Many philosophers think that science extensively uses the inferen-tial strategy known as abduction or inference to the best explanation (Harman 1965). Some of these philosophers further think that philosophy uses this strategy. But what exactly does this strategy involve?
Inference to the best explanation is a method for inferring to the likely truth of a certain hypothesis. Suppose that there is a phenomenon P that we wish to explain. Suppose too that there is a pool of pairwise incompat-ible hypotheses H1, H2, … , Hn. (For the hypotheses in the series to be
“pairwise incompatible” means that if you take any pair of these hypoth-eses, the two hypotheses selected are mutually incompatible.) Suppose that these hypotheses are such that, for each hypothesis Hi, were Hi true, it would explain P. Which of these hypotheses (if any) should be accepted as the explanation of P? It is natural to want to infer the hypothesis that is most likely. But which hypothesis is the most likely? We are no further forward, and it is not clear what resources are available to us to answer the question.
The method of inference to the best explanation reverses the order in which we answer these questions. Our first task is to select which hypoth-esis, if it were true, would best explain P. It is on that basis that we then say which hypothesis is the most likely to be true. The first task involves weighing up the explanatory credentials of each hypothesis. This is a
comparative task: we compare the credentials of each of H1, H2, … , Hn
against its rivals. To do this we need to consider such factors as the inter-nal consistency of the hypothesis, its scope, its fruitfulness, whether it is consistent with hypotheses that we already accept, the degree to which accepting it would increase our ontological and ideological (in Quine’s sense) commitments, the degree to which it avoids raising intractable issues, and so on.5 We also need to consider the difficult question of how these various factors should be weighed against each other. One hypoth-esis may have certain theoretical virtues to a greater degree than another, although the second hypothesis may have certain other theoretical vir-tues to a greater degree than the first. If we had to choose between the two hypotheses, which one should we choose? (See chapter 4, §6 and Lewis 1986, 133–34.)
To return to the main issue, suppose that a member of our pool of hypotheses can be selected as the best potential explanation of P. Suppose too that this hypothesis is a good enough potential explanation of P to be acceptable; that it meets some minimal requirement of explanatory power. We might also require that the hypothesis is significantly better than any nearest rival hypothesis (Dorr and Rosen 2001, §7). According to the strategy of inference to the best explanation, we are warranted to infer that that hypothesis is the (most likely) explanation of P. That is, we infer from the hypothesis that would best explain P, and that meets a suitable standard of explanatory power, to its being the hypothesis that most likely explains P. A hypothesis’s explanatory potential provides a reason to believe that the hypothesis is likely to be true.
A hypothesis can have a low epistemic probability in absolute terms, but a higher epistemic probability than each of many rival hypotheses.
A more cautious form of inference to the best explanation will not infer to a hypothesis’s likely truth (its having a high epistemic probability in absolute terms), but only to its being more likely (its having a higher epistemic probability) than its rival hypotheses.6
Of the two inference strategies considered here — theoretical unifica-tion, and inference to the best explanation — the last is the most widely appealed to by philosophers. (It is not always distinguished from the first, however.) For example, Swoyer thinks that inferences to the best explanation from certain truths about mathematics, semantics, or the laws of nature warrant philosophical conclusions about the existence of properties, understood as universals or properties that are identical between their instances (Swoyer 1999, esp. §§5–7). Armstrong, Bigelow
5 Thagard (1976) and McAllister (1989) spell out some of these factors.
6 See Okasha (2000, 697–98).
and Pargetter also use this strategy to infer certain philosophical hypoth-eses (Armstrong 1997, 235, and Bigelow and Pargetter 1990, 344–45).
There are two main difficulties facing philosophers’ appeal to inference to the best explanation. First, there are quite general questions about the justification, and even the rationality, of the strategy itself (van Fraassen 1989, ch. 6).7 Second, there are specific worries about the use of the strat-egy in philosophy (van Fraassen 1995, §iv). We will concentrate on the second difficulty.
Inference to the best explanation involves taking a pool of potential explanations, and inferring the likely truth of the member of the pool that, if it were true, would provide the best explanation of some target phenomenon. Inferences to the best explanation can be inferences from things of one type to other things of the same type. Typically, such an inference is from a sample of Ks having a common feature, F, to the conclusion that every K has F, or that many unexamined Ks have F. For example, an inference might be from the fact that a planet’s observed spatial locations form an ellipse to the conclusion that all of the planet’s spatial positions — its orbit — form an ellipse. Such an inference is an inference from things of one type to things of the same type, but some important philosophical examples of inference to the best explanation are not instances of that type of inference. For example, neither the inference from sensory experiences to the existence of physical objects, nor the inference from modal phenomena to the existence of Lewisian possible worlds are of that type. These examples are better modelled as inferences from entities of one type to entities of another type. Inferences of this type in science include the inference from observations of the bending of light waves in deep space to the existence of black holes, and the inference from observations of Brownian motion to the existence of molecules. In these scientific cases, the inferred entities are causally efficacious, and the scientific hypotheses that infer them make novel predictions. In conjunction with auxiliary hypotheses not specifically about black holes, scientific hypotheses about black holes are sufficiently detailed to make novel predictions that can subsequently be confirmed or disconfirmed. A similar point holds with respect to scientific hypoth-eses about molecules. By contrast, philosophical hypothhypoth-eses about the existence of the external world or the existence of possible worlds do not generate novel predictions. Consequently, philosophical hypotheses imperfectly emulate their scientific counterparts.
We have seen that inference to the best explanation licenses infer-ring the truth of a given hypothesis only if that hypothesis is a good
7 For replies, see Lipton (2004, 107–17, 151-63), Kvanvig (1994), and Okasha (2000).
enough potential explanation to be acceptable. In an inference to the best explanation, the pool of potential explanations may be “unfiltered” and include all possible candidate explanations, no matter how eccentric. Or it may be “filtered” and include only promising candidate explanations.
Assuming that the pool is unfiltered would markedly deviate from theory selection in actual scientific practice. In the latter case we do not begin by considering all possible theories about some phenomenon because the pool would be too large to generate or handle (Lipton 2004, 119). But if the pool is filtered, so that only what are antecedently considered to be promising candidates are admitted, then certain familiar philosoph-ical theories are in danger of being excluded at the outset.8 For instance, the “incredulous stare” facing modal realism testifies to how implaus-ible many philosophers find that theory (Lewis 1986, 133–35). Excluding modal realism from the pool for that reason would be to disqualify it as a candidate for explaining modal phenomena. The modal realist might take issue with a setting on the filter that excluded his theory from the pool. But if the argument between the modal realist and his opponents occurs at this early stage, it forestalls our going on to the next stage: of taking the pool of admitted candidates and inferring the best potential explanation of the phenomena to be explained. Accordingly, inference to the best explanation would have to wait upon a prior resolution of the dispute between the modal realist and his incredulous opponents, rather than provide that resolution itself. This would leave the role of inference to the best explanation in philosophy much less useful and interesting than it had promised to be. It would be a “bystander” to the crucial argu-ment between Lewis and his opponents, and that arguargu-ment would have to be conducted along independent lines.
What do these criticisms show? A friend of the use of inference to the best explanation may warn against conflating the effectiveness of this inferential method with its legitimacy (Vahid 2001, §5). To show that inference to the best explanation is legitimate is to show that it is truth-conducive: that following this method leads more often than not to true hypotheses. Following Sober, Vahid appeals to the role of background assumptions in guiding hypothesis choice. He claims that these assump-tions justify describing a given hypothesis as the best of a number of hypotheses. Moreover, if these assumptions are reliable ones, if they are well-confirmed, “our grounds for choosing the best explanation would then be firmly anchored in truth.” But to be an epistemically effective inferential method, the method cannot simply tell us which hypothesis is the best in an arbitrarily given pool. The hypothesis may merely be
8 This worry is shared by Nozick (1981, 12).
the best of a bad bunch. To be epistemically effective, then, the pool of hypotheses to which the method is applied needs to be suitably filtered.
Vahid looks to a substantial theory of knowledge to provide this filter. As an illustration, he considers a relevant alternatives theory of knowledge, such as the one found in Dretske (1981). Applied to the case at issue, a relevant alternatives theory would say that to know that hypothesis H is true, one need not rule out every alternative to H. One need only rule out every relevant alternative to it. The pool of hypotheses from which H is selected includes only all relevant alternatives to H. Context (including shared presuppositions in our epistemic community and the objective likelihood of certain situations) settles which hypotheses are relevant.
Appealing to well-confirmed hypotheses as background hypotheses raises the question of what method is used to confirm those hypotheses.
If the method of confirmation used is inference to the best explanation, then this defence of the legitimacy of inference to the best explanation is circular. We would be relying on certain hypotheses inferred by inference to the best explanation to defend the legitimacy of using inference to the best explanation to infer certain other hypotheses. Yet what is at issue is the legitimacy of the use of inference to the best explanation to infer any hypothesis. Some account of confirmation other than inference to the best explanation would need to be appealed to. And if an independent account is forthcoming, we would have to be told what the method of inference to the best explanation is then needed for.
Circularity also threatens the illustrative use of a relevant alternatives theory of hypothesis choice. This theory appeals to context to determine which hypotheses are relevant, and the context involves the objective likelihood of certain situations. Now making such a choice requires knowing what the context is. That will then require knowing the objective likelihood of the situations in question. But how is that to be done? It will not be done by inference to the best explanation, since the claims of objective likelihood need to be in place as part of the filter on potential hypotheses. (This, and the preceding, threat of circularity particularly face the views of Harman [1965] and Lycan [1998, 128] according to whom “all justified reasoning is fundamentally explanatory reasoning that aims at maximising the “explanatory coherence” of one’s total belief system.”) To avoid circularity, some other method has to be available for working out what the objective likelihood of various claims is. If such a method is forthcoming, we might wonder whether the method can be used more generally in working out the objective likelihood of hypoth-eses, and so we would have to be told why the method of inference to the best explanation is still needed.
In the next two sections we will consider two case studies of philo-sophical explanations: an inference to the best explanation for the mind-brain identity theory, and an inference to the best explanation to the postulation of the external world.
6. Case Study: The Mind-Brain Identity Theory
In chapter 4, §4 we examined the mind-brain identity theory. This theory claims that every mental property is identical to some physical property of the brain. Christopher Hill has appealed to the strategy of inference to the best explanation to infer to the likely truth of this theory. He argues as follows (Hill 1991, 23):
(P1) Inference to the best explanation: “If a theory provides a good explanation of a set of facts, and the explanation is better than any explanation provided by a compet-ing theory, then one has a good and sufficient reason to believe that the theory is true.”
(P2) Explanatory adequacy claim: The identity theory provides a good explanation of the one-to-one
correlation between instances of mental properties and instances of some physical properties: namely, that the properties are identical.
(P3) Explanatory superiority claim: The identity theory’s explanation is superior to the explanations provided by all rival theories.
(C) So there is good and sufficient reason to believe the mind-brain identity theory.
(P2) claims that the correlation between instances of a mental and a phys-ical property is best explained by the hypothesis that the properties are the same. Somewhat similarly, the best explanation of why the Cincinnati Strangler’s victims were invariably past girlfriends of Fred Jones is that the Cincinnati Strangler and Fred Jones are the same person. By con-trast with the identity theory, Hill claims that “A dualistic ‘explanation’
of a psychophysical law is usually little more than a euphemistic way of confessing that the law has the status of an unexplained primitive” (Hill 1991, 25).
The dualist will make some of the same objections to Hill’s argument from explanatory considerations as he made to the argument for the identity theory from Ockham’s Razor. The identity theory is the best explanation of the correlations between instances of mental and physical
properties only if it is possible that the theory is true. The dualist will raise the logically prior issue of whether it is possible for mental and physical properties to be identical, and typically he will argue that it is not possible. He will argue that mental properties have features, such as intrinsic intentionality or an experiential quality, that no physical prop-erty could have. If those arguments succeed, the identity theory cannot be the best explanation of the mental-physical correlations because that theory cannot be true.
Setting this response aside, we might wonder whether Hill’s identity theorist faces a similar charge to the one he makes against the dualist.
The dualist is charged with accepting certain unexplained primitives, namely, the mental-physical correlations in question. But the identity theorist faces a parallel charge of accepting certain unexplained primi-tives, namely, the identities between mental and physical properties.
Either these identities lack an explanation or they have an explanation.
If they lack an explanation, then the charge against the identity theorist sticks. If they have an explanation, then the charge of accepting certain unexplained primitives can be made with respect to their explanans, or with respect to whatever are the ultimate explanans that the identity theorist accepts. At some stage the identity theorist is going to run out of explanations and will have to accept certain unexplained primitives. Hill may reply that it matters how far you can extend a series of explanations.
The dualist gives up too soon, and the identity theorist does better by taking explanation at least a stage further (Rey 1998, 5–6).
It is natural to think that the fact that H1 explains more than H2 is one factor in assessing its worth, and would contribute toward a con-clusion that H1 is a better theory than H2 (where “better than” means overall better than, and not simply better explainer than). But it is not clear that scientific practice bears this out (van Fraassen 1980, 94–96).
Newton deliberately declined to explain why gravity occurred. He also deliberately declined to explain why there were six planets (as he and his contemporaries thought that there were). Widely accepted versions of quantum theory do not explain why there are correlations in the behaviour of particles that have interacted in the past. Perhaps one rea-son why the task of explaining these phenomena was shirked was that the theories available that would have explained them would either not have made novel correct predictions (as in the Newtonian examples), or they would not have been as observationally accurate as the standard theories were (as in the quantum theory example). A hypothesis that explains just about everything might nevertheless be bad because empty:
e.g., explaining whatever happens as the will of God. If philosophical theories are not in the business of making predictions, but can still be
in the business of giving explanations, perhaps this constraint would not apply. If so, the methodological principle mentioned at the begin-ning of this paragraph can be straightforwardly applied to the dispute between the identity theory and dualism. A different view, however, is that explanation is a theoretical virtue because it is conducive to accu-rate and wide-ranging predictions (van Fraassen 1980, 92). That view is not a threat to the explanatory status of the identity theory. That theory predicts for example, the discovery of neurological correlates for mental states. The view does, however, confront the explanatory status of various other philosophical theories. Neither modal realism nor mathematical Platonism, for example, makes predictions. So those theories’ claims to be explanatory conflict with van Fraassen’s view.
To sum up, the argument from explanatory factors for the mind-brain identity theory faces some of the objections that face the argument from simplicity for that theory. Furthermore, the argument needs to address a general query about whether explanations that do not generate additional predictive power need to be accepted.