Pergamon
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Stud. Hist. Phil. Sci., Vol. 31, No. 4, pp. 691–710, 2000
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Van Fraassen’s Critique of Inference to
the Best Explanation
Samir Okasha*
1. Introduction
In The Origin of Species, Darwin adduced a wide variety of evidence for his theory
of evolution by natural selection. The evidence included morphological data,
embryological data, data about the geographical distribution of organisms, and
much more. In each case, Darwin’s strategy was to argue that the data could not
easily be accounted for by the hypothesis of creation, but were exactly what we
would expect if the theory of evolution by natural selection were true. He continued:
it can hardly be supposed that a false theory would explain, in so satisfactory a manner
as does the theory of natural selection, the several large classes of facts above specified. It has recently been objected that this is an unsafe method of arguing; but it is
a method used in judging of the common events of life, and has often been used by
the greatest natural philosophers (Darwin, 1962, p. 476).
Unsafe or not, something very similar to Darwin’s ‘method of arguing’ occupies
a prominent role in many contemporary accounts of scientific method, where it is
usually called ‘inference to the best explanation’ (IBE). The phrase ‘inference to
the best explanation’ was introduced by Harman (1965), but the idea is old; C. S.
Peirce’s notion of ‘abduction’ is an obvious precursor, as is the Cartesian ‘method
of hypothesis’ which Newton and his followers repudiated. The basic schema of
IBE is straightforward: you start with a set of data, and infer the probable truth of
a hypothesis, on the grounds that the hypothesis provides a better explanation of
the data than do competing hypotheses. According to its proponents, IBE is a
paradigmatic, perhaps even the paradigmatic, form of non-demonstrative inference,
widely used in science, everyday life, and in philosophy itself. Glymour describes
* Department of Philosophy, London School of Economics, Houghton Street, London WC2A 2AE,
U.K. (e-mail: s.okasha@lse.ac.uk)
Received 18 October 1999; in revised form 7 February 2000.
PII: S0039-3681(00)00016-9
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IBE as a pattern of argument that ‘is not bounded by time or subject matter. One
can find such arguments in sociology, in psychometrics, in chemistry and astronomy, in the time of Copernicus, and in the most recent of our scientific journals’
(Glymour, 1984, p. 173).
Critics of IBE have focused on a variety of points. Doubts have been raised
about whether IBE is really just hypothetico-deductivism in disguise, about whether
the concept of ‘best explanation’ can be made precise, about whether IBE really
deserves pride of place over ordinary induction, and more. In response to these
and other worries, the IBE model has been articulated with increasing care and
sophistication in recent years.1 Consensus on the issue has by no means been
reached, but philosophers of many different stripes appear to agree that something
like IBE goes on a lot of the time, and provides a fairly accurate way of reconstructing numerous episodes of scientific reasoning, past and present.
Against this background, Bas van Fraassen’s attack on IBE in Laws and Symmetry (1989) is remarkable. For van Fraassen sees no merit at all in the idea of
IBE. He writes: ‘as long as the pattern of IBE is left vague, it seems to fit much
rational activity. But when we scrutinize its credentials, we find it seriously wanting’ (van Fraassen, 1989, p. 131). Van Fraassen’s scrutiny of IBE’s credentials is
penetrating and thorough, and poses a serious challenge to would-be defenders of
IBE. In what follows, I take up this challenge.
2. Background: van Fraassen’s Views on Induction
Van Fraassen’s opposition to IBE traces back to the days of The Scientific Image
(van Fraassen, 1980). Scientific realists had frequently invoked IBE in defence of
their belief in unobservable entities; as an anti-realist, van Fraassen objected.2 However, the realism/anti-realism issue does not feature prominently in Laws and Symmetry. In the latter work, van Fraassen’s attack on IBE is part of a broader attack
on received ideas about inductive inference. To understand this attack, it is necessary to look briefly at van Fraassen’s views on induction.3
Van Fraassen’s position on induction comprises a subtle amalgamation of themes
from various sources. He begins by describing what he calls the ‘traditional ideal
of induction’. This ideal was ‘a rule of calculation, that extrapolates from particular
data to general (or at least ampliative) conclusions. Part of the ideal is (a) that it
is a rule, (b) that it is rationally compelling . . . (c) that it is objective . . . and
1
Peter Lipton (1991) has provided the most detailed, book-length account of IBE.
Some readers of The Scientific Image mistakenly concluded that van Fraassen was happy with IBE,
so long as it is applied only at the level of observable phenomena. A misleading passage on p. 24 of
that work, concerning mice and nibbled cheese, is the source of this misinterpretation. The issue is
cleared up by van Fraassen in ‘Empiricism in the Philosophy of Science’ (van Fraassen, 1985) p. 295,
n. 19.
3
Van Fraassen’s views on induction can be found in Laws and Symmetry (van Fraassen, 1989), ch.
6, and van Fraassen (1985), pp. 252–296.
2
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finally, (d) that it is ampliative’ (ibid., p. 132, author’s emphasis). The so-called
‘straight-rule’ of induction is perhaps the most obvious example of something that
was meant to satisfy (a)–(d). But van Fraassen insists that the traditional ideal of
induction cannot be fulfilled. This opinion is motivated in part by theoretical arguments, and in part by the repeated failures of philosophers to actually produce the
supposed rules of induction.
But van Fraassen is no inductive sceptic; he grants the rationality of our beliefs
about the unobserved. What enables van Fraassen to reject the traditional ideal of
induction without falling into inductive scepticism is a particular thesis about
rationality. Rationality is a concept of permission, not obligation, he maintains: it
concerns what you may believe, not what you must.4 Therefore, rational belief
change need not be governed by rules which tell you how to respond to evidence;
two agents can respond very differently to the same evidence, without one of them
being irrational. Once we adopt a permissive conception of rationality, van Fraassen
holds, we can grant that no rules of induction exist, while allowing that rational
expectations of the future are possible.
Van Fraassen rejects the idea of ‘inductive logic’ in no uncertain terms, but he
is nonetheless a Bayesian of sorts.5 He accepts the Bayesian representation of opinion in terms of degrees-of-belief, and he agrees that synchronic probabilistic
coherence is a necessary condition of rationality. However, he does not accept the
Bayesian thesis that conditionalization is the only rational way to respond to new
evidence; though he allows that it is a rational way. Specifically, van Fraassen
holds that if you adopt a pre-set rule for updating your subjective probabilities in
the light of new evidence, then that rule had better be conditionalization; but you
are not rationally compelled to adopt any pre-set rule, nor therefore to conditionalize. In short, van Fraassen allows that you can rationally believe things that
are not entailed by your evidence, but denies that there are any rules—whether
IBE, straight-rule induction, conditionalization or any other—which you are rationally bound to follow.
3. Van Fraassen’s Critique of IBE
‘There are many charges to be laid against the epistemological scheme of Inference to the Best Explanation’, writes van Fraassen. ‘One is that it pretends to be
4
Van Fraassen draws a nice parallel here with an alleged difference between English and Prussian
law: in English law, everything is permitted except what is expressly forbidden, while in Prussian law,
everything is forbidden except what is expressly permitted. Our concept of rationality fits the English
not the Prussian model, van Fraassen thinks.
5
In ‘Empiricism in the Philosophy of Science’, van Fraassen writes: ‘inductive logic is a make-believe
theory. No-one has ever written its principles. Attempts to do so have always landed in incoherence or
fallen afoul of hilarious counterexamples’ (van Fraassen, 1985, p. 295). Van Fraassen is construing
‘inductive logic’ narrowly here—it is meant to satisfy the traditional ideal of induction. Other authors
use ‘inductive logic’ in a more inclusive sense, to include Bayesianism. (Bayesianism obviously does
not satisfy the traditional ideal of induction as defined by van Fraassen, for it trades in subjective
probabilities.)
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something other than it is. Another is that it is supported by bad arguments. A
third is that it conflicts with other forms of change of opinion, that we accept as
rational’ (ibid., p. 142).
What does IBE pretend to be? According to van Fraassen, it pretends to fulfil
the traditional ideal of induction, that is, to provide a rule for forming new beliefs
on the basis of the evidence, based on a comparative evaluation of hypotheses with
respect to how well they explain the evidence. But IBE cannot do this, van Fraassen
maintains, ‘for it is a rule that selects the best among the historically given hypotheses. We can watch no contest of the theories we have so painfully struggled to
formulate, with those no one has proposed. So our selection may well be the best
of a bad lot’ (ibid., p. 143). Since believing something involves (at least) believing
that it is more likely to be true than not, the ‘bad lot’ possibility disqualifies IBE
from being a rule which can tell us what to believe, van Fraassen argues. ‘For me
to take it that the best of set X will be more likely to be true than not, requires a
prior belief that the truth is already more likely to be found in X, than not’, he
writes (ibid., p. 143). In other words, if I do not believe that the truth lies within
the set of hypotheses whose explanatory credentials I am examining, then however
well the best hypothesis explains the data, I will not believe it. So IBE ‘cannot
supply the initial context of belief or opinion within which alone it can become
applicable. So it cannot be what “grounds” rational opinion’ (ibid., p. 149).
Van Fraassen hangs a lot on this little argument, so it is worth examining with
some care. Clearly van Fraassen is right that if we are trying to rank a set of
hypotheses according to how well they explain our data, only hypotheses we have
actually thought of will be in the ranking—that much is virtually tautological. And
clearly he is right that, if IBE is a rule that tells us to believe the best explanation
of our data, rational application of IBE requires a prior belief that the truth lies
within the set of hypotheses we rank. Nonetheless, van Fraassen’s ‘bad lot’ argument contains a certain ambiguity. Is his point that, as a matter of fact, the set of
hypotheses we consider may not contain the truth? Or is that we will not always
have reason to believe that the set contains the truth? The quotations above suggest
the latter; but when van Fraassen examines (and rejects) possible responses to the
‘bad lot’ argument, some of these responses appear to be directed at the former. For
example, one attempted response claims that scientists are by nature pre-disposed to
hit on a set of hypotheses that includes the truth. Now even if this were correct,
it would only show that the ‘bad lot’ possibility is in fact not normally realised;
it would not show that scientists typically have reason to believe that this is so.
The ‘predisposed to hit the truth’ response is only relevant if van Fraassen is arguing against the reliability of the IBE rule, rather than against the rationality of
employing it.
Of course, some philosophers would argue that the question of whether a pattern
of inference is reliable and whether it is rational are closely related; pure epistemological externalists might say that the two questions are actually one. Van Fraassen
Van Fraassen’s Critique of Inference to the Best Explanation
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never reveals his position on the internalism/externalism issue in epistemology,
and it is not a matter I wish to tackle here. My own view is that some hybrid of
internalism and externalism is probably most plausible: whether a pattern of inference is reliable is relevant to, but does not fully determine, whether it is rational
to use it. In any case, it is clear that the questions ‘is IBE reliable?’ and ‘is IBE
rational?’ are both of considerable interest in themselves, whatever their relation
to one another, so the importance of van Fraassen’s critique is not diminished by
his tendency to conflate the two.
One further feature of van Fraassen’s argument deserves mention at this stage.
Notice that van Fraassen locates IBE entirely within the ‘context of justification’:
he portrays it as a rule for choosing between hypotheses that have somehow already
arrived on the scene. Some proponents of IBE may indeed have viewed things this
way. But plausibly, explanatory considerations also play a role within the ‘context
of discovery’, to guide the process by which the set of hypotheses we are interested
in is generated initially. Given a puzzling phenomenon, we construct a number of
hypotheses to try to explain it, and choose the one we think explains the phenomenon best. Looked at this way, IBE is not simply a way of selecting between
already existing hypotheses, as per van Fraassen, but also a way of generating the
hypotheses on which the selection procedure operates.
Does the force of van Fraassen’s critique depend in any way on his construing
IBE as a means for choosing between already existing hypotheses? It may seem
as if the answer is ‘no’—surely the ‘bad lot’ possibility is equally germane whether
IBE is viewed in van Fraassen’s way or in the way suggested above? In fact,
matters are not quite so simple, as will become clear. But in order to meet van
Fraassen on his own ground, I accept his way of viewing IBE for the moment,
and set the issue of discovery versus justification to one side. The issue re-surfaces
in Section 8.
4.
Privilege, Force Majeure and Retrenchment
Van Fraassen considers three possible reactions to his own argument, entitled
privilege, force majeure and retrenchment respectively. The three are really four,
for retrenchment comes in two forms. I look at them in turn.
4.1. Privilege
‘Privilege’ was mentioned above—it is the suggestion that we are by nature predisposed to hit on a set of hypotheses that contains the truth. This optimistic opinion
of humans’ cognitive abilities may sound somewhat unlikely, particularly when
the hypotheses come from the higher reaches of science. But it is interesting to
note that many defenders of IBE have actually attempted defences of privilege.
For example, C. S. Peirce wrote: ‘it is a primary hypothesis underlying all abduction that the human mind is akin to the truth in the sense that in a finite number
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of guesses it will light upon the correct hypothesis’ (7.223).6 And Peter Lipton
admits that his position forces him to say that ‘scientists do have the knack of
thinking of the truth’, an ability which he calls ‘somewhat surprising’ (Lipton,
1996, p. 106).
Van Fraassen dismisses privilege very swiftly, claiming that it is ‘incapable of
either naturalistic or rationalist support’ (van Fraassen, 1980, p. 144). The rationalist support he considers involves an appeal to God, the naturalistic support an
appeal to natural selection; van Fraassen finds both suggestions wanting. The idea
of an evolutionary basis for privilege perhaps deserves more extended consideration
than van Fraassen gives it, though he does cite in support a critique of ‘evolutionary
epistemology’ by M. Piatelli-Palmerini. But I agree with van Fraassen that privilege
is an extremely difficult position to defend, if only because of the number of times
scientists have failed to ‘hit on the right range of hypotheses’ in the past.7 If there
is an innate predisposition to guess the truth, it is not one that manifests itself
very often.
4.2. Force majeure
Force majeure says that we have to choose among the historically given hypotheses, whether we like it or not. The historically given hypotheses may indeed be
a bad lot, but we have no option other than to choose one of them. We need a
‘rule of right reason’ to help us make our choice, and this rule is IBE (ibid., p. 144).
According to van Fraassen, the force majeure response is ‘doomed to fail. Circumstances may force us to act on the best alternative open to us. They cannot
force us to believe that it is, ipso facto, a good alternative’ (ibid., pp. 144–145).
Van Fraassen considers the reply that ‘the action reveals the belief’, the argument
that because scientists can be observed to actually choose certain theories, we can
infer that they must believe them to be true. He replies that in situations of forced
choice, action is not a reliable guide to belief, citing a parable of William James’s
to illustrate the point. A walker in the mountains has the choice of jumping over
a crevasse, or staying on the mountain all night. A fall and exposure both mean
near certain death. From the fact that the walker jumps, can we conclude that she
believed it likely she would get across? Clearly not: in the circumstances, even a
very low degree of belief would be reasonable to act on. Scientists are in much
the same boat, van Fraassen argues. Theirs is also a situation of forced choice—
6
Throughout, references to Peirce are to the Collected Papers of Charles Sanders Peirce (Peirce,
1935, 1958); ‘7.223’ means volume 7, paragraph 223.
7
An anonymous referee suggests that anyone who is committed to the basic realist idea that science
is moving towards the truth is in effect committed to privilege, and thus to the view that giving up
privilege entails abandoning scientific realism. I doubt that this is so. It is quite possible to hold that
the methods of science are broadly truth-conducive, without positing an innate ability to guess the truth.
For example, one might argue that although scientists do not have an innate predisposition to hit on a
set of hypotheses that contains the truth, scientific method does in fact provide a fallible indication of
whether any given set does or does not contain the truth, thus sustaining the basic realist thought without
endorsing privilege.
Van Fraassen’s Critique of Inference to the Best Explanation
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they are forced to choose the best available theory from a small handful, for the
purposes of pursuing research. Such choice ‘does not reveal any tendency to believe
in [the theory’s] truth’, he claims (ibid., p. 145).
Van Fraassen is certainly right to say we cannot always infer that a scientist
believes in the truth of her theory, simply because she chooses it over another.
Sometimes we can infer this, if only because the scientist explicitly says so—
witness the quotation from Darwin at the start of this paper. But the point about
forced choice is well taken. Is this really fatal to the claim that scientists use or
should use IBE, though? The defender of IBE could reply that van Fraassen is
construing her position too strictly. Certainly, if IBE is a rule whose use results
in the epistemic state of full belief, then IBE cannot be operative in the many cases
where a scientist accepts a theory but does not believe it outright. And if we allow
that scientists are being rational in these cases, we can hardly say that they should
be using IBE, if doing so would lead to full belief. But must IBE be thought of
in this way? Is it really impossible to reconcile the basic idea of IBE with the fact
that belief is not an all-or-nothing affair, but admits of degrees? This question leads
directly to the third response canvassed by van Fraassen, ‘retrenchment’.
4.3. Retrenchment
Van Fraassen writes: ‘the third reaction is to retrench: “Inference to the Best
Explanation” was a misnomer, and the rule properly understood leads to a revision
of judgement much more modest than inference to the truth of the favoured hypothesis . . . despite its name, it is not the rule to infer the truth of the best available
explanation. That is only a code for the real rule, which is to allocate our personal
probabilities with due respect to explanation. Explanatory power is a mark of truth,
not infallible, but a characteristic symptom’ (ibid., pp. 145–146).
Retrenchment is clearly the direction in which the defender of IBE needs to
move. By retrenching, she can accommodate the facts (i) that accepting a theory,
in the practical sense, does not imply fully believing it, or giving it subjective
probability of 1; and (ii) that subjective probability of 1 is rarely if ever the appropriate degree of confidence to have in an empirical proposition, especially in a
scientific theory.8
Retrenchment comes in two forms, van Fraassen tells us. According to the first
form, ‘the special features which make for explanation among empirically unrefuted theories, make them (more) likely to be true’ (ibid., p. 146). According to the
second, ‘the notion of rationality itself requires [explanatory] features to function as
8
But why does van Fraassen say that the retrencher must admit that the label ‘Inference to the best
Explanation’ was a misnomer? The answer is that van Fraassen uses the word ‘inference’ in a strict
way, so that inferences only take place when a rule is followed and the conclusion is ‘detached’. Merely
re-adjusting personal probabilities does not constitute inference, for van Fraassen. There is certainly a
tradition of using the word ‘inference’ in this strict way; see Jeffrey (1969), for example. But many
recent Bayesians, including those who reject the need for ‘rules of acceptance’ altogether, do still claim
to be offering a theory of inductive inference; see Earman (1992), for example.
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relevant factors in the rules for rational response to evidence’ (ibid., p. 146). Van
Fraassen’s real interest lies in trying to show that the second form of retrenchment
cannot work; I examine this aspect of his argument in the following section. But
it is worth looking briefly at his objections to retrenchment form 1.
Van Fraassen’s argument against retrenchment form 1 is puzzling. He poses the
rhetorical question: ‘is the best explanation we have likely to be true?’, and then
offers a negative answer. Here is his reasoning: ‘there are many theories, perhaps
never yet formulated but in accordance with all evidence so far, which explain at
least as well as the best we have now . . . most of them by far must be false. I
know nothing about our best explanation, relevant to its truth-value, except that it
belongs to this class, most of which is false. Hence it must seem very improbable
to me that it is true’ (ibid., p. 146).
This is puzzling for two reasons. Firstly, the argument is directed at the wrong
target. Recall that the point of ‘retrenching’ was to admit that scientists do not always
believe the truth of the theories they accept, while holding that considerations of
relative explanatory power nevertheless play a key role. So the retrencher does not
need to hold that the best explanation deserves a high epistemic probability, only that
it deserves a higher epistemic probability than alternative, less good explanations.
What van Fraassen presents as an argument against retrenchment form 1, is in fact
only an argument against a proponent of IBE who has refused to retrench, that is,
one who holds that the best explanation is very likely to be the truth. A real ‘retrencher’ could accept van Fraassen’s conclusion—that the best explanation deserves a low
epistemic probability in absolute terms—with equanimity.
Secondly, the premise of van Fraassen’s argument in any case looks most
implausible. Is it really true that for every theory, in every area of science, there
exist many other, perhaps unformulated theories which explain the relevant
phenomena just as well as the theory in question? What licenses van Fraassen in
thinking that underdetermination of this sort is ubiquitous? Perhaps there are some
examples where a given set of phenomena can be ‘equally well explained’ by two
competing theories, but it can hardly be assumed without argument that this is
always the case. Admittedly if we adopted a naı̈ve deductive-nomological (D-N)
model of explanation, or something like it, van Fraassen’s claim would hold, for
it is quite true that a given set of data will be logically implied by many different
theories, so long as we are sufficiently liberal about what counts as a ‘theory’. But
if a theory logically implies a datum, it does not follow that the theory explains
the datum, as everybody knows. Relative to typical post-positivist accounts of
explanation, there is no logical guarantee that a given set of data can be equally
well explained by more than one theory, let alone by many.9 Possibly van Fraassen’s claim can be made good, but the onus clearly rests on him to show how.
9
I have in mind ‘unificatory’ accounts of explanation of the sort defended by Kitcher, Friedman and
others, and ‘causal’ accounts of explanation of the sort defended by Salmon and others.
Van Fraassen’s Critique of Inference to the Best Explanation
699
So van Fraassen’s own argument against retrenchment form 1 is very weak. Can
the proponent of IBE take solace from this? In my view she cannot, for retrenchment form 1 actually falls to a simple dilemma. The retrencher claims that theories
which possess the features that make for explanation are more likely to be true
than ones which don’t. But what does she mean by ‘likely’ here? If likelihood
refers to rational degree of belief, then her position simply collapses into retrenchment form 2. If likelihood is explained in frequentist terms, then the retrencher’s
claim is that the proportion of true theories among those that exemplify the explanatory features, is greater than the proportion of true theories among those that do
not. But there is no way the retrencher can know that. Whatever the ‘explanatory
features’ happen to be, we can observe no correlation between those features and
theoretical truth, for we do not know which of our theories are true. At most we
could hope to observe a correlation between the features in question and continued
empirical success, which is no help, for we know nothing about the proportion of
empirically successful theories that are true. Interpreted in frequentist terms, the
retrencher’s claim may be true, but there is no way she can know. And there is
surely no third option for what ‘likely’ could mean.
To sum up, van Fraassen’s own argument against retrenchment form 1 misses
its mark, as its main premise is implausible and its conclusion irrelevant. But the
proponent of IBE cannot take hope from that. For depending on how ‘likely’ is
interpreted, retrenchment form 1 is either indefensible or else collapses into
retrenchment form 2.
5. Retrenchment Form 2: A Probabilistic Version of IBE?
Retrenchment form 2 is the suggestion that rationality itself requires explanatory
factors to play a role in determining how to respond to new evidence. More precisely, the retrencher hopes that ‘behind the naı̈ve rule of IBE there might lie a
recipe for adjusting our personal probabilities, in response to new experience, under
the aegis of explanatory success’ (ibid., p. 160). Having manoeuvred the defender
of IBE into this position, van Fraassen is now ready to deliver his knock-out punch,
for he claims to show that any such recipe leads to disaster, as it is guaranteed to
conflict with Bayesian rationality constraints. The upshot, says van Fraassen, is that
‘we should not listen to anyone who preaches a probabilistic version of Inference to
the Best Explanation, whatever the details’ (ibid., p. 169). If sustainable, this
remarkable conclusion would certainly be a very serious blow to IBE.
Van Fraassen imagines a Bayesian agent who is also a believer in IBE. The
agent is faced with a relatively simple statistical problem: she is trying to determine
the degree of bias of a given die, based on evidence about the outcomes of throws
of the die. The agent allocates prior probabilities to competing ‘bias’ hypotheses,
and conditionalizes on evidence as it becomes available, in the standard Bayesian
way. However, qua advocate of IBE, she also adopts the policy of adding ‘bonus
points’ to the posterior probabilities of hypotheses after conditionalization, on the
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basis of how well they explain the evidence. Hypotheses judged to explain the
evidence particularly well get the most ‘bonus points’. For example, if a certain
number has come up repeatedly, the hypothesis that the die is heavily biased in
favour of that number might be thought to explain the evidence very well. Van
Fraassen then proves that this strategy for belief revision is guaranteed to render
one liable to diachronic Dutch-Book. That is, a bookie who knows you employ
this strategy can construct a set of bets which you will judge to be fair, but will
lead you to lose your money whatever happens. (Van Fraassen’s proof is just a
special case of the well known proof, due to David Lewis and Paul Teller, that
Dutch-Book can be made against anyone who adopts an explicit rule for updating
other than conditionalization.) Van Fraassen concludes that a probabilistic version
of IBE violates the demands of Bayesian rationality.
It is important to be clear about exactly what the Lewis–Teller proof shows. The
proof does not show that Dutch-book can be made against anyone who does not
conditionalize. What the proof shows is that, if you adopt an explicitly formulated
plan for updating other than conditionalization, you are liable to Dutch-book.10
The reason for this restriction is simple: the bookie needs to know what your
updating strategy is, to construct a series of bets that leaves you with a certain
loss. Van Fraassen fully appreciates this crucial feature of the Lewis–Teller proof,
though some of his critics do not.11 Hence van Fraassen’s conclusion is not that
it is irrational to favour explanatory hypotheses, but rather that it is irrational to
adopt this policy as a rule.
There are many points at which van Fraassen’s argument might be contested.
Anyone unconvinced of the importance of probabilistic coherence would obviously
reject the move from ‘is liable to Dutch-book’ to ‘is irrational’ outright; but I will
not pursue this line of attack here. However, a related feature of van Fraassen’s
10
Teller summarizes his result as follows: assuming that a plan which leads to certain loss is unreasonable, then ‘no explicitly formulated plan for changing beliefs in the face of new evidence is reasonable
unless, for any [possible experience] Ei for which the plan specifies the beliefs to be adopted should
Ei occur, the plan calls for conditionalization on Ei if Ei occurs’ (Teller, 1973, p. 223). (Teller is making
the standard assumption here that degree of belief functions as a fair-betting quotient.)
11
Stephen Leeds writes: ‘Van Fraassen never explains what the relevant distinction might be between
violating conditionalization by a rule, and violating it at will, in virtue of which the former is irrational,
and the latter is not. Is it that a bookie might know the rule I am using, and take advantage of me, but
he cannot take advantage of me if I follow no rule? Obviously not: I might follow a rule, but keep it
secret; and a bookie might be able to predict my whims’ (Leeds, 1994, p. 220n.). Leeds is simply
wrong here: the distinction he considers is relevant, indeed crucially so. Of course the bookie might
be able to predict your whims, and hence fleece you, if you violate conditionalization, but not according
to a rule. But the point of the Lewis–Teller argument is that the bookie will definitely be able to fleece
you, if you engage in rule-governed violations of conditionalization—that is what makes it irrational
to do so. J. L. Kvanvig’s critique of van Fraassen’s argument is based on the same confusion. Kvanvig
also makes the bizarre remark that diachronic Dutch-book arguments show nothing about rationality,
because they ‘depend illegitimately on privileged information possessed by the bookie’ (Kvanvig, 1994,
p. 332). But this is the reverse of the truth—all the bookie knows is the agent’s updating rule, which
the agent knows too. Indeed Teller goes out of his way to stress that the bookie must not be granted
privileged information, saying ‘exploitation by dint of . . . greater knowledge . . . shows nothing derogatory about the agent’s plan for change of belief’ (Teller, 1973, p. 224).
Van Fraassen’s Critique of Inference to the Best Explanation
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strategy deserves mention. Suppose we grant him his point that using IBE conflicts
with Bayesian rationality constraints. Instead of concluding from this that using
IBE is irrational, why not conclude that the Bayesian model of inductive reasoning
is inadequate? If we think that IBE is an inference pattern widely used in science,
but are convinced by van Fraassen that IBE finds no place within the Bayesian
framework, surely it would be reasonable to view this as a shortcoming of the
Bayesian framework itself? Such an attitude need not involve rejecting the normative significance of Bayesianism altogether; it simply stems from the idea that an
acceptable model of scientific inference must sanction most of the inferences scientists actually make.
It is instructive here to draw a comparison with the ‘problem of old evidence’,
a notorious thorn in the side for Bayesians. This problem stems from the fact that
scientists often take evidence to support a theory, even though the evidence was
known about before the theory was constructed. For example, Einstein took the
precession of Mercury’s perihelion to support his general theory of relativity, even
though this data had been established by the mid-nineteenth century. But on a
Bayesian model, old evidence should have no confirming power; for if P(e)=1,
then it follows immediately that P(h/e)=P(h) for all h, and thus that e does not
confirm h, given the standard Bayesian definition of confirmation. Should we conclude that Einstein and others were irrational in taking old evidence to support
their theories? Virtually all philosophers say no: they see here a sticking point for
Bayesians. ‘If Bayesians cannot accommodate the well established scientific practice of attaching confirmatory weight to old evidence, so much the worse for them’,
is the usual reaction. Parity of reasoning suggests a similar response to van
Fraassen: if Bayesians cannot accommodate the well established scientific practice
of using IBE, so much the worse for the Bayesians.
Though tempting, this response to van Fraassen’s argument is ultimately unsuccessful, for the analogy with the problem of old evidence is imperfect. The problem
of old evidence arises for a fairly obvious reason: the Bayesian model assumes
that scientists are logically omniscient, while in reality they are not. Intuitively,
when scientists attach confirmatory weight to old evidence what they are doing is
responding to a new logical fact, rather than a new empirical fact. In the example
above, Einstein raised his degree of confidence in the general theory of relativity
when he learnt the logical fact that the general theory implies the correct value for
Mercury’s perihelion.12 But the Bayesian model can make no room for learning
logical facts, as it takes all agents to be logically omniscient from the start. Little
wonder, then, that no easy Bayesian reconstruction of Einstein’s reasoning can be
given. The source of the conflict between Bayesianism and the practice of taking
old evidence to confirm is thus transparent: it lies in the unrealistic idealizing
12
This diagnosis of the old evidence problem has been championed by Daniel Garber (1983). See
Earman (1992), ch. 5, for a good discussion.
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assumptions of the Bayesian model itself. But no parallel diagnosis can be applied
to defuse the conflict that van Fraassen finds. If we accept van Fraassen’s way of
modelling IBE within the Bayesian framework—as a rule for adding bonus points
to explanatory hypotheses—the conflict between IBE and Bayesian rationality constraints is inescapable; it cannot be explained away as the result of excessive idealization. So the analogy with the problem of old evidence fails at the crucial point.
But should we accept van Fraassen’s way of modelling IBE within the Bayesian
framework? That is the question to which I turn next.
6. How to Model IBE in Bayesian Terms
There is a general reason for being suspicious of van Fraassen’s claim that IBE
finds no place within the Bayesian framework. For IBE is closely related to the
hypothetico-deductive (H-D) account of confirmation, and Bayesians often pride
themselves on their ability to provide a probabilistic reconstruction of hypotheticodeductivism! The basic H-D idea is that a theory is confirmed when its observational implications turn out to be true. Bayesianism provides a qualified endorsement of this idea: if H entails e, then presuming that neither P(H) nor P(e) equals
one, it follows from the probability calculus that P(H/e)⬎P(H), and thus that e
confirms H.13 Now IBE, as usually presented, is not the same as H-D confirmation—IBE talks of theories explaining rather than entailing the data, and introduces the idea of comparing theories against one another. But given that philosophers have frequently tried to analyse explanation in terms of entailment, the
similarities between IBE and the H-D account are at least as important as their
differences.14 So if recent authors are right to think that Bayesianism vindicates
the basic H-D idea, then van Fraassen’s claim that IBE conflicts with Bayesian
requirements looks prima facie implausible. This suggests that van Fraassen may
not have found the correct way of representing IBE in Bayesian terms.
Recall how van Fraassen models IBE within the Bayesian framework. He
imagines an agent who adds ‘bonus points’ to the posterior probabilities of particularly explanatory hypotheses after conditionalization. This way of representing
IBE is essential to van Fraassen’s Dutch-book argument, but it is by no means
mandatory. Consider a typical example of IBE. A mother takes her five-year-old
child to the doctor. The child is obviously in some distress. On the basis of the
mother’s information, the doctor forms two competing hypotheses: that the child
has pulled a muscle, and that he has torn a ligament; call these H1 and H2 respect13
John Earman (1992) describes this reconstruction of the H-D method as one of the major ‘success
stories’ of Bayesianism.
14
Indeed, there is a case for saying that H-D confirmation is simply a limiting case of IBE, which
results from inserting the D-N account of explanation into the IBE model. Relative to more recent
accounts of explanation (see note 9), the similarity between IBE and H-D confirmation is less obvious.
But given that Hempel’s basic idea—that explanation is entailment in reverse—is not too far off the
mark, at least for a large class of cases, the claim in the text is justified.
Van Fraassen’s Critique of Inference to the Best Explanation
703
ively. A keen advocate of IBE, the doctor examines the child carefully, and decides
that H2 offers the better explanation of the observed symptoms; she therefore tentatively accepts H2—though she does not believe it outright—and rejects H1.
Suppose we ask the doctor to justify her reasoning. She answers: ‘firstly, preadolescent children very rarely pull muscles, but often tear ligaments. Secondly,
the symptoms, though compatible with either diagnosis, are exactly what we would
expect if the child has torn a ligament, though not if he has pulled a muscle.
Therefore the second hypothesis is preferable.’ This reasoning can be represented
in probabilistic terms as follows: ‘given the background information, the prior probability of H2 is higher than that of H1; the probability of the evidence conditional
on H2 is greater then its probability conditional on H1, therefore the posterior probability of H2 is greater than that of H1.’ Thus represented, the doctor’s use of IBE
is not incoherent by Bayesian standards; on the contrary, she has used explanatory
considerations as an aid for calculating the priors and likelihoods needed to apply
Bayes’s theorem itself.15
So we have two possible ways of representing our doctor’s reasoning in probabilistic terms—van Fraassen’s and the one suggested above. On van Fraassen’s
account, the doctor’s personal probability function undergoes a two-stage evolution—she conditionalizes then adds bonus points—while on my account, her probability function undergoes a one-stage evolution. This points to a general reason
for favouring my Bayesian representation of IBE over van Fraassen’s. For normally, when we engage in the type of inductive reasoning that proponents of IBE
are trying to model, there is no hint of a two-stage process—first responding to
the new evidence, and then taking explanatory considerations into account; rather,
we use explanatory considerations in order to decide how to respond to new evidence—the two processes are one. Modelling IBE in the way I have suggested—
as a way of determining priors and likelihoods—captures the phenomenology of
inferring to the best explanation much better than van Fraassen’s account.
It appears, then, that the conflict between IBE and Bayesianism alleged by van
Fraassen depends entirely on an idiosyncratic way of representing IBE in probabilistic terms. The correct way of representing IBE, I suggest, views the goodness
of explanation of a hypothesis vis-à-vis a piece of data as reflected in the prior
probability of the hypothesis P(H), and the probability of the data given the hypothesis P(e/H). The better the explanation, the higher is one or both of these probabilities. Relative to this account, favouring a hypothesis on the grounds that it
provides a better explanation of one’s data than other hypotheses, and indeed making it a rule to do so, is perfectly consistent with Bayesian principles. For fixed
15
Interestingly, Gilbert Harman has urged a point similar to this, by way of defending the autonomy
of IBE from Bayesian encroachment. He writes: ‘perhaps reasoning is concerned with subjective probability, but it is important to see that one fixes such probability by appeal to explanatory plausibility
rather than vice versa . . . one arrives at an estimate of subjective probability by considering the plausibility of various explanations’ (Harman, 1970, p. 94).
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P(e), Bayes’s theorem tells us that P(T/e) is an increasing function of P(T) and
P(e/T) and nothing else; so ending up with the highest degree of belief in the theory
which explains the data best is exactly what the good Bayesian conditionalizer
should do. No better reconciliation between Bayesianism and IBE could be
hoped for.
In the next section, I examine three possible objections that van Fraassen could
make to my attempt to marry IBE with Bayesianism.
7. Three Possible Objections and Replies
Objection (i): the claim that how well a theory T explains evidence e is reflected
by the terms P(T) and P(e/T) in Bayes’s theorem is entirely ad hoc; it admits of
no genuine rationale.
Reply: Not so. Factoring explanatory power into these two components reflects a
familiar feature of the concept of explanation. Goodness of explanation depends
on both the existence of an appropriate relation between explanans and explanandum, and on the plausibility of the explanans. Consider the question: does Newton’s
theory of gravitation explain Kepler’s laws of planetary motion? Intuitions differ
here: some people say yes, since Newton’s theory yields an elegant derivation of
Kepler’s laws; others say no, since contemporary physics tells us that Newton’s
theory is false. The existence of these conflicting intuitions is neatly explained by
viewing explanatory goodness as a composite of P(T) and P(e/T).
The same point can be made by modifying slightly the story of the doctor trying
to compare the pulled muscle hypothesis (H1) and the torn ligament hypothesis
(H2). Suppose now that torn ligaments are very rare in pre-adolescent children, but
as before, the data are just what we would expect, were the child’s ligaments in
fact torn. Intuitively, the torn ligament hypothesis is now less good an explanation
than it was in the original scenario. Although P(e/H2) is still high, the low antecedent probability of H2, given the background knowledge, reduces its explanatory
goodness. Again, we see that goodness of explanation is a function of both prior
probability and likelihood.
Interestingly, the account of IBE developed by Lipton (1991) explicitly distinguishes two factors, called ‘explanatory loveliness’ and ‘explanatory likeliness’,
which appear to correspond roughly to the terms P(e/T) and P(T) respectively. To
decide whether a given explanation of a phenomenon is lovely, we ask the question:
if it were true, would it render the phenomenon intelligible? Explanatory likeliness,
on the other hand, takes into account the overall credibility of the explanation.
Since Lipton’s account of IBE is developed with no reference to probabilistic concepts, my suggestion that explanatory goodness is a composite of P(e/T) and P(T)
dovetails neatly with his likeliness/loveliness distinction.16
16
One of Lipton’s examples appears to undermine my attempt to render his loveliness/likeliness
distinction in probabilistic terms. Lipton cites ‘opium puts people to sleep because of its dormative
powers’ as an example of a very likely but unlovely explanation: it is almost certainly true, but most
Van Fraassen’s Critique of Inference to the Best Explanation
705
Objection (ii): but there are many cases where both P(T) and P(e/T) are high,
and yet T does not explain e at all, less still provide the best explanation of e.
Reply: true but irrelevant. Certainly, T can be a well-established theory which
entails but fails to explain e, as many counterexamples to the D-N model of explanation show; in such a case, P(T) will be high and P(e/T) equal to one. But this
does not undermine my proposed way of modelling IBE in Bayesian terms. It only
highlights the obvious fact that not all cases of updating by Bayesian conditionalization involve explanatory considerations. My claim is that when scientists do attach
confirmatory weight to a theory because the theory yields a better explanation of
the evidence than rival theories, this piece of reasoning can be given a plausible
reconstruction in Bayesian terms. That is compatible with allowing that not all
cases of conditionalization are cases of IBE. So the fact that high values for P(T)
and P(e/T) do not suffice for T to explain e is not to the point.
Nor does the position I am defending strictly require that high values for P(T)
or P(e/T) are necessary for T to explain e; though in fact this claim is quite plausible. Why would one say that T is a good explanation of e, if one thought that T
were both implausible in itself, and conferred little credibility on e? What my
position does require is this: if one regards T1 as a better explanation of e than
T2, then one must either set P(e/T1)⬎P(e/T2), or P(T1)⬎P(T2), or both. This is
crucial to my proposed reconciliation of IBE with Bayesianism, and it seems perfectly reasonable. Indeed, it is hard to see what it could mean to believe that T1
explains e better than T2 if one’s personal probability function satisfied neither of
the above inequalities.17
Objection (iii): your arguments ultimately fail to engage with van Fraassen’s.
Van Fraassen was attacking the idea of a ‘recipe for adjusting our personal probabilities, in response to new experience, under the aegis of explanatory success’.
You have not produced such a recipe. The only updating recipe in your examples
is Bayesian conditionalization. You have simply shown that many cases of IBE can
be modelled as cases of conditionalization. So IBE has no independent rational
authority, on your account—its rational credentials are wholly derivative from
those of Bayesian conditionalization.
Reply: well, what you say is partly right. IBE, as defended here, is not strictly a
recipe for adjusting personal probabilities, at least if a ‘recipe’ is meant to subsume
unenlightening. But the probability that opium induces sleep, given that it has dormative powers, is
presumably very high, so if Lipton’s explanatory loveliness if reflected in high conditional probability,
as I have suggested, this should count as a lovely explanation. However in my view, ‘opium puts people
to sleep because of its dormative powers’ is not an explanation at all, so the example does not actually
tell against my probabilistic construal of Lipton’s distinction.
17
In this paragraph, I am assuming that we are not dealing with an ‘old evidence’ scenario, i.e. that
P(e)⫽1, so that the likelihood terms P(e/T1) and P(e/T2) can differ. This assumption is adopted partly
for simplicity, and partly because van Fraassen’s Dutch-book argument against IBE, to which I am
responding, obviously makes the assumption too. Intuitively, in an old evidence scenario, the relevant
question is whether P(e/T1) or P(e/T2) would have been bigger if one hadn’t already known e. However,
appealing to counterfactual degrees of belief in this way is fraught with difficulty, unsurprisingly. See
Earman (1992), ch. 5, and Eels (1985).
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every case of personal probability change; for not all such changes involve explanatory considerations. But van Fraassen has offered no reason for construing IBE so
narrowly, nor cited any evidence that IBE is viewed this way by its advocates.18
In any case, my analysis certainly refutes van Fraassen’s conclusion that ‘we should
not listen to anyone who preaches a probabilistic version of IBE, whatever the
details’, for this conclusion makes no mention of ‘recipes’.
As for whether IBE’s rational credentials are wholly derivative, the issue here
is subtle. IBE belongs to an old tradition of trying to describe the scientific method
in informal or semi-formal terms, a tradition that includes Descartes, Newton, Mill,
Whewell, Herschel and Popper among its ancestors. Writers in the Bayesian tradition have often tried to produce probabilistic reconstructions of the various
methodological strategies that the first tradition has uncovered.19 A fundamental,
and unresolved question is whether the Bayesians are explaining, or just representing these strategies. Those who say ‘representing’ think that the Bayesian
apparatus is ‘just a kind of tally device used to represent a more fundamental sort
of reasoning, whose essence does not lie in the assignment of little numbers to
propositions in accord with the probability axioms’, in the words of Earman (1992,
p. 59); those who say ‘explaining’ deny that there is a more fundamental sort of
inductive reasoning.
A proper response to the query about the derivative status of IBE would require
a resolution of the ‘representation versus explanation’ issue, which is beyond the
scope of this paper. However in the next section, I point to a number of facets of
inductive reasoning where Bayesianism is silent, but IBE provides illumination.
8. IBE Illuminates Where Bayesianism is Silent
In Section 3, I noted that van Fraassen construes IBE as a selection procedure
that operates on hypotheses that already exist, rather than as a way of generating
hypotheses de novo. It should now be clear why van Fraassen does that. In order
to generate the alleged tension between IBE and Bayesianism, he needs a situation
to which the Bayesian model can actually be applied. And notoriously, Bayesians
have nothing to say about situations where agents invent new hypotheses in
response to experience. Change of opinion of this sort eludes Bayesian represen18
C. S. Peirce certainly did not regard his abduction as the only form of non-deductive inference,
for he explicitly contrasted it with induction. Admittedly, Harman does seem to suggest that all nondeductive inferences are subsumable under IBE, but here he is surely exaggerating. Indeed Harman’s
attempt to show that ‘next-case induction’ is really IBE in disguise is patently unconvincing. Regarding
the inference from ‘all observed A’s are B’s’ to ‘the next observed A will be B’, Harman writes: ‘here,
one must compare the hypothesis that the next A will be different from the preceding A’s with the
hypothesis that the next A will be similar to the preceding A’s’, recommending that we choose the
hypothesis that is ‘better in the light of all the evidence’ (Harman, 1965, p. 91). But this says nothing
about explanation! Picking the hypothesis that is ‘better in the light of all the evidence’ cannot be bad
advice, but the distinctive idea of IBE is supposed to be that one picks a hypothesis that explains
the evidence.
19
Horwich (1982) and Howson and Urbach (1989) are the most prominent recent examples.
Van Fraassen’s Critique of Inference to the Best Explanation
707
tation entirely, for Bayesian models assume the domain of the agent’s probability
function to remain identical, before and after the receipt of new evidence. So van
Fraassen’s exclusion of IBE from the ‘context of discovery’ was actually essential
to his argument. Only by viewing IBE as a decision procedure that operates on
pre-existing hypotheses could van Fraassen generate the supposed conflict between
IBE and Bayesian updating.
But of course, there is no real reason to exclude IBE from the context of discovery; I followed van Fraassen’s lead purely for the sake of argument. Explanatory
considerations invariably guide the construction of new theories; indeed, often the
point of inventing a new theory is to explain an anomalous phenomenon. Advocates
of IBE have emphasised this; typically, they have not regarded IBE as a selection
procedure operating on already existing hypotheses, à la van Fraassen. For C. S.
Peirce, abduction certainly played a role in the context of discovery: ‘abduction is
the process of forming an explanatory hypothesis. It is the only logical operation
which introduces any new ideas’ (5.171). And discussing the role of abduction in
perceptual judgements, Peirce wrote: ‘the abductive suggestion comes to us like a
flash’ (5.182).20 More recently, Peter Lipton has cited the ability of the IBE model
to illuminate the process by which new theories are invented and discovered, as
one of the major advantages of IBE over hypothetico-deductivism (Lipton, 1991,
p. 88). To the extent that Peirce’s and Lipton’s views are typical of how IBE is
regarded by its advocates, van Fraassen has introduced a significant element of
distortion into the position he is attacking.
These reflections point to one clear advantage of IBE over Bayesianism. In those
cases where agents respond to new evidence by inventing new hypotheses, the
Bayesian model is silent. But IBE provides a useful, if schematic account of what
is going on: the agents are trying to explain the new evidence. They think that the
best, or perhaps the only, explanation of the evidence lies outside the space of
possibilities they have previously considered, so rather than conditionalizing, they
invent a new hypothesis. It is worth stressing that van Fraassen himself does not
regard such ‘non-conditionalizing’ changes of opinion as in any way illegitimate;
he does not think we are ever rationally compelled to conditionalize. But by abjuring the concept of IBE altogether, van Fraassen deprives himself of a decent theoretical description of what is going on, for at least a large range of non-conditionalizing changes of opinion.21 In an area where Bayesianism is notoriously silent, IBE
provides a modicum of illumination.
20
It should be noted, however, that Peirce’s writings are sometimes ambiguous on the question of
whether abduction is a process of forming new hypotheses, or of selecting among ones that already
exist. According to Fann (1970), Peirce’s views on this issue evolved over the course of his life.
21
In addition to lacking a good description of these cases, van Fraassen is unable to explain why
agents sometimes accommodate new evidence by inventing new theories, rather than by conditionalizing. Arguably, IBE does furnish such an explanation—the agents think the best explanation of the
evidence lies outside the range of possibilities previously considered—though this is perhaps more
controversial than the point about description in the text.
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I have focused on the problem posed for the Bayesian when agents accommodate
their experiences by inventing new theories, rather than by conditionalizing.
Charles Chihara (1987) has described a related type of case, which is in some ways
even more problematic for the Bayesian. In Chihara’s example, a prince is imprisoned in a room for a week. Each morning, he is given a crimson ball containing
a number. On the seventh morning, he has to guess the number contained in the
last ball; if he succeeds, he wins the princess, if he fails, he is thrown to the lions.
By the sixth day, the prince is still unable to see any pattern in the sequence of
numbers he has been given. All six numbers are odd two-digit natural numbers;
the prince assumes that the seventh will be too, but that still leaves 84 equi-probable
alternatives to choose between. Then that afternoon, he has a flash of inspiration.
He notices that the six numbers he has are the Gödel numbers of the first six letters
of the word ‘crimson’ (according to the system of Gödel numbering used by the
King’s logician). Unsurprisingly, the prince’s degree of belief in the hypothesis
that the seventh ball will contain the Gödel number of the letter ‘n’, 69, soars. The
prince is right, and survives.22
Chihara argues, convincingly, that the prince’s reasoning cannot be modelled in
Bayesian terms. Chihara’s case differs from the sort of theory-invention envisaged
previously in two ways. First, the change in the prince’s degree of belief in the
hypothesis that the seventh number will be 69 was not the result of any new data;
all the data was already available. Second, before noticing the pattern of Gödel
numbers, the prince had already assigned a degree of belief to the hypothesis that
the seventh number will be 69. As Chihara notes, merely thinking up new possibilities can dramatically alter the distribution of subjective probabilities to propositions one has already explicitly considered. While the Bayesian can give no
good account of this, the proponent of IBE can. Explanatory considerations clearly
played a role in the prince’s reasoning. The prince realised that the best explanation
of his data was that the sequence of numbers was a sequence of Gödel numbers
spelling out the word ‘crimson’; realising this led to the dramatic increase in his
degree of confidence that the seventh number would be 69. IBE yields a simple
rationalization of the change in the prince’s personal probability function. Anyone
who agrees that the prince was behaving rationally, but eschews the notion of IBE
outright, owes us an alternative account of what the prince was doing.
In Section 6 I argued, contra van Fraassen, that IBE can be reconciled with
Bayesian conditionalization. In this section, I have argued that IBE can accommodate certain aspects of our inductive practices which the Bayesian cannot. This may
look like a contradiction; but appearances deceive. The point is this. To generate the
alleged tension between IBE and Bayesian conditionalization, van Fraassen had to
do two things. First, he had to exclude IBE from the context of discovery, in order
22
Note how well Peirce’s description—‘the abductive suggestion comes to us like a flash’—fits Chihara’s example.
Van Fraassen’s Critique of Inference to the Best Explanation
709
to construct a situation to which the Bayesian model is applicable. Second, he had
to model IBE in Bayesian terms in an idiosyncratic way. The apparently contradictory aspects of my argument simply focus on these two different aspects of van
Fraassen’s treatment of IBE. Where the Bayesian model is applicable, that is, where
the ‘space of possibilities’ remains fixed and no new hypotheses are invented, using
IBE can be rendered compatible with Bayesian conditionalization, as Sections 6
and 7 establish. In at least some cases where the Bayesian model is not applicable,
IBE nonetheless provides an illuminating account of what is going on, as the argument of this section establishes.
9. Conclusion
According to van Fraassen, when IBE is scrutinized carefully, its credentials are
found seriously wanting. By scrutinizing van Fraassen’s own arguments, we see
that this conclusion can be resisted. Van Fraassen’s point of departure was the ‘bad
lot’ argument. That argument forced the defender of IBE to retrench, and talk the
language of degrees of belief. Van Fraassen then argued that IBE conflicts with
Bayesian rationality constraints; this argument was shown to depend on an idiosyncratic way of representing IBE in probabilistic terms. A better way was proposed:
goodness of explanation is reflected in the priors and likelihoods needed to apply
Bayes’s theorem itself. This proposal was defended against various objections.
Finally, I noted that IBE can handle certain types of belief revision where conceptual change is involved that are notoriously problematic for the Bayesian.
Of course, the foregoing analysis leaves plenty of questions unanswered. I have
said nothing about what the relation of explanation actually consists in, and offered
no criteria for ranking explanations in order of their goodness. It may seem surprising that a defence of IBE can remain neutral on such key questions. But van
Fraassen’s attack on IBE takes no stand on these questions either, and my aim has
only been to show that IBE can withstand the force of that attack. Darwin’s ‘method
of arguing’ lives to fight on.
Acknowledgements—Thanks to Atocha Aliseda, Bill Newton-Smith, Peter Lipton, Dorothy Edgington
and James Ladyman for discussion and comments.
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