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Metaphysics and Induction

by Gary Gutting

Gary Gutting received the Ph.D. from Saint Louis University in 1968 with a dissertation on "The Logic of Discovery in Theoretical Physics." He joined the faculty of Notre Dame as Assistant Professor of Philosophy. The following article appeared in Process Studies, pp. 171-178, Vol. 1, Number 3, Fall, 1971. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.

A view held by many contemporary metaphysicians is that the problem of induction, so much discussed by philosophers of science, arises only because of mistaken metaphysical views; in particular views (deriving from Hume) about the nature of the causal relation and/or about the internal relations among different entities.1 Contrary to this view, I will try to show: (I) That a rejection of the Humean view of causality in favor of one which allows for some sort of real relation of production (or "implication") between cause and effect is neither a sufficient nor a necessary condition for solving the problem of induction; (II) That a rejection of Hume’s metaphysical atomism in favor of some sort of theory of essential internal relations among entities is likewise neither a sufficient nor a necessary condition for the solution of this problem.

I. Induction and Causality

Hume’s own discussion of induction (or, to use his language, "reasonings about matters of fact") in the first Enquiry is, of course, tied to his theory of causality. He begins by asking for the foundation of inferences made about matters of fact that are not immediately given to us and answers this initial question with the claim that all inferences about matters of fact are based on cause-effect relations. He then inquires about the foundation of assertions about cause-effect relations and decides that they must be based on experience since, the cause and its effect being contingently related entities, we cannot deduce a priori the latter from the former. Hume next asks, What is the foundation for these experiential arguments for the existence of cause-effect relations? In answering this question, Hume generalizes his discussion in a very significant way. He proposes a line of argument that purports to show that all arguments from experience (not just those for the existence of cause-effect relations) are rationally unjustifiable:

If a body of like color and consistency with that bread which we have formerly eaten be presented to us, we make no scruple of repeating the experiment and foresee with certainty like nourishment and support. Now this is a process of the mind or thought of which I would willingly know the foundation. It is allowed on all hands that there is no known connection between the sensible qualities color, consistency, etc. and the secret powers to produce nourishment and support, and, consequently, that the mind is not led to form such a conclusion concerning their constant and regular conjunction by anything which it knows of their nature. As to past experience, it can be allowed to give direct and certain information of those precise objects only, and that precise period of time which fell under its cognizance: But why this experience should be extended to future times and to other objects which, for aught we know, may be only in appearance similar, this is the main question on which I would insist. (1:47f)

For our purposes, the most striking thing about this argument is that it does not appeal to Hume’s doctrine that causality involves no relation between the cause and effect other than constant conjunction. In fact, Hume accepts, for purposes of this argument, the more ordinary idea that there is some power in the cause that produces the effect ("the secret powers to produce nourishment and support"). To feel the force of Hume’s contention, we need only agree that the kind of effect produced by a cause is not determined simply by the external appearances of the cause; e.g., that the nutritive powers of bread are not present because of its color shape, texture, etc. We do not need to agree that, when eating of bread is followed by nourishment, the bread did not produce (by powers exercised by it on our body) the nourishment. In short, Hume’s problem is not the metaphysical one of whether or not some kinds of things in fact causally produce other kinds of things; but rather the epistemological one of determining what kinds of things will, in the future, produce certain other kinds of things. This latter problem arises, no matter what our view of causality, as long as we agree that the appearances of a thing prior to its causal activity do not determine the effects of this activity.

To illustrate further the point I am making here, consider one of the examples of truly productive causality which Whitehead gives as a refutation of Hume’s constant conjuction theory:

In the dark, the electric light is suddenly turned on and the man’s eyes blink. . . . The sequence of percepts, in the mode of presentational immediacy, are the flash of light, feeling of eye-closure, instant of darkness. . . According to the philosophy of organism, the man also experiences another percept in the mode of causal efficacy. He feels that the experiences of the eye in the matter are causal of the blink. The man himself will have no doubt of it. In fact, it is the feeling of causality which enables the man to distinguish the priority of the flash. . . The man will explain his experience by saying, "The flash made me blink"; and, if his statement be doubted, he will reply, "I know it, because I felt it." (PR 265f)

Suppose we accept completely the account Whitehead gives here, but that we ask the man in question a further question: "If tomorrow you find yourself in a dark room and a light is suddenly turned on, will you again blink?" Presumably he will reply that, other things being equal, he will. Why does he say this? Because he is convinced that the same causes in the same situations will have the same effects -- hence his qualifications of "other things being equal." The important point is that the circumstances tomorrow be sufficiently similar to those of today. Without knowing this, our knowledge of the relation of causal productivity establishes nothing.

I think the above discussion indisputably shows that acceptance of a theory of genuinely productive causality is not a sufficient condition for a solution to the problem of induction. Moreover, I think a little further reflection will show that acceptance of such a theory is not even a necessary condition for a solution to the problem. For suppose that it were; i.e., suppose that, for us to be rationally justified in predicting that the past conjunctions of C and E will occur in the future, it were necessary that we be justified in believing that C is causally productive of E. This would mean that we could never be rationally justified in expecting the future repetition of conjunctions between events that we know are not causally related. For example, in spite of all the supporting instances, there would be no rational foundation for believing that when barometers drop there will be a storm or that when the bell rings the students will leave the classroom. But surely we are rationally justified in believing things of this sort, just as we are rationally justified in believing the countless constant conjunctions discovered by science between quantities that are not causally related.

Thus, having good reason to believe that there is a relation of production between two kinds of things (or two events) is neither a sufficient nor a necessary condition for having good reason to believe that in the future things of this kind will act as they did in the past. But perhaps it can be shown that some sort of information about productive causal relations is a necessary condition for justified inductive inferences. For example, isn’t it the case that we are justified in believing that a storm will occur when a barometer drops only because we have reason to believe that the storm and the barometer-drop are products of a common cause? It may well be true that, if we know there is a regularity in drops of barometers being followed by occurrences of storms, we also know that there is a common cause for the two events. But surely it is wrong to say that having the latter knowledge is a reason for our having the former. Quite the contrary: the reason we believe the storm and barometer-drop have a common cause is that we are already convinced of the regularity of their conjunction. And, more generally, it is already-justified beliefs about regularities that, for the most part, provide the foundation for our conjectures about the existence of relations of causal production. And in the cases like Whitehead’s blink example where we do seem to have direct knowledge of casual production, this knowledge is surely not necessary for us to be justified in asserting a regular connection between light flashes and blinks (e.g., we could assert the regularity on the basis of records of experiments done on other persons).

In summary: (1) Having good reason to believe that events of type C have in the past causally produced events of type E is not a sufficient condition for reasonably asserting that events of type C will in the future be followed by events of type E. For to justify the prediction in any particular case we must also know that the future event of type C is sufficiently similar to the past event of type C. (2) Having good reason to believe that events of type C have in the past causally produced events of type E is not a necessary condition for reasonably asserting that events of type C will in the future be followed by events of type B. For we are justified in predicting the future conjunction of events that we know are not causally related. (3) Having good reason to believe that events of type C and E have a common productive cause is not a necessary condition for reasonably asserting that events of type C will in the future be followed by events of type F. For, in many cases, it is precisely our justified belief that a regularity will be observed between C and E which is the reason for believing that C and E have a common cause. (Nor, of course, could this condition be sufficient, for the same kind of reasons relevant to [l])

II. Induction and Internal Relations

The acceptance of a theory of real causal production does not provide a basis for solving the problem of induction because that problem is not concerned with the nature of the connection between "causally" connected events but with the relation between our knowledge of past instances of such connected events to the probability of future occurrences of similar instances. Schematically, we are not concerned with the relation between C1 and E1 or with the relation between C2 and E2 ; but we are concerned with the relation between the pairs (C1E1) and (C2E2). (C1 and C2 are things of the same type -- e.g., loaves of bread -- which act, at different times, as causes of their respective effects, E~ and E, -- e.g., nutrition.) The problem of induction is: How can we know that the similarity between C1 and C2 is great enough to make likely the similarity of E1 and E2? This formulation suggests that what is needed metaphysically is a doctrine that will provide a genuine link between (C1E1) and (C2E2) -- a link that will provide enough essential continuity between the two pairs of events to make likely the sufficient amount of similarity needed to ground an inductive inference rationally. Such a link seems to be provided by metaphysical theories which posit real internal relations between past and future events. Whitehead, for example, holds that what any given actual entity is depends, to a great extent, on what the actual entities in its past were; for a large part of the present actual entity’s nature consists in its internal re-realization (via "prehension") of the natures of past actual entities. Since on this view the actual entity is, to a great extent, itself a projection of the past, it would seem that we are justified in projecting its future behavior on the basis of the known behavior of past actual entities.

Whitehead develops this kernel of thought in his treatment of the problem of induction:

Another way of stating this explanation of the validity of induction is, that in every forecast there is a presupposition of a certain type of actual entities, and that the question then asked is, Under what circumstances will these entities find themselves? The reason that an answer can be given is that the presupposed type of entities requires a presupposed type of data for the primary phases of these actual entities; and that a presupposed type of data requires a presupposed type of social environment. Hence when we have presupposed a type of actual occasions, we have already some information as to the laws of nature in operation throughout the environment. (PR 311)

For the purposes of our discussion, let us translate this account into the language of Hume’s example of the loaves of bread. If we ask, Will loaf of bread A (today) nourish us, as did loaf of bread B (yesterday)? we presuppose by the very form of the question that we have the same general kind of entity today that we had yesterday (both are loaves of bread). Now, according to the Whiteheadian doctrine of internal relations, to be a loaf of bread means to have incorporated a certain kind of structure from things in one’s past (this is the "presupposed type of data"). But this, in turn, means that to be a loaf of bread is to be part qf a certain kind of environment -- i.e., to have certain types of entities in one’s immediate past. Consequently, as soon as we talk about "a loaf of bread," we are necessarily talking about a certain kind of physical environment. But part of being "a certain kind of physical environment" is being governed by certain kinds of physical laws (i.e., regularities in cause-effect sequences). As a result, when we talk about today’s loaf of bread, we are necessarily discussing something that obeys the same kind of laws of nature as did yesterday’s loaf of bread. Since the nutrition follows the eating of bread in virtue of laws of nature, we can justifiably conclude that today’s bread, like yesterday’s, will produce nutrition.

I think we may take this argument of Whitehead’s as typical of the kind of solution to the problem of induction that can be based on a metaphysical theory of internal relations. However, as I will now try to show, this solution is not an acceptable one; and, in fact, a metaphysics of internal relations, like a theory of productive causality, is neither (1) a sufficient nor (2) a necessary condition for a solution to the problem of induction.

(1) As the quotation from Whitehead shows, the argument based on internal relations requires for its cogency the assumption that the cause whose future effect we are predicting be of the same type as the cause whose effect we have observed in the past. Thus, we have the same problem of determining sufficient similarity that we discussed in connection with theories of productive causality. Whitehead himself is aware of this problem. After noting that the core of the justification of induction is the claim that the future entity and environment are somehow "analogous" to the past entity and environment (from which it follows that similar laws "dominate" the two environments), he says:

Now the notions of ‘analogy’ and of ‘dominance’ both leave a margin of uncertainty. We can ask, How far analogous? and How far dominant? If there were exact analogy, and complete dominance, there would be a mixture of certainty as to general conditions and of complete ignorance as to specific details. But . . . our conscious experience involves a baffling mixture of certainty, ignorance, and probability. (PR 3120

Let us try to develop the point Whitehead is making more thoroughly in terms of the bread example. We have knowledge of a past situation (S) in which an entity (x) possessing the set of properties (B) that prompt us to call it "bread" produced the set of properties (N) that we call "nutrition." Now we encounter another situation (S) involving an entity (y) which also possesses the set of properties B. Will it produce the set of properties N? The theory of internal relations allows us to say that, to the extent that the two things sharing the set of properties B are alike, they will obey the same laws of nature and hence produce the same result. But to what extent are these two things alike? In addition to the known common properties B (and some known but presumably irrelevant different properties) they surely each have an indefinite number of other properties which we do not know about. How do we know that these unknown differences will not make a significant difference in the kinds of laws relevant to x and y? For example, y may be laced with arsenic or be a clever synthetic product which simulates all the external properties of bread but has no nutritional value. Of course, no one would claim that such possibilities are out of the question. It is only a question of what will probably happen. But then we must ask, Why is the case of no significant difference in the outcome of eating the bread the most probable case?

The theory of internal relations can give us no answer. Even if, on the basis of it, we admit that the same set of laws governs the two situations, S and S1, we still have no way of knowing that the particular laws that are applicable to the behavior of x will be applicable to the behavior of y. For example, even given the same physics and chemistry for S and S1, different laws will be relevant depending on whether y is "ordinary" bread or laced with arsenic. Once again, there is an epistemological problem of determining sufficient similarity, which cannot be resolved by any metaphysical views.

We know how we would proceed in practice. We would examine what for the particular situation, we regard as a sufficient number of relevant properties of y (fewer in an ordinary situation in our own kitchen, more if we have received the bread by mail from an unknown person and have recently escaped several attempts on our life). If these properties were shared with x, then we would conclude that the effect of y would probably be nutrition. This is undoubtedly the correct procedure to follow, although how to justify it has been long disputed. However, we can at least point out that the procedure is not justified by appealing to the fact (founded on the theory of internal relations) that S and S1 are governed by the same set of laws of nature. For the problem is rather, which of these laws apply to the behavior of y. To answer this question, we need to know how similar y is to x, given that it is similar with regard to the set of properties B. But the metaphysics of internal relations gives us no basis for answering this question. At the best, it can tell us that if there is a sufficient similarity, the same laws will apply.

Whitehead implicitly concedes the insufficiency of the metaphysics of internal relations when, to obtain a basis for making probable assertions about future events, he introduces two special assumptions about the relation of actual occasions to their environments:

Each actual occasion objectifies the other actual occasions in its environment. This environment can be limited to the relevant portion of the cosmic epoch. It is a finite region of the extensive continuum, so far as adequate importance is concerned in respect to individual differences among actual occasions. Also, in respect to the importance of individual differences, we may assume that there is a lower limit to the extension of each relevant occasion within this region. (PR 313, italics added)

Whitehead introduces these two assumptions to guarantee that the thing about which we want to make a prediction will have only a finite number of properties relevant to the future behavior in which we are interested. Given this, he will argue (in terms of a Keynesian statistical theory of probability) that the more relevant properties common to x and y we find, the more likely it is that all the relevant properties are common. Quite apart from any questions that might be raised against Keynes’s approach or statistical probability in general, it is obvious that the two assumptions Whitehead introduces to insure the "limitation of independent variety" are not logical consequences of the metaphysical doctrine of internal relations. (I.e., the fact that what an entity is depends on its relations to everything else does not imply that "everything else" is a finite set or that only a finite set of "everything else" is significant -- for some purpose -- in the determination of what that entity is.) This shows that for Whitehead’s account in particular internal relations are not a sufficient condition for a solution to the problem of induction.

(2) We can also readily see that, for Whitehead, the doctrine of internal relations cannot even be a necessary condition for the validity of inductive inferences. For, given the Keynesian approach to statistical probability (which Whitehead seems to accept in all relevant respects) the only prerequisite for a validation of induction is a limitation of independent variety, such as Whitehead insures by the introduction of his two hypotheses. Now it is true that Whitehead states these hypotheses in terms of the theory of internal relations (saying, in effect, that only a finite number of these relations are ever relevant for the behavior of a given actual entity). But it would be just as possible to guarantee the limitation by hypotheses that were not formulated in such terms (as, for example, Keynes himself did). All that is needed is that we somehow have good reason to believe that the properties of an entity relative to its future behavior are finite in number. And surely no one could successfully maintain that these properties could be finite in number only if they are determined by the entity’s internal relations to other entities. Even in the most atomistic Humean universe, this kind of finitude is quite possible.

Further, even outside the framework of Keynes’s theory, probability approaches to induction seem to have shown that a validation of induction can be given with far weaker factual assumptions than the doctrine of internal relations. For example, even his critics agree that D. C. Williams’ attempt at an a priori defense of induction achieves its desired aim if we add the assumption that our statistical samples are random.2 Of course, if Williams really must add this assumption, then his program is a failure, since he thinks that such an assumption would have itself to be based on inductive evidence and so would render the argument circular. But the proponents of metaphysical validations of induction must clearly hold (to avoid circularity) that their metaphysical views are derived from methods other than the inductive. Consequently, against them, it is perfectly appropriate to point out that there are alternative assertions about the world which, supposing them to be justified by metaphysical methods independent of induction, would validate induction without the assumption of the doctrine of internal relations. This, I think, suffices to show that this doctrine is not a necessary condition for a solution to the problem of induction.

To summarize this section (1) The doctrine of internal relations is not a sufficient condition for solving the problem of induction because, like the doctrine of causal production, it gives us no information on the crucial question of the essential similarity of the past and the present cause. (2) Nor is the doctrine a necessary condition for the solution, since there are other independent metaphysical assertions which, if justified in a non-circular way, would be able to support a solution.


1. David Hume, An Inquiry Concerning Human Understanding. Indianapolis: Library of Liberal Ants, 1955.


1. See, for example, D. J. B. Hawkins, Causality and Implication (London: Sheed & Ward, 1937), Ch. VI; A. C. Ewing, The Fundamental Questions of Philosophy (London: Routledge & Kegan Paul, 1951); PR II, Ch. 9. For a discussion of Whitehead’s views on induction, cf. the exchange between J. W. Robson and M. W. Gross, "Whitehead’s Answer to Hume," Journal of Philosophy, 38 (1941), 85-102. These essays are reprinted in George L. Kline (ed.), Alfred North Whitehead: Essays on his Philosophy, 1963. Also of interest is Harold Taylor’s comment on the Robson-Gross exchange, "Hume’s Answer to Whitehead," Journal of Philosophy 38 (1941). 409-16.

2. Williams’ treatment is in The Ground of Induction (Cambridge, Mass.: Harvard University Press, 1947). One of his most acute critics is F. L. Will, "Donald Williams’ Theory of Induction," Philosophical Review, 57 (1948), 236 ff.

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