Inference to the Best Explanation (Andrew Pickin)
Outline
In the first section, Lipton’s partial solution to the descriptive problem of induction
is sketched; the second section contemplates an objection made against Lipton’s
account; the third section is the conclusion.
Introduction
When thinking about induction, it is useful to differentiate the problem of
description from the problem of justification. The former is the problem of giving a
satisfying account of the way in which we make inductive inferences, both in science
and in ordinary life. The latter is the problem of certifying that our inductive
inferences fulfil the role that they are supposed to fulfil. If, for instance, we think that
inductive inferences ought to be rational, then the problem of justification is the
problem of establishing that they are rational.
Lipton proposes Inference to the Best Explanation as a partial solution to the
problem of description. Inference to the Best Explanation1, henceforth known as IBE,
is only intended as a partial solution because it ‘can only ever be a part of a very
complicated story’2; IBE does not offer a complete account of the way in which we
make inductive inferences. The positive claim of IBE is that explanatory
considerations are, in practice, an important guide to making inferences, because we
often infer the hypothesis that would, if true, best explain the evidence before us.
Hence the phrase Inference to the Best Explanation.
Lipton identifies two sorts of best explanation: likeliest explanations and loveliest
explanations. The likeliest explanation amongst competing explanations is the most
probable of the competitors. The loveliest is the explanation that would, if true, offer
the greatest increase in understanding. The two categories are distinct; given a pool of
competing explanations, it is possible for one explanation to be the likeliest, and
another the loveliest. Lipton does not mean by IBE, Inference to the Likeliest
Explanation. The reason for this is that Inference to the Likeliest Explanation, which
1
In this essay, Inference to the Best Explanation will always refer to Lipton’s version of Inference to
the Best Explanation.
2
Lipton (2004:62)
says that inferences are guided by considering which amongst competing explanations
is most probable, is empty. Alternatively, Lipton says that we should construe IBE as
Inference to the Loveliest Explanation. IBE then becomes the stronger claim that
inferences are guided by considering which amongst competing explanations is
loveliest. If we assume that we aim to make likely inferences, then this amounts to
saying that loveliness is our guide to likeliness.
At this stage, there are two questions that we should ask: First, what is an
explanation? Second, what are the factors that make an explanation the loveliest
explanation?
In response to the first question, Lipton adopts the causal model of explanation. The
basic premise of the causal model is that to explain a phenomenon is to give
information about its causal history. This immediately precludes the causal model
from being a complete account of explanation. The reason for this is that there exist
non-causal explanations; for example, mathematical explanations. However, Lipton’s
discussion of the causal model3 is not meant to be a complete account. Rather, the
idea is to take a model that is plausible in many cases—the vast majority of
explanations do seem to be causal explanations—and develop the model so that it
becomes a fuller account. An obvious gap in the causal model as stated is that it fails
to account for the causal selectivity of causal explanations; it cannot be that any piece
of information about a phenomenon’s causal history is an explanation of the
phenomenon. Lipton focuses his discussion of the causal model on filling that gap.
In reply to our second question, that of determining the factors that make an
explanation the loveliest explanation, Lipton first suggests scope, precision,
mechanism, unification, and simplicity. He writes,
Better explanations explain more types of phenomena, explain them with
greater precision, provide more information about underlying mechanisms,
unify apparently disparate phenomena, or simplify our overall picture of the
world.4
3
4
Lipton (2004), chap. 3
Lipton (2001:106)
Further, he proposes that the concealed structure of a request for the explanation of
some phenomenon will often have the form of a contrastive why-question. (A
contrastive why-question is a question of the form, ‘Why P rather than Q?’) Since
Lipton thinks that a necessary feature of a causal explanation for ‘Why P rather than
Q?’ is that it cites ‘a causal difference between P and not-Q, consisting of a cause of P
and the absence of a corresponding event in the case of not-Q’5, he is provided with
an additional method for evaluating explanations.
Salmon’s criticism
Salmon thinks that IBE is untenable. He holds that the solution to the problem of
description can be found in a Bayesian approach. His Bayesian account has inference
as a two-stage process.6 Suppose that we are trying to choose between a large group
of competing hypotheses to account for some evidence E. In the first stage we make
the group smaller by eliminating those hypotheses with low prior probability. The
prior probability of a hypothesis is the probability of the hypothesis being true on
suitable background evidence. In the second stage, we calculate the posterior
probability of each hypothesis using Bayes’s theorem:
P(H│E.B) = [P(H│B)P(E│H.B)] ∕ P(E│B)7
To do this we need to estimate P(E│H.B), the likelihood of E, and P(E│B), the prior
probability (or expectedness, as Salmon calls it) of the evidence. The remaining
hypothesis (from the first stage) with the highest posterior probability is the
hypothesis that we infer—providing its posterior probability is high enough to satisfy
us.
Salmon believes that IBE is untenable because he thinks that explanatory
considerations play a much smaller role in inductive inferences than the role that IBE
assigns them. Considerations that are broadly explanatory will enter into determining
the large group of hypotheses, but there is no reason to suppose that explanatory
virtues (those features of explanations that make them lovely) should enter into the
5
Lipton (2004:42)
Salmon (2001a:83-84)
7
H is the hypothesis; B is the suitable background evidence.
6
first stage, of determining the prior probabilities, or the second stage, of determining
the posterior probabilities. To give weight to his argument, Salmon presents the
worked-bone example.
The worked-bone example may be summarised as follows: Not long ago, an object
that was a piece of worked bone—a human artifact—was discovered in the northern
Yukon. By radiocarbon dating its age was set at 27,000 years. However, at the time of
discovery, it was believed that humans had inhabited the area for only 12,000 years.
Three hypotheses were entertained: (1) the artifact was created in the Yukon about
27,000 years ago by a human artisan who was a member of the continuous human
population of the New World that has existed from then until now; (2) the artifact was
created in the Yukon about 27,000 years ago by a member of a human group that
temporarily occupied the New World around that time, but which subsequently
returned to the Old World or left no descendants; (3) the artifact was created in the
Yukon much more recently from the bone of an animal that had died around 27,000
years ago, whose carcass had been preserved in a frozen condition for many
millennia.
The point of this example is to show that even in scenarios where the case for IBE is
strongest, the Bayesian account trumps it. And since the two accounts are
incompatible, at least according to Salmon, IBE cannot be right even in the scenarios
where it seems most plausible. In the following quote, Salmon explains why he thinks
that the worked-bone scenario is a promising one for IBE:
The problem with the explanation using the first hypothesis is that it leaves
unexplained a gap of several thousand years in the evidential record. Given that
a great deal of archaeological effort has been expended in seeking out the
earliest sites of human habitation, this gap is implausible…The problem with
the explanation using the second hypothesis is its ad hoc character. Again, an
explanatory gap appears…The virtue of the third hypothesis is absence of any
such explanatory gaps. Following this line of reasoning, we could say that the
third hypothesis is most likely the true hypothesis because it accords best with
our total body of relevant evidence.8
8
Salmon (2001a:78-79)
In spite of this, Salmon thinks that the Bayesian account provides the accurate
description of how archaeologists came to accept the third hypothesis. By Bayes’s
theorem, the hypothesis whose product of prior probability with likelihood is greatest,
will have the greatest posterior probability.9 Salmon claims that the third hypothesis
has the greatest product, and that determining this does not depend on explanatory
considerations. He writes:
I do not believe that archaeologists set up three different explanations,
comparing them with respect to their explanatory virtues without regard for the
truth of the premises, and then say that the premises of the best are most likely
to be true. Rather, I think, they make a rough estimate of the prior probabilities
of the hypotheses, make (at least implicitly) Bayesian-type inferences to the
posterior probabilities of the hypotheses, and then prefer (but not necessarily
adopt), for purposes of explaining the existence of the artifact, the one with the
highest posterior probability.10
The final part of this passage shows that Bayesianism puts inference before
explanation; we make an inference, and if we want to give an explanation of the
evidence then we are entitled to appeal to the inferred hypothesis. With IBE, on the
other hand, explanation is prior to inference. I think that this is the fundamental reason
why Salmon sees a conflict between Bayesianism and IBE.
Lipton’s strategy for meeting Salmon’s criticism is to show that the perceived
conflict between IBE and Bayesianism is illusory. This allows him to accept that
Bayesian considerations are involved in the worked-bone example—for instance, he
can accept that the archaeologists will prefer the hypothesis with the highest posterior
probability, and that judgements of prior probabilities and likelihoods play a role in
the inference,—without viewing this as a problem for IBE. If he can show that IBE
and Bayesianism are compatible, then Salmon’s criticism is deflected. However, even
if compatibility is established, the worked-bone example still poses a threat to IBE.
Recall that the central claim of IBE is that explanatory considerations guide
inferences; ‘scientists judge that an hypothesis is likely to be correct because it is
9
Salmon (2001a:85): see equation (14)
Salmon (2001a:83)
10
lovely’. What Lipton needs to do to successfully defend IBE from the worked-bone
example is not only show that IBE and Bayesianism are compatible, but also give
credibility to the idea that IBE is playing an important part in the inference to the third
hypothesis. What Lipton does to meet this challenge is demonstrate how explanatory
considerations help to ‘lubricate the Bayesian mechanism’11 in general.
Lipton suggests four ways in which the Bayesian mechanism is lubricated. I sketch
the first three below. (The fourth is somewhat peripheral in this discussion.)
1.Lipton advances that explanatory considerations help to assess likelihoods, by
suggesting that we sometimes judge how likely E is on H by considering how well
H would explain E.
2.He claims that explanatory considerations facilitate the determination of prior
probabilities; for example, explanatory virtues such as unification and simplicity
seem to play this role.
3.Bayesianism, as presented in this essay, does not tell us which evidence, and which
background evidence, should be fed into Bayes’s theorem. Lipton suggests that
explanatory considerations can help here as well. For example, we often discover
supporting evidence for a hypothesis by seeing what it would explain.
Conclusion
It is hard to come down emphatically on either side of the Lipton-Salmon debate.
For one thing, both IBE and the Bayesian account are complex and carefully
constructed descriptions of a complicated process: inductive inference. Thus, there are
no easy arguments to refute either. Secondly, Lipton and Salmon agree on many
issues, and on the issues on which they do disagree, their differences, as Salmon
acknowledges, are subtle.12 It is difficult to see a clear-cut ideological divide—in stark
contrast to many other philosophical debates.
Salmon’s key contention is that explanatory considerations do not have to enter into
the Bayesian evaluation.13 In support of this contention he gives several examples in
which it appears that explanatory considerations are playing a part, but on closer
11
Lipton (2001:111)
Salmon (2001b:121)
13
Salmon (2001b:129)
12
examination it turns out that the judgement is wrong. Lipton, on the other hand,
provides several examples to attempt to persuade us that explanatory considerations
are present, and are guiding the Bayesian evaluation. A proper adjudication of these
two views would rely on a close study of the examples provided by the proponents.
Unfortunately, I have not had time to carry out that study here.
Bibliography
Lipton, P., (2004). Inference to the Best Explanation. London and New York:
Routledge
Lipton, P., (2001). ‘Is Explanation a Guide to Inference?’, in G. Hon and S. S.
Rakover (eds) Explanation: Theoretical Approaches and Applications, Dordrecht:
Kluwer
Salmon, W., (2001a). ‘Explanation and Confirmation: A Bayesian Critique of
Inference to the Best Explanation’, in G. Hon and S. S. Rakover (eds) Explanation:
Theoretical Approaches and Applications, Dordrecht: Kluwer
Salmon, W., (2001b). ‘Reflections of a Bashful Bayesian: A Reply to Peter Lipton’, in
G. Hon and S. S. Rakover (eds) Explanation: Theoretical Approaches and
Applications, Dordrecht: Kluwer