponent of probability attitude, the following: "The majority of those interested in induction, including a rational principle not derived from sense experience, as our ground of generalising (scientific judgments). Even if you are enthusiast empiricist, you have to confess that there is something not derived from experience, namely, that what applies to some instances of a kind equally applies to all the instances belonging to it; hence our generalizations. Thus, Russell holds that we are obliged at the end to rest in induction to an unempirical basis, the so-called principle of induction. (Those who consider induction as the only scientific method think that all logic is empirical, and it is not expected of them to hold that induction requires a logical principle improvable by induction itself; such principle must be a priori).

    Now, most logicians, including Russell, maintain that experience alone is not sufficient and then we either accept the principle of induction as indebatable assumption, or seek in vain for a justification of predicating future phenomena from the present".

    "The question naturally arises, how can we judge the validity of inferring future events from past ones without recourse to any rational principle" such as the principle of induction suggested by Russell? Or is there a justification that new experiment be similar to past ones? In defence of empiricism, we [main turn???] ask: what is meant by rational justification? This may mean that the conclusion is certainly true, or that induction is to be considered as deduction the conclusion of which be implied in its premises ... Induction in this sense has no rational justification, for induction is no deduction".

    "But such meaning is accepted neither in the sciences nor in ordinary way of speaking. If I was told one day that (a) will play chess with (b), and all that I know about them is that both had played six times in the past, and (a) won the game in four times out of six, while (b) won twice, then I am justified in saying that the probability of a's winning is expected. Similarly, it is more probable that a falling body may come to the ground, the sun will rise tomorrow [than not] [???]. That is probability not certainty; but that is what the sciences are prepared to accept, because certainty is not expected save in mathematical propositions'[6]

    (1) We maintain that induction paves the way to scientific generalisations, but we wish to regard it not as deduction, but another sort of inference which proceeds from particular to general without need of any a priori principles. This topic will be considered at length in a later chapter, let it suffice now to say that we shall never prove that a normal person know by induction a great number of generalisations; we can have no proof to convince such person of this knowledge. How can we convince someone that if he eats he becomes hungry no longer, when he denies such process? Such person is similar to the idealist who denies the existence of the external world or any objective reality outside his own concepts. We cannot convince the idealist that he approves of the objective reality of his family, even if we are sure of that since he lives with them and other people. It is the same with the person who denies his knowledge of ordinary generalisations.

    We may distinguish three sorts of certainty: logical, subjective and objective; the first concerns deductive inference; the second is a personal affair, while objective certainty concerns induction, and the last certainty is not proved but only postulated and explained. Further, it is absurd to find a rational justification of induction if by this is meant deductive process involving the law [of] non-contradiction. For inductive conclusion cannot be logically certain.

    On the other hand, if it is meant by justification the claim that the negation of inductive conclusion is probable, then this is an important claim since it involves that inductive conclusion cannot be a postulate. We shall later be concerned with the condition of reasonable postulates.

    (2) If we follow the empiricistic line of thought we shall not reject only inductive science but also any degree of probability for inductive inference. The representative quotation mentioned above shows that such probability depends on probability calculus, but it will be shown later that such calculus does not lead to increasing probability of inductive conclusion unless it does also lead to confirming the rationalistic conception of causality, but empiricism rejects such conception. Thus, empirical logic faces a dilemma, either it leaves the empiricistic conception of causality and adopts the rationalistic conception, or it excludes the rationalistic conception of causality and insists on the empiricistic conception, but then it will be unable to explain the probability of induction.

    We mean by this attitude, an empiricistic one that deprives induction of any objective validity but connects it with habit; and David Hume is a clear representative. Modern Behaviourism, a great modern school of psychology, later come to continue the Human tradition and transfer it from the field of philosophy to that of psychology.

    Hume tries to clarify the problem of induction as follows. All inference concerning matters of fact is based on causal relation, and this relation is the sole relation which goes beyond the senses and informs us of entities that we do not perceive. If you ask some one about the cause of his belief in any absent matter of fact, he would justify such belief by means of his knowledge of another fact causally connected with it, he would say that he believes that x is sick because he saw a doctor visiting him. Or that if he was going yesterday to throw himself into fire, we are justified to say that he may be burnt, because there is a causal relation between thrown into fire and being burnt. We may now ask, how do we know such relation? The source of such knowledge is experience which enables us to observe the concomitance between both events. We may further ask, how do we know that actual concomitance between two events will happen in the future? We are in need of a justification of the principle that the future will be similar to the past. That was Hume's formulation of the problem. He solves the problem by saying that the justification of uniformity in nature is not logical but psychological and this can be done by giving analysis of cause-effect relation.

    Perceptions are either impressions or ideas for Hume, and these are distinguished by virtue of the degree of vividness connected with impressions. And impressions include all sensations, emotions and sentiments. Whereas ideas are fading copies of impressions when the object of perception is absent. For instance, when we look at the sea, we perceive it vividly and clearly and here we get an impression, but when we turn our back to it, we get an idea, a copy of such impression. Hume then maintains that impressions are prior to ideas, that every idea, simple or complex, has, for its origin, an impression.

    Impressions for Hume, are of two kinds, impressions of sense and those of reflection. When we see a lion we obtain an impressions of it, which is clear and vivid, and when the lion disappears, the mind is able to keep an idea of the beast. Such idea produces in the mind fear and aversion, and these may be called impressions. And the operation by which we recall our first impressions is memory, our second impressions is imagination. Ideas of memory differ from ideas of imagination in clarity and vividness as well as their being literal copies of the original impressions, whereas imagination is free. However, freedom of imagination does not involve invention but is somehow derived from a previous impression; it is free in the sense that it is able to manipulate various ideas and construct out of them what it will.

    Among those ideas produced by impression, there are certain relations which make the mind proceeds from an idea to another, and such is called association. Relations of association are three; likeness, contiguity in place or time, and causality, the last being the most important. For it involves only one of the two terms of the relation; for instance, when I put water on fire, the causal relation stirs in me the idea of the heat, though I get no impression of such heat; I get an impression of only one of its terms, i.e., water being on fire. The case is different with relation of likeness and contiguity, because they make the mind pass from on idea to another like it or contiguous to it.

    Now, we may ask, what gives rise in our mind to the idea of cause and effect? What impression gives rise to our idea of cause? And Hume replies that the idea of cause means not merely the spatial or temporal contiguity of two phenomena, but necessity. But from what impression can we get the idea of necessity. Suppose we saw the event concomitant with another event (b) once, then we cannot say with certainty that there is a relation between them.

    But suppose that such concomitance has happened several times, then we are justified in claiming a causal relation. Thus repetition and coexistence is the source of our idea of necessity. Hume clarifies his position by saying that repetition and coexistence is not the source of necessity, but necessity comes from an extra impression, that is, readiness of the mind to pass from one thing to another usually accompanying it.

    Such is the nature of necessity involved in the causal relation; it is something in mind not in things; however, we are disposed to apply it to things outside us and think that all events do have such relation among them. Now, Hume could explain inductive inference and its jump from particular to universal in a subjective manner based on, mental habit and psychological necessity, not objectively in term of external reality. This does not mean that he doubted inductive conclusions and in proposition based on experience; on the contrary, he believed in them. But what does he mean by belief? Belief is an idea involving vividness and force. As has already been said, Hume makes impressions more vivid and clearer than ideas. Now, certain ideas may obtain such vividness and clarity and thus become beliefs; the main difference between belief and imagination is that the former is an idea which acquires the vividness and force of impression, while the latter is an idea which does not.

    Such vividness and force of belief depend on two things: (a) there being a vivid impression of something (or an idea of memory which has enjoyed the vividness of impressions); (b) the concomitance of this something with some other thing, then the mind passes from one to the other.

    We have hitherto discussed Hume's psychological treatment of induction. We now turn to the physiological treatment of induction, that is, explaining it in terms of conditioned reflex provided by Behaviourism. Such theory regards inductive inference as a sort of correlation between a conditioned stimulus and certain reaction, instead of a correlation between two ideas in the mind in Hume's theory. The law of conditioned reflex is the Behaviouristic starting point which may be stated as follows. When an event leads to a certain reaction, the former is a stimulus, the latter a reaction, and if such event frequently occurs together with something, this something is said to be sufficient to give rise to that reaction. This law applies equally to man and animal. The traditional example of the law is Pavlov's experiment of a horse which is found to have more saliva on seeing food; when we condition the appearance of food with ringing a bell, it is found that saliva increases as the bell is heard even if there is no food. Ringing the bell becomes a condition of a certain reaction.

    Now, Behaviourism claims that inductive inference could be explained in terms of some form of that law; for example, if (b) being a stimulus leads to certain reaction, and if (a) is frequently found to occur with (b), (a) becomes a conditioned stimulus giving rise to that reaction. Thus, we know the existence of (b) whenever we see (a).

    In comment, two points may be stated. First, is the reaction stimulated by (b) what we mean when we say we perceive (b), or we mean that the perception is represented in a psychological element by such physiological reaction? Second, is it possible to explain induction merely as discovering a conditioned stimulus for it? It is the latter question that concerns us.

    Induction cannot be explained in terms of stimulus reaction, because we mean by inductive inference either that (b) occurs when (a) does, or that whenever we see (a) we see (b). The former case is a particular one, the latter is so general that goes beyond mere observation and experiment. If, for the sake of argument, physiological explanation fits inductive conclusions in particular cases, it does not fit with general hypothetical inductive statements, that is, if (a) happens, (b) does, For generalisation is not a reaction to stimuli but something new. Further, we do not use induction merely to make clear that (a) is succeeded by (b), but we use it also to prove the existence of the external world. It will be argued in the final chapter that the real ground of our belief in the external world is induction, and that inductive conclusions are not merely frequency of occurrence in the field of perception but they have some novelty differing from all previous reactions. Therefore, inductive inference is to be distinguished from [law-] conditioned reflex.

Notes:

[3]J.S. Mill. A system of logic, p. 255, Longman. London, 1947.

[4]Ibid., P. m/m256. Mill gives 5 canons not four; the author neglects the third being repetitious; his third can[on] on here is the fifth for Mill ( Translator ).

[5]Mill, A system op. cit., p. 260. This method is given in Mill as the fourth canon. (Tr.).

[6](1) Zaki Naguib, Positivistic Logic, pp. 504-8, (Originally in Arabic). Cairo, 1951.

[7]Zaki Naguib, D. Hume (In Arabic) p. 75 Cairo. 1955.

[8]Zaki Naguib, D. Hume, (in Arabic ), Cairo, 1954, pp. 85-6.

[9]Positivistic Logic rejects this proposition even as probable, because any proposition not derived from experience is senseless and in turn not a proposition at all logically speaking though it may be a proposition syntactically.

[10]Al- Sheneiti, The Philosophy of Hume (in Arabic), P. 182