Inference to the Best Explanation

Peter Lipton

• Publisher: Routledge
• Year: 2003
• ISBN:
  9781134548279
• Edition: 2
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of Inference to the Best Explanation, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In Inference to the Best Explanation, Peter Lipton gives this important and influential idea the development and assessment it deserves.The second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of Inference to the Best Explanation has also been updated throughout and includes a new bibliography.

Chapter 1Induction

Underdetermination

We infer some claims on the basis of other claims: we move from premises to a conclusion. Some inferences are deductive: it is impossible for the premises to be true but the conclusion false. All other inferences I call ‘inductive’, using that term in the broad sense of non-demonstrative reasons. Inductive inference is thus a matter of weighing evidence and judging probability, not of proof. How do we go about making these judgments, and why should we believe they are reliable? Both the question of description and the question of justification arise from underdetermination. To say that an outcome is underdetermined is to say that some information about initial conditions and rules or principles does not guarantee a unique solution. The information that Tom spent five dollars on apples and oranges and that apples are fifty cents a pound and oranges a dollar a pound underdetermines how much fruit Tom bought, given only the rules of deduction. Similarly, those rules and a finite number of points on a curve underdetermine the curve, since there are many curves that would pass through those points.

Underdetermination may also arise in our description of the way a person learns or makes inferences. A description of the evidence, along with a certain set of rules, not necessarily just those of deduction, may underdetermine what is learned or inferred. Insofar as we have described all the evidence and the person is not behaving erratically, this shows that there are hidden rules. We can then study the patterns of learning or inference to try to discover them. Noam Chomsky’s argument from ‘the poverty of the stimulus’ is a good example of how underdetermination can be used to disclose the existence of additional rules (1965: ch. 1, sec. 8, esp. 58–9). Children learn the language of their elders, an ability that enables them to understand an indefinite number of sentences on first acquaintance. The talk young children hear, however, along with rules of deduction and any plausible general rules of induction, grossly underdetermine the language they learn. What they hear is limited and includes many ungrammatical sentences, and the little they hear that is well formed is compatible with many possible languages other than the one they learn. Therefore, Chomsky argues, in addition to any general principles of deduction and induction, children must be born with strong linguistic rules or principles that further restrict the class of languages they will learn, so that the actual words they hear are now sufficient to determine a unique language. Moreover, since a child will learn whatever language he is brought up in, these principles cannot be peculiar to a particular human language; instead, they must specify something that is common to all of them. For Chomsky, determining the structure of these universal principles and the way they work is the central task of modern linguistics.

Thomas Kuhn provides another well-known example of using underdetermination as a tool to investigate cognitive principles. He begins from an argument about scientific research strikingly similar to Chomsky’s argument about language acquisition (1970; 1977, esp. ch. 12). In most periods in the history of a developed scientific specialty, scientists are in broad agreement about which problems to work on, how to attack them and what counts as solving them. But the explicit beliefs and rules scientists share, especially their theories, data, general rules of deduction and induction, and any explicit methodological rules, underdetermine these shared judgments. Many possible judgments are compatible with these beliefs and rules other than the ones the scientists make. So Kuhn argues that there must be additional field-specific principles that determine the actual judgments. Unlike Chomsky, Kuhn does not argue for principles that are either innate or in the form of rules, narrowly construed. Instead, scientists acquire through their education a stock of exemplars – concrete problem solutions in their specialty – and use them to guide their research. They pick new problems that look similar to an exemplar problem, they try techniques that are similar to those that worked in that exemplar, and they assess their success by reference to the standards of solution that the exemplars illustrate. Thus the exemplars set up a web of ‘perceived similarity relations’ that guide future research, and the shared judgments are explained by the shared exemplars. These similarities are not created or governed by rules, but they result in a pattern of research that mimics one that is rule governed. Just how exemplars do this work, and what happens when they stop working, provide the focus of Kuhn’s account of science.

As I see it, Chomsky and Kuhn are both arguing for unacknowledged principles of induction, even though the inferences in the one case concern grammaticality rather than the world around us and even though the principles governing the inference in the other case are determined by exemplars rather than by rules (cf. Curd and Cover 1998: 497). In both cases, inferences are drawn that are not entailed by the available evidence. However, here underdetermination is taken to be a symptom of the existence of highly specialized principles, whether of language acquisition or of scientific research in a particular field at a particular time, since the underdetermination is claimed to remain even if we include general principles of induction among our rules. But it is natural to suppose that there are some general principles, and the same pattern of argument applies there. If an inference is inductive, then by definition it is underdetermined by the evidence and the rules of deduction. Insofar as our inductive practices are systematic, we must use additional principles of inference, and we may study the patterns of our inferences in an attempt to discover what those principles are and to determine what they are worth.

Justification

The two central questions about our general principles of induction concern description and justification. What principles do we actually use? Are these good principles to use? The question of description seems at first to take priority. How can we even attempt to justify our principles until we know what they are? Historically, however, the justification question came first. One reason for this is that the question of justification gets its grip from skeptical arguments that seem to apply to any principles that could account for the way we fill the gap between the evidence we have and the inference we make. It is the need for such principles rather than the particular form they take that creates the skeptical trouble.

The problem of justification is to show that our inferential methods are good methods, fit for purpose. The natural way to understand this is in terms of truth. We want our methods of inference to be ‘truth-tropic’, to take us towards the truth. For deduction, a good argument is one that is valid, a perfect truth conduit, where if the premises are true, the conclusion must be true as well. The problem of justification here would be to show that arguments we judge valid are in fact so. For induction, such perfect reliability is out of the question. By definition, even a good inductive argument is one where it is possible for there to be true premises but a false conclusion. Moreover, it is clear that the reasonable inductive inferences we make are not entirely reliable even in this world, since they sometimes sadly take us from truth to falsehood. Nevertheless, it remains natural to construe the task of justification as that of showing truth-tropism. We would like to show that those inductive inferences we judge worth making are ones that tend to take us from true premises to true conclusions.

A skeptical argument that makes the problem of justification pressing has two components, underdetermination and circularity. The first is an argument that the inferences in question are underdetermined, given only our premises and the rules of deduction; that the premises and those rules are compatible not just with the inferences we make, but also with other, incompatible inferences. This shows that the inferences in question really are inductive and, by showing that there are possible worlds where the principles we use take us from true premises to false conclusions, it also shows that there are worlds where our principles would fail us. Revealing this underdetermination, however, does not yet generate a skeptical argument, since we might have good reason to believe that the actual world is one where our principles are at least moderately reliable. So the skeptical argument requires a second component, an argument for circularity, which attempts to show that we cannot rule out the possibility of massive unreliability that underdetermination raises without employing the very principles that are under investigation, and so begging the question.

Although it is not traditionally seen as raising the problem of induction, Descartes’s ‘First Meditation’ (1641) is a classic illustration of this technique. Descartes’s goal is to cast doubt on the ‘testimony of the senses’, which leads us to infer that there is, say, a mountain in the distance, because that is what it looks like. He begins by arguing that we ought not to trust the senses completely, since we know that they do sometimes mislead us, ‘when it is a question of very small and distant things’. This argument relies on underdetermination, on the fact that the way things appear does not entail the way they are; but it does not yet have the circularity component, since we can corroborate our inferences about small and distant things without circularity by taking a closer look (Williams 1978: 51–2). But Descartes immediately moves on from the small and the distant to the large and near. No matter how clearly we seem to see something, it may only be a dream, or a misleading experience induced by an evil demon. These arguments describe possible situations where even the most compelling sensory testimony is misleading. Moreover, unlike the worry about small and distant things, these arguments also have a circle component. There is apparently no way to test whether a demon is misleading us with a particular experience, since any test would itself rely on experiences that the demon might have induced. The senses may be liars, giving us false testimony, and we should not find any comfort if they also report that they are telling us the truth.

The demon argument begins with the underdetermination of observational belief by observational experience, construes the missing principle of inference on the model of inference from testimony, and then suggests that the reliability of this principle could only be shown by assuming it. Perhaps one of the reasons Descartes’s arguments are not traditionally seen as raising the problem of justifying induction is that his response to his own skepticism is to reject the underdetermination upon which it rests. Descartes argues that, since inferences from the senses must be inductive and so raise a skeptical problem, our knowledge must instead have a different sort of foundation for which the problem of underdetermination does not arise. The cogito and the principles of clarity and distinctness that it exemplifies are supposed to provide the non-inductive alternative. Circularity is also avoided since the senses do not have to justify themselves, even if the threat of circularity notoriously reappears elsewhere, in the attempt to justify the principles of clarity and distinctness by appeal to an argument for the existence of God that is to be accepted because it itself satisfies those principles. Another reason why Descartes is not credited with the problem of induction may be that he does not focus directly on the principles governing inferences from experience, but rather on the fallibility of the conclusions they yield.

The moral Descartes draws from underdetermination and circularity is not that our principles of induction require some different sort of defence or must be accepted without justification, but that we must use different premises and principles, for which the skeptical problem does not arise. Thus he attempts to wean us from the senses. For a skeptical argument about induction that does not lead to the rejection of induction, we must turn to its traditional home, in the arguments of David Hume.

Hume also begins with underdetermination, in this case that our observations do not entail our predictions (1748: sec. IV). He then suggests that the governing principle of all our inductive inferences is that nature is uniform, that the unobserved (but observable) world is much like what we have observed. The question of justification is then the question of showing that nature is indeed uniform. This cannot be deduced from what we have observed, since the claim of uniformity itself incorporates a massive prediction. But the only other way to argue for uniformity is to use an inductive argument, which would rely on the principle of uniformity, leaving the question begged. According to Hume, we are addicted to the practice of induction, but it is a practice that cannot be justified.

To illustrate the problem, suppose our fundamental principle of inductive inference is ‘More of the Same’. We believe that strong inductive arguments are those whose conclusions predict the continuation of a pattern described in the premises. Applying this principle of conservative induction, we would infer that the sun will rise tomorrow, since it has always risen in the past; and we would judge worthless the argument that the sun will not rise tomorrow since it has always risen in the past. One can, however, come up with a factitious principle to underwrite the latter argument. According to the principle of revolutionary induction, ‘It’s Time for a Change’, and this sanctions the dark inference. Hume’s argument is that we have no way to show that conservative induction, the principle he claims we actually use for our inferences, will do any better than intuitively wild principles like the principles of revolutionary induction. Of course conservative induction has had the more impressive track record. Most of the inferences from true premises that it has sanctioned have also had true conclusions. Revolutionary induction, by contrast, has been conspicuous in failure, or would have been, had anyone relied on it. The question of justification, however, does not ask which method of inference has been successful; it asks which one will be successful.

Still, the track record of conservative induction appears to be a reason to trust it. That record is imperfect (we are not aspiring to deduction), but very impressive, particularly as compared with revolutionary induction and its ilk. In short, induction will work because it has worked. This seems the only justification our inductive ways could ever have or require. Hume’s disturbing observation was that this justification appears circular, no better than trying to convince someone that you are honest by saying that you are. Much as Descartes argued that we should not be moved if the senses give testimony on their own behalf, so Hume argued that we cannot appeal to the history of induction to certify induction. The trouble is that the argument that conservative inductions will work because they have worked is itself an induction. The past success is not supposed to prove future success, only make it very likely. But then we must decide which standards to use to evaluate this argument. It has the form ‘More of the Same’, so conservatives will give it high marks, but since its conclusion is just to underwrite conservatism, this begs the question. If we apply the revolutionary principle, it counts as a very weak argument. Worse still, by revolutionary standards, conservative induction is likely to fail precisely because it has succeeded in the past, and the past failures of revolutionary induction augur well for its future success (Skyrms 1986: ch. II). The justification of revolutionary induction seems no worse than the justification of conservative induction, which is to say that the justification of conservative induction looks very bad indeed.

The problem of justifying induction does not show that there are other inductive principles better than our own. Instead it argues for a deep symmetry: many sets of principles, most of them wildly different from our own and incompatible with each other, are yet completely on a par from a justificatory point of view. This is why the problem of justification can be posed before we have solved the problem of description. Whatever inductive principles we use, the fact that they are inductive seems enough for the skeptic to show that they defy justification. We fill the gap of underdetermination between observation and prediction in one way, but it could be filled in many other ways that would have led to entirely different predictions. We have no way of showing that our way is any better than any of the other ways that would certify their own reliability. Each is on a par in the sense that it can only argue for its principles by appeal to those very principles. And it is not just that the revolutionaries will not be convinced by the justificatory arguments of the conservatives: the conservatives should not accept their own defense either, since among their standards is one which says that a circular argument is a bad argument, even if it is in one’s own aid. Even if I am honest, I ought to admit that the fact that I say so ought not to carry any weight. We have a psychological compulsion to favor our own inductive principles but, if Hume is right, we should see that we cannot even provide a cogent rationalization of our behavior.

It seems to me that we do not yet have a satisfying solution to Hume’s challenge and that the prospects for one are bleak. (Though some seem unable to give up trying. See e.g. Lipton 2000 and forthcoming.) There are, however, other problems of justification that are more tractable. The peculiar difficulty of meeting Hume’s skeptical argument against induction arises because he casts doubt on our inductive principles as a whole, and so any recourse to induction to justify induction appears hopeless. But one can also ask for the justification of particular inductive principles and, as Descartes’s example of small and distant things suggests, this leaves open the possibility of appeal to other principles without begging the question. For example, among our principles of inference is one that makes us more likely to infer a theory if it is supported by a variety of evidence than if it is supported by a similar amount of homogenous data. This is the sort of principle that might be justified in terms of a more basic inductive principle, say that we have better reason to infer a theory when all the reasonable competitors have been refuted, or that a theory is only worth inferring when each of its major components has been separately tested. Another, more controversial, example of a special principle that might be justified without circularity is that, all else being equal, a theory deserves more credit from its successful predictions than it does from data that the theory was constructed to fit. This appears to be an inductive preference most of us have, but the case is controversial because it is not at all obvious that it is rational. On the one hand, many people feel that only a prediction can be a real test, since a theory cannot possibly be refuted by data it is built to accommodate; on the other, that logical relations between theory and data upon which inductive support exclusively depends cannot be affected by the merely historical fact that the data were available before or only after the the...

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Table of Contents
• Preface to the second edition
• Preface to the first edition
• Introduction
• 1 Induction
• 2 Explanation
• 3 The causal model
• 4 Inference to the Best Explanation
• 5 Contrastive inference
• 6 The raven paradox
• 7 Bayesian abduction
• 8 Explanation as a guide to inference
• 9 Loveliness and truth
• 10 Prediction and prejudice
• 11 Truth and explanation
• Conclusion
• Bibliography
• Index