Bonjour on Induction

W. Russ Payne Ph.D.

Laurence Bonjour proposes an a-priori solution to the problem of induction in the last chapter of his In Defense of Pure Reason.[1]  He argues that we have a-priori grounds for thinking that the best explanation (meaning the explanation that is most likely to be true) for the truth of the premises of an inductive argument is the truth of the generalization we inductively infer.  The idea of justifying inductive inference as a case of inference to the best explanation is not entirely new.  David Armstrong, for instance, argues that “induction is . . . rational “because it is a case of inference to the best explanation.”[2]   What Bonjour provides is a detailed discussion of why we should take objective law-like generalizations to provide the best explanation of inductive premises.  Also novel in Bonjour’s treatment is the casting of this reasoning as a-priori.  The purpose of this paper is to explain and make some progress towards evaluating this proposed a-priori solution to the problem of induction. 

The problem of induction was first raised by David Hume.  Inductive argument, in its standard form, draws a conclusion about what is generally the case or what will prove to be the case in some as yet unobserved instance, from some limited number of observed instances.  Since the conclusions of inductive arguments make claims about instances beyond those cited in the premises, it is possible for the premises of an inductive argument to be true and yet its conclusion false.  The problem of induction is the problem of explaining how the premises of an inductive argument can nevertheless provide us with a reason for accepting its conclusion.  Hume suggests that every inductive argument involves a principle of induction as a suppressed premise which, if rationally defensible, would render induction rational.  This principle of induction tells us roughly that unobserved instances are likely to follow the pattern of observed instances.  If a principle of induction is to render inductive inferences rational, we require grounds for thinking that such a principle is true.  Hume offers a now familiar dilemma against the possibility of justifying any principle of induction.  Since there is no contradiction in denying a principle of induction, it cannot be justified a-priori.  And any empirical argument for induction will itself be inductive and hence make use of the very principle of induction in need of support.  So, concludes Hume, we have no grounds for accepting inductive inferences as rational.[3]

Hume’s notion of a principle of induction is problematic.  A principle of induction asserts some degree of uniformity in nature as a means of underwriting inductive inferences. To provide the requisite support for induction and yet be defensible as true, a principle of induction would apparently have to assert uniformity in nature in just those respects where inductive reasoning is cogent.  But there is no non-question begging means of formulating just what sort of uniformity an adequate principle of induction should assert.  The problem of induction, however, can be reformulated without mention of any principle of induction as a suppressed premise in inductive argument.  We can instead ask what rational grounds we have for accepting induction as a rational rule of inference.  Again, there is no contradiction in supposing an inductive rule of inference to be irrational and any inductive grounds for accepting an inductive rule of inference will beg the question by employing that rule of inference. 

Bonjour’s proposed a-priori solution to the problem of induction involves rejecting a key component of Hume’s epistemology.  Namely, he rejects the notion that all a-priori reasoning is grounded in the principle of non-contradiction.  Bonjour takes a-priori justification for a belief to just be a reason not grounded in experience (11).  A role for rational insight is recognized (107).  Rational insight affords the possibility of grasping or apprehending the necessity of a proposition.  It is such insight that allows us to grasp, for instance, that there are no round squares.  Bonjour’s rationalism differs from classical rationalism, however, in allowing that rational insight is fallible.  Our capacity to grasp necessary truths, does not automatically warrant certainty.  A discussion of Bonjour’s rationalism is beyond the scope of this project.  Though it will be apparent where this general epistemological stance enters into the justification of induction.

We tend to think of induction as a kind of reasoning or argument that makes a claim to cogency.  The problem of induction is the problem of showing how the premises of an inductive argument can provide rational support for its conclusion.  Bonjour argues that if inductive argument is rational, then it must be understandable as rational a-priori.

The problem of induction arises in the first place after all from viewing induction as a mode of reasoning or argument that claims to be rationally cogent, that is, one in which the (probable) truth of the conclusion is at least claimed to follow in a rationally intelligible way from the truth of the premises.  But what does it mean for a conclusion to follow rationally, whether certainly or probably, from a set of premises?  I submit that it can mean only that one who understands the premises is thereby in a position to see or grasp or apprehend, either directly or via some series of individually cogent steps, that if those premises are true, then the conclusion either must be true (if the argument is conclusive), or is probably true (if the argument is less than conclusive), where this seeing or grasping or apprehending can only be a-priori in character.   (203)

If this line of argument is correct, and here I will suppose that it is, it rules out any empirical or inductive justification of inductive reasoning.  But this leaves open the possibility that the skeptic is right in denying the rationality of induction, and the possibility that induction is not really inferential after all.  First, let us briefly consider the possibility that inductive generalization is non-inferential.  Bonjour discusses and rejects the non-inferential pragmatic treatment of induction offered by Reichenbach.[4]  Reichenbach proposes that inductive generalizations are posits.  Posits are not beliefs inferred from evidence but rather something like bets accepted or rejected based on evidence.  In accepting posits, we assume that nature is not chaotic.  We have no grounds for thinking it unlikely that nature is not chaotic.  But if there are objective regularities, it is only through making posits and refining these in accordance with our observations that we can happen onto the truth.   Still, should we come to accept true posits, we lack any justification for believing them to be true.  Our experience does not even afford us grounds for thinking it unlikely that nature is chaotic. Reichenbach’s pragmatic treatment of induction fails to refute the skeptic.  As Bonjour finds the rationality of induction intuitively compelling, he is therefore unsatisfied with the pragmatic account. 

But taking inductive generalizations to be posits analogous to bets does not exhaust the non-inferential accounts one might give of inductive generalization. One might take the truth of inductive generalizations to be simply perceived or observed in their various instances.  We speak this way sometimes.  We might say of someone that we have observed a pattern in his or her behavior.  Or we might say that we recognize a

tendency of certain kinds of things to produce some type of phenomenon in certain kinds of situations.   In psychology the capacity for pattern recognition is investigated as a perceptual phenomenon, not as a matter of cognitive deliberation.  We might take such a non-inferential view of inductive generalization and still allow that inductive prediction is inferential.  But given perceived empirical generalizations, the inference involved in prediction can be understood as deductive.  A view of inductive generalization as non-inferentially perceived suggests that the epistemological problem of induction is at least poorly formulated in terms of a mistaken conception of how general empirical beliefs are formed and accepted.  Perhaps the problem can be reformulated as one of observational support.  Or perhaps the problem of induction was just illusory all along.  But in the interest of evaluating Bonjour’s view, I will leave this non-inferential approach aside and suppose that induction is inferential.

Taking induction to be inferential, Bonjour motivates his a-priori justification of induction on the grounds that the rationality of inductive inference is intuitively compelling.  In recognizing a compelling intuition that induction is rational, I believe Bonjour overstates what is at stake in the effort to justify induction.  I share the intuition that what we commonly regard as inductive reasoning is the exercise of a rational method.  But I do not think satisfying this intuition requires a justification of induction argument.  The deductivist approach developed by Popper accepts skepticism about inductive reasoning but re-describes what we regard as induction as a process of conjecture and refutation.  While this process does not provide us with positive reasons for believing those conjectures that are consistent with the evidence, the process does provide us with knowledge of the falsity of those conjectures that conflict with the evidence.  Bonjour does not address Popper in any detail.  But Popper’s deductivism, whether we accept it or not, requires us to acknowledge that what is at stake is not the intuition that what passes for inductive reasoning is the exercise of a rational method.  Rather, what is at stake is just the intuition that inductive reasoning provides us with positive rational grounds for accepting inductive generalization.  I do not find the later intuition nearly so compelling as the former.

With this understood, let us suppose that induction is inferential and that, as Bonjour has argued, if induction is rational, then we must be able to understand how inductive premises support their conclusions a-priori.   Bonjour offers two theses which, taken together, are to provide an a priori justification of induction.  These are as follows:

I-1:  In a situation in which a standard inductive premise obtains, it is highly likely that there is some explanation (other than mere coincidence or chance) for the convergence and constancy of the observed proportion (and the more likely, the larger the number of cases in question).  (208)

I-2:  So long as the possibility that observation itself affects the proportion of As that are Bs is excluded, the best explanation, that is, the most likely to be true, for the truth of a standard inductive premise is the straight inductive explanation, namely that the observed proportion of m/n accurately reflects (within a reasonable degree of approximation) a corresponding objective regularity in the world (and this likelihood increases as the number of observations and the variety of collateral circumstances of observation increases).  (212)

Thesis (I-1) tells us that when the observed cases of As that are B converges on some proportion m/n, it is likely that there is some explanation for this convergence other than mere coincidence.  For any properties A and B, there will be some ratio of observed instances of As that are B.  But it is only where that ratio converges on some value m/n with increased numbers of observed instances that we have inductive support for thinking that. in general, the proportion of As that are B is m/n.  A straight inductive explanation of the truth of an inductive premise indicating that the proportion of observed As that are B is m/n is just that “it is an objective lawful fact about the world . . .that approximately m/n of all As are B . . . and the observed cases represent an unbiased sample of As and thus accurately reflect this objective regularity” (208).  (I-2) asserts that in the standard case, the straight inductive explanation is most likely to be the true account of the truth of the inductive premise.  (I-2) sets aside cases such as quantum phenomenon where the act of observation affects what is observed.  There are special epistemic issues pertaining to cases where observation affects the evidence.  But the classical problem of induction is not concerned with these.  Rather, the problem of induction concerns understanding how inductive generalizations and predictions are supported by observed instances assuming that observation does not taint the evidence.  Where observation does taint the evidence, no inductive conclusion is warranted and so no justification of induction is required.

Bonjour takes (I-1) to be relatively unproblematic.  He writes, “Once general prejudices about a-priori knowledge have been defused, the a-priori status of (I-1) seems sufficiently obvious to require little discussion” (208).  Answering general objections to a-priori knowledge is one of the main projects in Bonjour’s Defense of Pure Reason.  Time does not allow for any adequate discussion of this larger project.  But assuming the larger project is successful, the way is open to accepting (I-1) on grounds of direct rational insight.

Bonjour argues in some detail for (I-2).  The task here is to show that the straight inductive explanation of the truth of an inductive premise is more likely to be true than the disjunction of all other possible non-inductive explanations of the inductive premise (again, supposing observation does not affect the evidence). Straight inductive explanations entail the truth of inductive conclusions.  So if a straight inductive explanation is likely to be true given the truth of an inductive premise on a-priori grounds, then induction is justified a-priori.  Non-inductive explanations account for the truth of an inductive premise in some way that does not make the truth of the associated inductive conclusion likely.  Bonjour considers normal non-inductive explanations, those compatible with the outlook of common sense and science, and argues that normal non-inductive explanations are unlikely to be true relative to a straight inductive explanation of the truth of an inductive premise.  Mere chance would not explain the convergence of observed cases on a proportion m/n in the premises of an inductive argument.  So a normal non-inductive explanation must involve some further factor that accounts for the evidence without making the inductive conclusion likely to be true.  So suppose that the proportion of As that are B is influenced by the presence of a third factor C.  In this case, the proportion of As that are observed to be B may be an artifact of the presence or absence of C in the observed instances.  Given the influence of C, there are two ways in which a straight inductive explanation of the observed proportion of As and Bs can be unlikely to be true.  One is where there is a lawful relation between being A and being C, but the observed instances of As are biased in that the presence or absence of C does not reflect the general lawful proportion.  The other is where there is no lawful relation between being A and being C.  In the first case, it is highly unlikely that increased numbers of observations under varied circumstances will converge in a stable ratio of As that are B if the observed cases of As that are C does not reflect the lawful ratio of As that are C.  But if the lawful ratio of As that are C is reflected in the observed cases, then the straight inductive explanation is warranted.  In the second case, where there is no lawful relation between being A and being C yet the presence of C has an influence on the presence of B, it is highly unlikely that we find a convergence on a stable ratio of As that are B with increased numbers of observed cases under varied circumstances.  So a straight inductive explanation of the truth of an inductive premise is much more likely to be true than a normal non-inductive explanation.

 But what should be said about non-normal non-inductive explanations of the observed evidence.  We have, with reason, set aside cases where observation affects the evidence.  Bonjour takes skeptical non-inductive explanations, those invoking Cartesian demons, for instance, to be special cases of observation affecting the evidence.  Where our observation results in our being deceived by a Cartesian demon, we are concerned with a more general skeptical problem.  Answering the Cartesian skeptic is an independent epistemological project.  The problem of induction arises even if we assume an adequate answer to the Cartesian skeptic.  We ought not expect a solution to the problem induction to also answer concerns about Cartesian demons.

A further sort of non-normal, non-inductive explanation of the inductive evidence has yet to be considered adequately, however.  It may be that the truth of an inductive premise is adequately explained by a local law-like relation between properties.  In this case, an unqualified inductive generalization is not warranted.  The possibility that law-like regularities might change from one spatio-temporal region to another is present in Hume’s original problem.  Bonjour takes an adequate response to the problem of induction on this point to require defending “a non-Humean, metaphysically robust conception of objective regularity (or objective necessary connection)” (214).  With good reason, he takes this project to be beyond the scope of his book.  Like Bonjour, I am optimistic about the prospects for a non-Humean metaphysics of properties, laws and causation.  There are at two such views on offer in the current literature.  One is the view independently offered by Armstrong[5], Dretske[6] and Tooley[7] that laws are nomic relations that hold between universals. Universals A and B being nomically related necessitates that if a thing is A, then it is (or has an objective propensity to be) B.  Each of these authors takes nomic relations to hold between universal contingently.  The other metaphysics of objective necessary connections is the view that universals have their causal powers essentially.  On this view, laws are best seen as metaphysically necessary accounts of the essential nature of properties.  This view is advocated by Sydney Shoemaker[8], and Brian Ellis and Caroline Lierse[9] among others (including myself).

I do think some theory of objective necessary connections is required for providing a solution to the problem of induction.  Armstrong argues for this claim in some detail in What is a Law of  Nature.[10]  But only a theory that rules out gruesome or Goodmanesque universals and nomic relations will do.  Bonjour passes over Goodman’s new problem of induction, deeming it to have little relevance to Hume’s classical problem of induction (189).  But concerning the present point, whether or not law-like regularities might be local, Goodman’s new problem seems very relevant.  It is not enough to reject a Humean metaphysic in favor of recognizing necessary connections between universals.  We must also show that nomically related universals and nomic relations themselves cannot be gruesome (e.g., indexed to spatio-temporal regions).  Armstrong undermines the prospects of a solution to the problem of induction on his own view by allowing nomic relations to hold between “quasi-universals,” universals indexed to particulars or spatio-temporal regions (such as being a negatively charged body on earth).  Armstrong allows nomic relations between “quasi-universals” in order to accommodate the possibility of changes in the laws of nature over periods of the history of the universe.  I think this is a mistake for Armstrong.  The intuition that the laws might change strikes me as dispensable.  It is not worth undermining a solution to the problem of induction. 

On the alternative view that properties have their causal powers essentially, it may be possible to accommodate the intuition that the laws might change and yet preserve the integrity of the proposed solution to the problem of induction.  If properties have their causal powers essentially, then the laws of nature must be necessary truths.  This rules out the possibility of the laws changing over time.  But it does not rule out the possibility that one class of properties are instantiated during one period of the history of the universe while fundamentally different properties are instantiated during others.  This preserves the intuition, but not at the price of undermining the rationality of induction.

I have a substantial degree of sympathy for the a-priori approach to justifying induction offered by Bonjour.  For several years I have been more or less satisfied with Popper’s deductivist approach to the question of induction.  But mere satisfaction with Popper does not render a positive justification of induction undesirable.  When I teach the problem of induction, I regularly ask my students to consider whether Hume’s dilemma for justifying induction employs a false dichotomy.  And it is specifically the possibility of abductive support for induction I have had in mind in raising this question.  I believe Bonjour has done us a valuable service in launching a substantive exploration of this potential means of support for induction. The 20^th century produced a small handful of widely known and well-developed, if not entirely successful, approaches to the problem of induction.  I’d like to see the abductive a-priori approach offered by Bonjour developed further and ultimately enter those ranks.

Works Cited

Armstrong, D. M.  What is a Law of Nature.  Cambridge University Press, 1983.

Bonjour, Laurence.  In Defense of Pure Reason.  Cambridge UK:  Cambridge University Press, 1998.

Dretske, Fred.  "The Laws of Nature."  Philosophy of Science, 44 (1977) 248-68.

Ellis, Brian.  Scientific Essentialism.  Cambridge: Cambridge University Press, 2001.

Ellis, Brian and Caroline Lierse.  “Dispositional Essentialism,” Australasian Journal of Philosophy.  72  (March 1994) 27-45.

Goodman, Nelson.  Fact Fiction and Forecast.  Harvard University Press, 1955.

Hume, David.  Enquiries Concerning Human Understanding.  Edited by P. H. Nidditch.  3^rd. edition.  Oxford:  Clarendon Press, 1975.

Hume, David.  A Treatise of Human Nature.  Edited by P. H. Nidditch.  2^nd edition.  Oxford:  Clarendon Press, 1978.

Shoemaker, Sydney. "Causality and Properties," in Time and Cause, ed. Peter van Inwagen, 109-135.  Dordrecht: Reidel, 1980.

Tooley, Michael.  "The Nature of Laws." Canadian Journal of Philosophy 7 (1977):  667-98.