Chapter 3. Induction And Empiricism
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.
On the First and Third Questions
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.
On the second question
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.
Answer to that question
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". 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"
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".. 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'
(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.
Examination of psychological attitude
Hume explains what is meant by belief in two ways:
(A) The difference between idea and belief is not in content but in our way of recognising them. If there is an idea and we judge that the object of such idea exists, then we have two different things, the difference is not known by recognising elements in the second case which are absent in the first, thus the idea of existence is not different from something existing. Hence existence is not an attribute added to other attributes of an object of perception. And our belief in the existence of something has nothing added to the mere existence of it. Nevertheless, there is clear distinction between identifying an idea of an object in my mind and my belief that such object exists. Since this distinction is not a constituent of the contents of the idea, then it is a product of the way of identifying it.
(B) This distinction is due to the advent of idea in our mind in a forceful and vivid way; if the idea is feeble it is not a belief. Thus belief may be defined as a vivid and forceful idea.
In discussion of Hume's theory of belief, we observe two things. First, we agree with Hume that a belief differs from an idea not in having an element of existence to its content, but in our way of identifying it. But we disagree in justifying such difference. In claiming that existence is not a characteristic of belief, we see that it may be an element of the content of idea as well; if we do not believe that there is a bird with two heads, then we may have an idea of it, and may further conceive its existence without our believing it. Therefore, the element of existence may be included in both idea and object, and we have to find out a characteristic which distinguishes them, it is our way of perceiving an object which gives belief. Hume arrived at the same conclusion from a different premise, namely, that existence is not an element added to the properties of the object of perception. This is based on his principle that an idea is necessarily a copy of an impression, and since there is no impression from which the idea of existence is derived, Hume has to say that existence is not a distinct idea.
Secondly, we observe that certain ideas may be vivid and effective without being beliefs, such as that which we get from illusion; a stick the lower part of which is immersed in water is observed as if it were broken. It may be objected that our belief in the straightness of stick is due to discovery of visual illusion and with the help of actual impressions: thus such belief is nothing but an idea possessed of vitality and force. The objection does not alter our position that the idea of straightness of the stick is vivid without being a belief.
Further, in explaining belief as vivid idea, Hume supposes that this vividness is derived from an impression, either directly as copy, or indirectly as causally related; and this means that any idea not derived form impression is not a belief. But this does not accord with reality, because we may have a number of beliefs without there being copies of impressions. How could Hume explain someone's belief that a ghost frightens him, so long as he had not received an impression of ghost? We must distinguish two things in matters of belief, explanation and evaluation. To explain it we have to distinguish an idea from a belief. And we should give an explanation which applies to all beliefs, regardless of judging it true or false.
(2) Causality and Reason
Hume maintains that causal principle does not arise in pure reason, and cannot be deduced from the law of non-contradiction, it is known to us through experience and not a priori. If something as cause has not happened in connection with some other thing as effect in experience, we cannot perceive causal relation. "If we suppose Adamto have perfect mental acts" Hume says, "he could not have deduced from liquidity and transparence of water that he would suffocate when he sinks in it". We have to distinguish causal principle from causal relations among events. By the former, we mean that every event has a cause, by the latter the relations of heat to extension, boiling to evaporation, eating to nourishment. Rationalism claims that causal principle is known a priori, and that causal relation is perceived a priori. Aristotelians, among rationalists, maintain that our knowledge of the principle is a priori and not derived from experience, while our knowledge that heat is the cause of extension of iron is so derived.
Thus, concerning causal relations, Hume and Aristotelians agree. Let us now discuss Hume position of our knowledge of causal principle. We agree with Hume that this principle is not deduced from the law of non-contradiction, for there is no contradiction in the occurrence of an event without any cause. Now there are two attempts to defend the view of medieval Aristotelians that causal principle is unempirical.
The first attempt may be stated as follows. All events are contingent; by contingency is meant that existence and non-existence are equally possible. Then, for an event to occur, there must be something having the power of giving existence to it the event, rather than not, and this something is the cause. This argument, if discussed thoroughly, is merely a deduction of cause from itself, thus it is a petty principle or that the argument presupposes causality.
The second attempt way formulated thus.
(a) Every essence is possible by itself, and does not exist unless something pushed its existence by necessity.
(b) Every possible essence must not exist except by virtue of an external cause, because its possible existence means that its existence and non-existence are equally acceptable. By necessity is meant that its existence is more probable than non-existence.
Therefore, since necessity of possible essence does not arise except by virtue of an external cause, then it cannot come into existence except by means of a cause. This argument, like the former, is formally invalid because it uses causality as premise, which is meant to be proved.
We suggest that if rationalism is to defend the causal principle as a priori, it should claim that the principle is an ultimate proposition in the mind, instead of saying that it is logically deduced from ultimate principles, and thus it becomes impossible to deduce an ultimate proposition from another. Naturally, Hume would reject the suggestion but we shall have occasion later to defend it.
(3) Causality and Experience
When Hume maintained that causal relations cannot be deductively inferred one from another, he claimed also that they cannot be empirically inferred. For all knowledge of the external world is derived from sensible impressions, and we get no impression of causal relation as necessary, we never get an impression of something that can be deduced from impression of anther. All that is acquired from experience is that the effect follows its cause as a matter of fact: if moving billiard-ball is seen to come across another at rest, this is seen to move, so that our sight is affected in such a way that a moving ball is succeeded by another moving ball. Thus, Hume concluded hat causal relation can only be given a psychological, not a logical empirical, explanation: no necessity between food and nutrition, but constant connection between our ideas of both.
Hume's rejection of causality as involving necessity raises two questions, namely, how can we understand the idea of causality as involving necessity since every idea is to be a copy of impression? and how do we believe in causality as objective relation between any two events independently of experience? Hume answered the former by showing that our idea of causality derives from an impression preceding another. And he admitted that the latter involves real problem and claimed that the causal relation is subjective not objective, that is, it lies in our mind as a relation between two ideas not between two events in the world.
If we accept Hume's answer of the first question, then we admit our having the concept of causality. We may then ask whether causality has an objective reality? Although we get, in Hume's opinion, the idea of cause from an impression of connection, there is no reason preventing us of asking whether such idea has objective reality.
Suppose, [???]with Hume, that we cannot get the idea of causality by pure reason, we cannot prove that pure reason refutes causality; that is to say, it is probable that every event must have a cause, since it cannot be confirmed or refuted by reason. On the other hand, we wish to ask whether there is any empirical evidence for the probability of the proposition about causality in objective reality. Hume maintained that there is none, but we shall have occasion later to show such probability.
(4) Concept of Causality
For Hume, every simple idea is a copy of an impression, and when he tries in vain to find out an impression of causality which involves logical necessity, he supposed an impression derived from a connection among certain ideas of succession, and saw that the succession of such ideas stirs in the mind a certain impression of expectation, when we get an impression of the first event we expect the other to occur. It is noticed here that such mental expectation is inferred from Hume's dictum that impressions are prior to ideas, but we see that this dictum is based on induction.
For all simple ideas, in Hume's opinion, are similar to simple impression, and though the idea of causality is not reached by induction, it must have been reached, as idea, by induction. Now, if inductive inference has no objective value, as Hume claims, so is causality. But Hume's application of induction to our idea of cause is invalid, because successful generalisation should not apply to those kinds of things which have specific differences with other kinds. For example, if we find by induction that all metals except gold extend by heat, we cannot include gold in our generalisation for its specific difference from iron, copper etc. Our idea of causality is similar to gold in this respect: if we find that all ideas are preceded by impressions, we cannot say this of our idea of cause which is specifically different from other ideas.
(5) Belief in causality
Let us first state Hume's theory of belief. It is an idea having a high degree of vividness and strength which is derived from a vivid impression or another idea.
When we have two ideas involving causal relation, the former being vivid is belief, and when we move from the idea of cause to that of effect, this requires a similar one once idea is related to an impression it becomes a belief, and if an idea is not so related it requires two things in order to become a belief: (a) a certain relation with another idea which enables us to proceed from the one to the other; such mental habit results from repeated concomitance between any two events in experience; (b) that the other idea should be also vivid. Now, we may criticize such theory by bringing the following points.
(a) Belief in causality involves two propositions, one of which is categorical, e.g., iron extends in heat, the other is hypothetical such as iron extends if exposed to heat. But whereas Hume's theory of belief explains our belief in the former proposition, it does not explain our belief in the latter. For which idea could be taken to be belief in the hypothetical proposition? Is it our idea of the extension of iron or that of heat as cause of extension? Hume cannot have chosen the first answer, because our idea of the extension of iron cannot be a belief unless it acquires a high degree of vividness from its relation to our idea of heat, but our idea of heat has no such degree since it did not occur in fact. The idea of cause, in the case of hypothetical proposition, is not vivid but a mere hypothesis and thus cannot be a belief.
On the other hand, Hume cannot accept the answer that the belief which we possess, in the case of giving a hypothetical proposition, is that heat is the cause of extension. For Hume denies that there are causal relations in objective reality and claims only that such relations are among our ideas. Then when we supply a hypothetical proposition involving causality, we mean, for Hume, the mental habit which helps to proceed from the idea of heat to that of extension.
When we reflect on this, we find that we talk not about the future of events in reality, but the future of our mental habits. Thus Hume cannot on his theory explain our belief in causality in the course of future events. In other words, if we have the right to suppose future to be similar to the past and present, we may apply his supposition to objective reality. But if, as Hume insists, we are not justified in our belief in uniformity, we have no right to talk about the future of mental habits. We may conclude that Hume's theory fails to explain inductive inference which provides hypothetical as well as categorical statements.
(b) Hume gives a ground to establish his theory of inductive inference and causality. He asks, why we need innumerable cases to reach a conclusion without being satisfied with only a small number of cases; and he gives his answer. Whereas the conclusion which the mind reaches from contemplating one circle are the same as when we see a number of circles, we cannot conclude from seeing only one body moving by impulse that all bodies, move by impulse. For in the latter case we require repetition of concomitance between those objects, thus we acquire a habit of inferring the one from the other so that all inferences in experience are effects of habit not by reasoning.
But we may explain the validity of inductive inference including our beliefs in causality and uniformity without recourse to Hume's theory. Suppose we observe an event (a) followed once by another event (b), we may say that their concomitance happened by chance, and that (b) is caused by a yet unknown event (c). But if (a) is always followed by (b) in such a way that wherever (a) occurs, (b) follows, then chance is eliminated; repetition and absence of exception is a basis of inductive inference, not in terms of mental habits but in terms of objective reality, as known in probability calculus.
(c) Suppose someone tried to find out the effect of a certain drug on people having a certain disease, and found that this drug gives rise to some physiological phenomenon, then he would conclude that the drug is the cause of that phenomenon. Suppose, further, that such a person discovered that his partner intended to mislead him by providing those cases susceptible for such phenomenon, then our person would give up claiming a causal relation between the drug and that phenomenon. Here we are entitled to admit the objective reality of cause relations in the course of events apart from our ideas, because our experiment involves that certain phenomena should have as yet undiscovered causes. And Hume-ian habit fails to explain such cases.
(d) If belief expresses a vivid idea, how does Hume explain our doubt in a proposition when its truth or falsehood on a par? He may answer by saying that our idea of the existence and the non-existence of its objective reference is not vivid. If we are in doubt whether rain fell yesterday, then our idea of falling idea or not-falling are faint, and thus no belief. Further, Hume's criterion of belief does not work when we have no doubt but probability of an occurrence.
Now, we may provide some criteria for the probability of rain's falling yesterday, namely, clouds or bad weather etc. If these are noticed to occur in most cases when rain falls, then there is probability that rain falls when such conditions occur gain; then the idea of rain's falling is probable not a belief.
Probability is of two kinds: (a) that which depends on frequency such as the high frequency of rain's falling in the example mentioned above, (b) that which depends on a logical basis. For instance, suppose we are told of the death of only one person among the passengers of an aeroplane; suppose further that all the passengers were three men, then the probability of the death any of them is 1/3, the death of one among two of them is 2/3 Now, Hume's theory of probability fits with the first kind but not with the second.
Physiological Explanation of Induction
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.