## 1. Abduction: The General Idea



You happen to know that Tim and Harry have recently had a terrible row
that ended their friendship. Now someone tells you that she just saw
Tim and Harry jogging together. The best explanation for this that you
can think of is that they made up. You conclude that they are friends
again.



One morning you enter the kitchen to find a plate and cup on the
table, with breadcrumbs and a pat of butter on it, and surrounded by a
jar of jam, a pack of sugar, and an empty carton of milk. You conclude
that one of your house-mates got up at night to make him- or herself a
midnight snack and was too tired to clear the table. This, you think,
best explains the scene you are facing. To be sure, it might be that
someone burgled the house and took the time to have a bite while on
the job, or a house-mate might have arranged the things on the table
without having a midnight snack but just to make you believe that
someone had a midnight snack. But these hypotheses strike you as
providing much more contrived explanations of the data than the one
you infer to.



Walking along the beach, you see what looks like a picture of Winston
Churchill in the sand. It could be that, as in the opening pages of
Hilary Putnam's book *Reason, Truth, and History*,
(1981), what you see is actually the trace of an ant crawling on the
beach. The much simpler, and therefore (you think) much better,
explanation is that someone intentionally drew a picture of Churchill
in the sand. That, in any case, is what you come away believing.



In these examples, the conclusions do not follow logically from the
premises. For instance, it does not follow logically that Tim and
Harry are friends again from the premises that they had a terrible row
which ended their friendship and that they have just been seen jogging
together; it does not even follow, we may suppose, from all the
information you have about Tim and Harry. Nor do you have any useful
statistical data about friendships, terrible rows, and joggers that
might warrant an inference from the information that you have about
Tim and Harry to the conclusion that they are friends again, or even
to the conclusion that, probably (or with a certain probability), they
are friends again. What leads you to the conclusion, and what
according to a considerable number of philosophers may also warrant
this conclusion, is precisely the fact that Tim and Harry's
being friends again would, if true, *best* *explain* the
fact that they have just been seen jogging together. (The proviso that
a hypothesis be true if it is to explain anything is taken as read
from here on.) Similar remarks apply to the other two examples. The
type of inference exhibited here is called *abduction* or,
somewhat more commonly nowadays, *Inference to the Best*
*Explanation*.


### 1.1 Deduction, induction, abduction



Abduction is normally thought of as being one of three major types of
inference, the other two being deduction and induction. The
distinction between deduction, on the one hand, and induction and
abduction, on the other hand, corresponds to the distinction between
necessary and non-necessary inferences. In deductive inferences, what
is inferred is *necessarily* true if the premises from which it
is inferred are true; that is, the truth of the premises
*guarantees* the truth of the conclusion. A familiar type of
example is inferences instantiating the schema



> 
> All *A*s are *B*s.
>   
> 
> *a* is an *A*.
>   
> 
> Hence, *a* is a *B*.
> 



But not all inferences are of this variety. Consider, for instance,
the inference of "John is rich" from "John lives in
Chelsea" and "Most people living in Chelsea are
rich." Here, the truth of the first sentence is not guaranteed
(but only made likely) by the joint truth of the second and third
sentences. Differently put, it is not necessarily the case that if the
premises are true, then so is the conclusion: it is logically
compatible with the truth of the premises that John is a member of the
minority of non-rich inhabitants of Chelsea. The case is similar
regarding your inference to the conclusion that Tim and Harry are
friends again on the basis of the information that they have been seen
jogging together. Perhaps Tim and Harry are former business partners
who still had some financial matters to discuss, however much they
would have liked to avoid this, and decided to combine this with their
daily exercise; this is compatible with their being firmly decided
never to make up.



It is standard practice to group non-necessary inferences into
*inductive* and *abductive* ones. Inductive inferences
form a somewhat heterogeneous class, but for present purposes they may
be characterized as those inferences that are based purely on
statistical data, such as observed frequencies of occurrences of a
particular feature in a given population. An example of such an
inference would be this:



> 
> 96 per cent of the Flemish college students speak both Dutch and
> French.
>   
> 
> Louise is a Flemish college student.
>   
> 
> Hence, Louise speaks both Dutch and French.
> 



However, the relevant statistical information may also be more vaguely
given, as in the premise, "Most people living in Chelsea are
rich." (There is much discussion about whether the conclusion of
an inductive argument can be stated in purely qualitative terms or
whether it should be a quantitative one--for instance, that it
holds with a probability of .96 that Louise speaks both Dutch and
French--or whether it can *sometimes* be stated in
qualitative terms--for instance, if the probability that it is
true is high enough--and sometimes not. On these and other issues
related to induction, see Kyburg 1990 (Ch. 4). It should also be
mentioned that Harman (1965) conceives induction as a special type of
abduction. See also Weintraub 2013 for discussion.)



The mere fact that an inference is based on statistical data is not
enough to classify it as an inductive one. You may have observed many
gray elephants and no non-gray ones, and infer from this that all
elephants are gray, *because that would* *provide the best
explanation for why you have observed so many gray elephants*
*and no non-gray ones*. This would be an instance of an
abductive inference. It suggests that the best way to distinguish
between induction and abduction is this: both are *ampliative*,
meaning that the conclusion goes beyond what is (logically) contained
in the premises (which is why they are non-necessary inferences), but
in abduction there is an implicit or explicit appeal to explanatory
considerations, whereas in induction there is not; in induction, there
is *only* an appeal to observed frequencies or statistics. (I
emphasize "only," because in abduction there may also be
an appeal to frequencies or statistics, as the example about the
elephants exhibits.)



A noteworthy feature of abduction, which it shares with induction but
not with deduction, is that it violates *monotonicity*, meaning
that it may be possible to infer abductively certain conclusions from
a *subset* of a set *S* of premises which cannot be
inferred abductively from *S* as a whole. For instance, adding
the premise that Tim and Harry are former business partners who still
have some financial matters to discuss, to the premises that they had
a terrible row some time ago and that they were just seen jogging
together may no longer warrant you to infer that they are friends
again, even if--let us suppose--the last two premises alone
do warrant that inference. The reason is that what counts as the best
explanation of Tim and Harry's jogging together in light of the
original premises may no longer do so once the information has been
added that they are former business partners with financial matters to
discuss.


### 1.2 The ubiquity of abduction



The type of inference exemplified in the cases described at the
beginning of this entry will strike most as entirely familiar.
Philosophers as well as psychologists tend to agree that abduction is
frequently employed in everyday reasoning. Sometimes our reliance on
abductive reasoning is quite obvious and explicit. But in some daily
practices, it may be so routine and automatic that it easily goes
unnoticed. A case in point may be our trust in other people's
testimony, which has been said to rest on abductive reasoning; see
Harman 1965, Adler 1994, Fricker 1994, and Lipton 1998 for defenses of
this claim. For instance, according to Jonathan Adler (1994, 274f),
"[t]he best explanation for why the informant asserts that
*P* is normally that ... he believes it for duly responsible
reasons and ... he intends that I shall believe it too,"
which is why we are normally justified in trusting the
informant's testimony. This may well be correct, even though in
coming to trust a person's testimony one does not normally seem
to be aware of any abductive reasoning going on in one's mind.
Similar remarks may apply to what some hold to be a further, possibly
even more fundamental, role of abduction in linguistic practice, to
wit, its role in determining what a speaker means by an utterance.
Specifically, it has been argued that decoding utterances is a matter
of inferring the best explanation of why someone said what he or she
said in the context in which the utterance was made. Even more
specifically, authors working in the field of pragmatics have
suggested that hearers invoke the Gricean maxims of conversation to
help them work out the best explanation of a speaker's utterance
whenever the semantic content of the utterance is insufficiently
informative for the purposes of the conversation, or is too
informative, or off-topic, or implausible, or otherwise odd or
inappropriate; see, for instance, Bach and Harnish 1979 (92f), Dascal
1979 (167), and Hobbs 2004. As in cases of reliance on speaker
testimony, the requisite abductive reasoning would normally seem to
take place at a subconscious level.



Abductive reasoning is not limited to everyday contexts. Quite the
contrary: philosophers of science have argued that abduction is a
cornerstone of scientific methodology; see, for instance, Boyd 1981,
1984, Harre 1986, 1988, Lipton 1991, 2004, and Psillos 1999.
According to Timothy Williamson (2007), "[t]he abductive
methodology is the best science provides" and Ernan McMullin
(1992) even goes so far to call abduction "the inference that
makes science." To illustrate the use of abduction in science,
we consider two examples.



At the beginning of the nineteenth century, it was discovered that the
orbit of Uranus, one of the seven planets known at the time, departed
from the orbit as predicted on the basis of Isaac Newton's
theory of universal gravitation and the auxiliary assumption that
there were no further planets in the solar system. One possible
explanation was, of course, that Newton's theory is false. Given
its great empirical successes for (then) more than two centuries, that
did not appear to be a very good explanation. Two astronomers, John
Couch Adams and Urbain Leverrier, instead suggested (independently of
each other but almost simultaneously) that there was an eighth, as yet
undiscovered planet in the solar system; that, they thought, provided
the best explanation of Uranus' deviating orbit. Not much later,
this planet, which is now known as "Neptune," was
discovered.



The second example concerns what is now commonly regarded to have been
the discovery of the electron by the English physicist Joseph John
Thomson. Thomson had conducted experiments on cathode rays in order to
determine whether they are streams of charged particles. He concluded
that they are indeed, reasoning as follows:



> 
> 
> As the cathode rays carry a charge of negative electricity, are
> deflected by an electrostatic force as if they were negatively
> electrified, and are acted on by a magnetic force in just the way in
> which this force would act on a negatively electrified body moving
> along the path of these rays, I can see no escape from the conclusion
> that they are charges of negative electricity carried by particles of
> matter. (Thomson, cited in Achinstein 2001, 17)
> 
> 
> 



The conclusion that cathode rays consist of negatively charged
particles does not follow logically from the reported experimental
results, nor could Thomson draw on any relevant statistical data. That
nevertheless he could "see no escape from the conclusion"
is, we may safely assume, because the conclusion is the best--in
this case presumably even the only plausible--explanation of his
results that he could think of.



Many other examples of scientific uses of abduction have been
discussed in the literature; see, for instance, Harre 1986,
1988 and Lipton 1991, 2004. Abduction is also said to be the
predominant mode of reasoning in medical diagnosis: physicians tend to
go for the hypothesis that best explains the patient's symptoms
(see Josephson and Josephson (eds.) 1994, 9-12; see also
Dragulinescu 2016 on abductive reasoning in the context of
medicine).



Last but not least, abduction plays a central role in some important
philosophical debates. See Shalkowski 2010 on the place of abduction
in metaphysics (also Bigelow 2010), Krzyzanowska, Wenmackers, and
Douven 2014 and Douven 2016a for a possible role of
abduction in the semantics of conditionals, and Williamson
2017 for an application of abduction in the philosophy of logic.
Arguably, however, abduction plays its most notable philosophical role
in epistemology and in the philosophy of science, where it is
frequently invoked in objections to so-called underdetermination
arguments. Underdetermination arguments generally start from the
premise that a number of given hypotheses are empirically equivalent,
which their authors take to mean that the evidence--indeed, any
evidence we might ever come to possess--is unable to favor one of
them over the others. From this, we are supposed to conclude that one
can never be warranted in believing any particular one of the
hypotheses. (This is rough, but it will do for present purposes; see
Douven 2008 and Stanford 2009, for more detailed accounts of
underdetermination arguments.) A famous instance of this type of
argument is the Cartesian argument for global skepticism, according to
which the hypothesis that reality is more or less the way we
customarily deem it to be is empirically equivalent to a variety of
so-called skeptical hypotheses (such as that we are beguiled by an
evil demon, or that we are brains in a vat, connected to a
supercomputer; see, e.g., Folina 2016). Similar arguments have been
given in support of scientific antirealism, according to which it will
never be warranted for us to choose between empirically equivalent
rivals concerning what underlies the observable part of reality (van
Fraassen 1980).



Responses to these arguments typically point to the fact that the
notion of empirical equivalence at play unduly neglects explanatory
considerations, for instance, by defining the notion strictly in terms
of hypotheses' making the same predictions. Those responding
then argue that even if some hypotheses make exactly the same
predictions, one of them may still be a better explanation of the
phenomena predicted. Thus, if explanatory considerations have a role
in determining which inferences we are licensed to make--as
according to defenders of abduction they have--then we might
still be warranted in believing in the truth (or probable truth, or
some such, depending--as will be seen below--on the version
of abduction one assumes) of one of a number of hypotheses that all
make the same predictions. Following Bertrand Russell (1912, Ch. 2),
many epistemologists have invoked abduction in arguing against
Cartesian skepticism, their key claim being that even though, by
construction, the skeptical hypotheses make the same predictions as
the hypothesis that reality is more or less the way we ordinarily take
it to be, they are not equally good explanations of what they predict;
in particular, the skeptical hypotheses have been said to be
considerably less simple than the "ordinary world"
hypothesis. See, among many others, Harman 1973 (Chs. 8 and 11),
Goldman 1988 (205), Moser 1989 (161), and Vogel 1990, 2005; see
Pargetter 1984 for an abductive response specifically to skepticism
regarding other minds. Similarly, philosophers of science have argued
that we are warranted to believe in Special Relativity Theory as
opposed to Lorentz's version of the aether theory. For even
though these theories make the same predictions, the former is
explanatorily superior to the latter. (Most arguments that have been
given for this claim come down to the contention that Special
Relativity Theory is ontologically more parsimonious than its
competitor, which postulates the existence of an aether. See
Janssen 2002 for an excellent discussion of the various reasons
philosophers of science have adduced for preferring Einstein's
theory to Lorentz's.)


## 2. Explicating Abduction



Precise statements of what abduction amounts to are rare in the
literature on abduction. (Peirce did propose an at least fairly
precise statement; but, as explained in the supplement to this entry,
it does not capture what most nowadays understand by abduction.) Its
core idea is often said to be that explanatory considerations have
confirmation-theoretic import, or that explanatory success is a (not
necessarily unfailing) mark of truth. Clearly, however, these
formulations are slogans at best, and it takes little effort to see
that they can be cashed out in a great variety of prima facie
plausible ways. Here we will consider a number of such possible
explications, starting with what one might term the "textbook
version of abduction," which, as will be seen, is manifestly
defective, and then going on to consider various possible refinements
of it. What those versions have in
common--unsurprisingly--is that they are all inference
rules, requiring premises encompassing explanatory considerations and
yielding a conclusion that makes some statement about the truth of a
hypothesis. The differences concern the premises that are required, or
what exactly we are allowed to infer from them (or both).



In textbooks on epistemology or the philosophy of science, one often
encounters something like the following as a formulation of
abduction:



ABD1
Given evidence *E* and candidate explanations
*H*1,..., *H**n* of
*E*, infer the truth of *that* *H**i*
which best explains *E*.


An observation that is frequently made about this rule, and that
points to a potential problem for it, is that it presupposes the
notions of candidate explanation and best explanation, neither of
which has a straightforward interpretation. While some still hope that
the former can be spelled out in purely logical, or at least purely
formal, terms, it is often said that the latter must appeal to the
so-called theoretical virtues, like simplicity, generality, and
coherence with well-established theories; the best explanation would
then be the hypothesis which, on balance, does best with respect to
these virtues. (See, for instance, Thagard 1978 and McMullin 1996.)
The problem is that none of the said virtues is presently particularly
well understood. (Giere, in Callebaut (ed.) 1993 (232), even makes the
radical claim that the theoretical virtues lack real content and play
no more than a rhetorical role in science. In view of recent formal
work both on simplicity and on coherence--for instance, Forster
and Sober 1994, Li and Vitanyi 1997, and Sober 2015, on simplicity and
Bovens and Hartmann 2003 and Olsson 2005, on coherence--the first
part of this claim has become hard to maintain; also, Schupbach and
Sprenger (2011) present an account of explanatory goodness directly in
probabilistic terms. Psychological evidence casts doubt on the second
part of the claim; see, for instance, Lombrozo 2007, on the role of
simplicity in people's assessments of explanatory goodness and
Koslowski *et al*. 2008, on the role of coherence with
background knowledge in those assessments.)



Furthermore, many of those who think ABD1 is headed along the right
lines believe that it is too strong. Some think that abduction
warrants an inference only to the *probable* truth of the best
explanation, others that it warrants an inference only to the
*approximate* truth of the best explanation, and still others
that it warrants an inference only to the *probable*
*approximate* truth.



The real problem with ABD1 runs deeper than this, however. Because
abduction is ampliative--as explained earlier--it will not
be a sound rule of inference in the strict logical sense, however
abduction is explicated exactly. It can still be *reliable* in
that it mostly leads to a true conclusion whenever the premises are
true. An obvious necessary condition for ABD1 to be reliable in this
sense is that, *mostly*, when it is true that *H* best
explains *E*, and *E* is true, then *H* is true as well
(or *H* is approximately true, or probably true, or probably
approximately true). But this would not be *enough* for ABD1 to
be reliable. For ABD1 takes as its premise only that some hypothesis
is the best explanation of the evidence *as compared to other
hypotheses in a* *given set*. Thus, if the rule is to be
reliable, it must hold that, at least typically, the best explanation
relative to the set of hypotheses that we consider would also come out
as being best in comparison with any other hypotheses that we might
have conceived (but for lack of time or ingenuity, or for some other
reason, did not conceive). In other words, it must hold that at least
typically the *absolutely* best explanation of the evidence is
to be found among the candidate explanations we have come up with, for
else ABD1 may well lead us to believe "the best of a bad
lot" (van Fraassen 1989, 143).



How reasonable is it to suppose that this extra requirement is usually
fulfilled? Not at all, presumably. To believe otherwise, we must
assume some sort of privilege on our part to the effect that when we
consider possible explanations of the data, we are somehow predisposed
to hit, inter alia, upon the absolutely best explanation of those
data. After all, hardly ever will we have considered, or will it even
be possible to consider, *all* potential explanations. As van
Fraassen (1989, 144) points out, it is *a priori* rather
implausible to hold that we are thus privileged.



In response to this, one might argue that the challenge to show that
the best explanation is always or mostly among the hypotheses
considered can be met without having to assume some form of privilege
(see Schupbach 2014 for a different response, and see Dellsen
2017 for discussion). For given the hypotheses we have managed to come
up with, we can always generate a set of hypotheses which jointly
exhaust logical space. Suppose
*H*1,...,*H**n* are the
candidate explanations we have so far been able to conceive. Then
simply define *H*n+1 := !*H*1
[?] ... [?] !*H**n* and add this new
hypothesis as a further candidate explanation to the ones we already
have. Obviously, the set
{*H*1,...,*H*n+1} is exhaustive,
in that one of its elements must be true. Following this in itself
simple procedure would seem enough to make sure that we never miss out
on the absolutely best explanation. (See Lipton 1993, for a proposal
along these lines.)



Alas, there is a catch. For even though there may be many hypotheses
*H**j* that imply *H*n+1 and, had
they been formulated, would have been evaluated as being a better
explanation for the data than the best explanation among the candidate
explanations we started out with, *H*n+1 itself will
in general be hardly informative; in fact, in general it will not even
be clear what its empirical consequences are. Suppose, for instance,
we have as competing explanations Special Relativity Theory and
Lorentz's version of the aether theory. Then, following the
above proposal, we may add to our candidate explanations that neither
of these two theories is true. But surely this further hypothesis will
be ranked quite low *qua* explanation--if it will be
ranked at all, which seems doubtful, given that it is wholly unclear
what its empirical consequences are. This is not to say that the
suggested procedure may never work. The point is that in general it
will give little assurance that the best explanation is among the
candidate explanations we consider.



A more promising response to the above "argument of the bad
lot" begins with the observation that the argument capitalizes
on a peculiar asymmetry or incongruence in ABD1. The rule gives
license to an absolute conclusion--that a given hypothesis is
true--on the basis of a comparative premise, namely, that that
particular hypothesis is the best explanation of the evidence relative
to the other hypotheses available (see Kuipers 2000, 171). This
incongruence is not avoided by replacing "truth" with
"probable truth" or "approximate truth." In
order to avoid it, one has two general options.



The first option is to modify the rule so as to have it require an
absolute premise. For instance, following Alan Musgrave (1988) or
Peter Lipton (1993), one may require the hypothesis whose truth is
inferred to be not only the best of the available potential
explanations, but also to be *satisfactory* (Musgrave) or
*good enough* (Lipton), yielding the following variant of
ABD1:



ABD2
Given evidence *E* and candidate explanations
*H*1,..., *H**n* of
*E*, infer the truth of *that* *H**i*
which explains *E* best, provided *H**i* is
satisfactory/good enough *qua* explanation.


Needless to say, ABD2 needs supplementing by a criterion for the
satisfactoriness of explanations, or their being good enough, which,
however, we are still lacking.



Secondly, one can formulate a symmetric or congruous version of
abduction by having it sanction, given a comparative premise, only a
comparative conclusion; this option, too, can in turn be realized in
more than one way. Here is one way to do it, which has been proposed
and defended in the work of Theo Kuipers (e.g., Kuipers 1984, 1992,
2000).



ABD3
Given evidence *E* and candidate explanations
*H*1,..., *H**n* of
*E*, if *H**i* explains *E* better than
any of the other hypotheses, infer that *H**i* is
closer to the truth than any of the other hypotheses.


Clearly, ABD3 requires an account of closeness to the truth, but many
such accounts are on offer today (see, e.g., Niiniluoto 1998).



One noteworthy feature of the congruous versions of abduction
considered here is that they do not rely on the assumption of an
implausible privilege on the reasoner's part that, we saw, ABD1
implicitly relies on. Another is that if one can be certain that,
however many candidate explanations for the data one may have missed,
none equals the best of those one *has* thought of, then the
congruous versions license exactly the same inference as ABD1 does
(supposing that one would not be certain that no potential explanation
is as good as the best explanation one has thought of if the latter is
not even satisfactory or sufficiently good).



As mentioned, there is widespread agreement that people frequently
rely on abductive reasoning. Which of the above rules *exactly*
is it that people rely on? Or might it be still some further rule that
they rely on? Or might they in some contexts rely on one version, and
in others on another (Douven 2017, forthcoming)? Philosophical
argumentation is unable to answer these questions. In recent years,
experimental psychologists have started paying attention to the role
humans give to explanatory considerations in reasoning. For instance,
Tania Lombrozo and Nicholas Gwynne (2014) report experiments showing
that *how* a property of a given class of things is explained
to us--whether mechanistically, by reference to parts and
processes, or functionally, by reference to functions and
purposes--matters to how likely we are to generalise that
property to other classes of things (see also Sloman 1994 and Williams
and Lombrozo 2010). And Igor Douven and Jonah Schupbach (2015a),
(2015b) present experimental evidence to the effect that
people's probability updates tend to be influenced by
explanatory considerations in ways that makes them deviate from
strictly Bayesian updates (see below). Douven (2016b) shows that, in
the aforementioned experiments, participants who gave more weight to
explanatory considerations tended to be more accurate, as determined
in terms of a standard scoring rule. (See Lombrozo 2012 and 2016 for
useful overviews of recent experimental work relevant to explanation
and inference.) Douven and Patricia Mirabile (2018) found some
evidence indicating that people rely on something like ABD2, at least
in some contexts, but for the most part, empirical work on the
above-mentioned questions is lacking.



With respect to the normative question of which of the previously
stated rules we *ought* to rely on (if we ought to rely on any
form of abduction), where philosophical argumentation should be able
to help, the situation is hardly any better. In view of the argument
of the bad lot, ABD1 does not look very good. Other arguments against
abduction are claimed to be independent of the exact explication of
the rule; below, these arguments will be found wanting. On the other
hand, arguments that have been given in favor of abduction--some
of which will also be discussed below--do not discern between
specific versions. So, supposing people do indeed commonly rely on
abduction, it must be considered an open question as to which
version(s) of abduction they rely on. Equally, supposing it is
rational for people to rely on abduction, it must be considered an
open question as to which version, or perhaps versions, of abduction
they ought to, or are at least permitted to, rely on.


## 3. The Status of Abduction



Even if it is true that we routinely rely on abductive reasoning, it
may still be asked whether this practice is rational. For instance,
experimental studies have shown that when people are able to think of
an explanation for some possible event, they tend to overestimate the
likelihood that this event will actually occur. (See Koehler 1991, for
a survey of some of these studies; see also Brem and Rips 2000.) More
telling still, Lombrozo (2007) shows that, in some situations, people
tend to grossly overrate the probability of simpler explanations
compared to more complicated ones. Although these studies are not
directly concerned with abduction in any of the forms discussed so
far, they nevertheless suggest that taking into account explanatory
considerations in one's reasoning may not always be for the
better. (It is to be noted that Lombrozo's experiments
*are* directly concerned with some proposals that have been
made for explicating abduction in a Bayesian framework; see Section
4.) However, the most pertinent remarks about the normative status of
abduction are so far to be found in the philosophical literature. This
section discusses the main criticisms that have been levelled against
abduction, as well as the strongest arguments that have been given in
its defense.


### 3.1 Criticisms



We have already encountered the so-called argument of the bad lot,
which, we saw, is valid as a criticism of ABD1 but powerless against
various (what we called) congruous rules of abduction. We here
consider two objections that are meant to be more general. The first
even purports to challenge the core idea underlying abduction; the
second is not quite as general, but it is still meant to undermine a
broad class of candidate explications of abduction. Both objections
are due to Bas van Fraassen.



The first objection has as a premise that it is part of the meaning of
"explanation" that if one theory is more explanatory than
another, the former must be more informative than the latter (see,
e.g., van Fraassen 1983, Sect. 2). The alleged problem then is that it
is "an elementary logical point that a more informative theory
cannot be more likely to be true [and thus] attempts to describe
inductive or evidential support through features that require
information (such as 'Inference to the Best Explanation')
must either contradict themselves or equivocate" (van Fraassen
1989, 192). The elementary logical point is supposed to be "most
[obvious] ... in the paradigm case in which one theory is an
extension of another: clearly the extension has more ways of being
false" (van Fraassen 1985, 280).



It is important to note, however, that in any other kind of case than
the "paradigm" one, the putative elementary point is not
obvious at all. For instance, it is entirely unclear in what sense
Special Relativity Theory "has more ways of being false"
than Lorentz's version of the aether theory, given that
they make the same predictions. And yet the former is generally
regarded as being superior, *qua* explanation, to the latter.
(If van Fraassen were to object that the former is not really more
informative than the latter, or at any rate not more informative in
the appropriate sense--whatever that is--then we should
certainly refuse to grant the premise that in order to be more
explanatory a theory must be more informative.)



The second objection, proffered in van Fraassen 1989 (Ch. 6), is
levelled at probabilistic versions of abduction. The objection is that
such rules must either amount to Bayes' rule, and thus be
redundant, or be at variance with it but then, on the grounds of
Lewis' dynamic Dutch book argument (as reported in Teller 1973),
be probabilistically incoherent, meaning that they may lead one to
assess as fair a number of bets which together ensure a financial
loss, come what may; and, van Fraassen argues, it would be irrational
to follow a rule that has this feature.



However, this objection fares no better than the first. For one thing,
as Patrick Maher (1992) and Brian Skyrms (1993) have pointed out, a
loss in one respect may be outweighed by a benefit in another. It
might be, for instance, that some probabilistic version of abduction
does much better, at least in our world, than Bayes' rule, in
that, on average, it approaches the truth faster in the sense that it
is faster in assigning a high probability (understood as probability
above a certain threshold value) to the true hypothesis (see Douven
2013, 2020, and Douven and Wenmackers 2017; see Climenhaga
2017 for discussion). If it does, then following that rule
instead of Bayes' rule may have advantages which perhaps are not
so readily expressed in terms of money yet which should arguably be
taken into account when deciding which rule to go by. It is, in short,
not so clear whether following a probabilistically incoherent rule
must be irrational.



For another thing, Douven (1999) argues that the question of whether a
probabilistic rule is coherent is not one that can be settled
independently of considering which other epistemic and
decision-theoretic rules are deployed along with it; coherence should
be understood as a property of packages of both epistemic and
decision-theoretic rules, not of epistemic rules (such as
probabilistic rules for belief change) in isolation. In the same
paper, a coherent package of rules is described which includes a
probabilistic version of abduction. (See Kvanvig 1994, Harman 1997,
Leplin 1997, Niiniluoto 1999, and Okasha 2000, for different responses
to van Fraassen's critique of probabilistic versions of
abduction.)


### 3.2 Defenses



Hardly anyone nowadays would want to subscribe to a conception of
truth that posits a necessary connection between explanatory force and
truth--for instance, because it stipulates explanatory
superiority to be necessary for truth. As a result, a priori defenses
of abduction seem out of the question. Indeed, all defenses that have
been given so far are of an empirical nature in that they appeal to
data that supposedly support the claim that (in some form) abduction
is a reliable rule of inference.



The best-known argument of this sort was developed by Richard Boyd in
the 1980s (see Boyd 1981, 1984, 1985). It starts by underlining the
theory-dependency of scientific methodology, which comprises methods
for designing experiments, for assessing data, for choosing between
rival hypotheses, and so on. For instance, in considering possible
confounding factors from which an experimental setup has to be
shielded, scientists draw heavily on already accepted theories. The
argument next calls attention to the apparent reliability of this
methodology, which, after all, has yielded, and continues to yield,
impressively accurate theories. In particular, by relying on this
methodology, scientists have for some time now been able to find ever
more instrumentally adequate theories. Boyd then argues that the
reliability of scientific methodology is best explained by assuming
that the theories on which it relies are at least approximately true.
From this and from the fact that these theories were mostly arrived at
by abductive reasoning, he concludes that abduction must be a reliable
rule of inference.



Critics have accused this argument of being circular. Specifically, it
has been said that the argument rests on a premise--that
scientific methodology is informed by approximately true background
theories--which in turn rests on an inference to the best
explanation for its plausibility. And the reliability of this type of
inference is precisely what is at stake. (See, for instance, Laudan
1981 and Fine 1984.)



To this, Stathis Psillos (1999, Ch. 4) has responded by invoking a
distinction credited to Richard Braithwaite, to wit, the distinction
between premise-circularity and rule-circularity. An argument is
premise-circular if its conclusion is amongst its premises. A
rule-circular argument, by contrast, is an argument of which the
conclusion asserts something about an inferential rule that is used in
the very same argument. As Psillos urges, Boyd's argument is
rule-circular, but not premise-circular, and rule-circular arguments,
Psillos contends, *need not* be viciously circular (even though
a premise-circular argument is always viciously circular). To be more
precise, in his view, an argument for the reliability of a given rule
*R* that essentially relies on *R* as an inferential
principle is not vicious, provided that the use of *R* does not
guarantee a positive conclusion about *R*'s reliability.
Psillos claims that in Boyd's argument, this proviso is met. For
while Boyd concludes that the background theories on which scientific
methodology relies are approximately true on the basis of an abductive
step, the use of abduction itself does not guarantee the truth of his
conclusion. After all, granting the use of abduction does nothing to
ensure that the best explanation of the success of scientific
methodology is the approximate truth of the relevant background
theories. Thus, Psillos concludes, Boyd's argument still
stands.



Even if the use of abduction in Boyd's argument might have led
to the conclusion that abduction is *not* reliable, one may
still have worries about the argument's being rule-circular. For
suppose that some scientific community relied not on abduction but on
a rule that we may dub "Inference to the Worst
Explanation" (IWE), a rule that sanctions inferring to the
*worst* explanation of the available data. We may safely assume
that the use of this rule mostly would lead to the adoption of very
unsuccessful theories. Nevertheless, the said community might justify
its use of IWE by dint of the following reasoning: "Scientific
theories tend to be hugely unsuccessful. These theories were arrived
at by application of IWE. That IWE is a reliable rule of
inference--that is, a rule of inference mostly leading from true
premises to true conclusions--is surely the worst explanation of
the fact that our theories are so unsuccessful. Hence, by application
of IWE, we may conclude that IWE is a reliable rule of
inference." While this would be an utterly absurd conclusion,
the argument leading up to it cannot be convicted of being viciously
circular anymore than Boyd's argument for the reliability of
abduction can (if Psillos is right). It would appear, then, that there
must be something else amiss with rule-circularity.



It is fair to note that for Psillos, the fact that a rule-circular
argument does not guarantee a positive conclusion about the rule at
issue is not sufficient for such an argument to be valid. A further
necessary condition is "that one should not have reason to doubt
the reliability of the rule--that there is nothing currently
available which can make one distrust the rule" (Psillos 1999,
85). And there is plenty of reason to doubt the reliability of IWE; in
fact, the above argument *supposes* that it is unreliable. Two
questions arise, however. First, why should we accept the additional
condition? Second, do we really have *no* reason to doubt the
reliability of abduction? Certainly *some* of the abductive
inferences we make lead us to accept *falsehoods*. How many
falsehoods may we accept on the basis of abduction before we can
legitimately begin to distrust this rule? No clear answers have been
given to these questions.



Be this as it may, even if rule-circularity is neither vicious nor
otherwise problematic, one may still wonder how Boyd's argument
is to convert a critic of abduction, given that it relies on
abduction. But Psillos makes it clear that the point of philosophical
argumentation is not always, and in any case need not be, to convince
an opponent of one's position. Sometimes the point is, more
modestly, to assure or reassure oneself that the position one
endorses, or is tempted to endorse, is correct. In the case at hand,
we need not think of Boyd's argument as an attempt to convince
the opponent of abduction of its reliability. Rather, it may be
thought of as justifying the rule from within the perspective of
someone who is already sympathetic towards abduction; see Psillos 1999
(89).



There have also been attempts to argue for abduction in a more
straightforward fashion, to wit, via enumerative induction. The common
idea of these attempts is that every newly recorded successful
application of abduction--like the discovery of Neptune, whose
existence had been postulated on explanatory grounds (see Section
1.2)--adds further support to the hypothesis that abduction is a
reliable rule of inference, in the way in which every newly observed
black raven adds some support to the hypothesis that all ravens are
black. Because it does not involve abductive reasoning, this type of
argument is more likely to also appeal to disbelievers in abduction.
See Harre 1986, 1988, Bird 1998 (160), Kitcher 2001, and Douven
2002 for suggestions along these lines.


## 4. Abduction versus Bayesian Confirmation Theory



In the past decade, Bayesian confirmation theory has firmly
established itself as the dominant view on confirmation; currently one
cannot very well discuss a confirmation-theoretic issue without making
clear whether, and if so why, one's position on that issue
deviates from standard Bayesian thinking. Abduction, in whichever
version, assigns a confirmation-theoretic role to explanation:
explanatory considerations contribute to making some hypotheses more
credible, and others less so. By contrast, Bayesian confirmation
theory makes no reference at all to the concept of explanation. Does
this imply that abduction is at loggerheads with the prevailing
doctrine in confirmation theory? Several authors have recently argued
that not only is abduction compatible with Bayesianism, it is a
much-needed supplement to it. The so far fullest defense of this view
has been given by Lipton (2004, Ch. 7); as he puts it, Bayesians
should also be "explanationists" (his name for the
advocates of abduction). (For other defenses, see Okasha 2000, McGrew
2003, Weisberg 2009, and Poston 2014, Ch. 7; for discussion, see Roche
and Sober 2013, 2014, and McCain and Poston 2014.)



This requires some clarification. For what could it mean for a
Bayesian to be an explanationist? In order to apply Bayes' rule
and determine the probability for *H* after learning *E*,
the Bayesian agent will have to determine the probability of *H*
conditional on *E*. For that, he needs to assign unconditional
probabilities to *H* and *E* as well as a probability to
*E* given *H*; the former two are mostly called "prior
probabilities" (or just "priors") of, respectively,
*H* and *E*, the latter the "likelihood" of
*H* on *E*. (This is the official Bayesian story. Not all of
those who sympathize with Bayesianism adhere to that story. For
instance, according to some it is more reasonable to think that
conditional probabilities are basic and that we derive unconditional
probabilities from them; see Hajek 2003, and references
therein.) How is the Bayesian to determine these values? As is well
known, probability theory gives us more probabilities once we have
some; it does not give us probabilities from scratch. Of course, when
*H* implies *E* or the negation of *E*, or when
*H* is a statistical hypothesis that bestows a certain chance on
*E*, then the likelihood follows "analytically."
(This claim assumes some version of Lewis' (1980) Principal
Principle, and it is controversial whether or not this principle is
analytic; hence the scare quotes.) But this is not always the case,
and even if it were, there would still be the question of how to
determine the priors. This is where, according to Lipton, abduction
comes in. In his proposal, Bayesians ought to determine their prior
probabilities and, if applicable, likelihoods on the basis of
explanatory considerations.



Exactly how are explanatory considerations to guide one's choice
of priors? The answer to this question is not as simple as one might
at first think. Suppose you are considering what priors to assign to a
collection of rival hypotheses and you wish to follow Lipton's
suggestion. How are you to do this? An obvious--though still
somewhat vague--answer may seem to go like this: Whatever exact
priors you are going to assign, you should assign a higher one to the
hypothesis that explains the available data best than to any of its
rivals (provided there is a best explanation). Note, though, that your
neighbor, who is a Bayesian but thinks confirmation has nothing to do
with explanation, may well assign a prior to the best explanation that
is even higher than the one you assign to that hypothesis. In fact,
his priors for best explanations may even be consistently higher than
yours, not because in his view explanation is somehow related to
confirmation--it is not, he thinks--but, well, just because.
In this context, "just because" is a perfectly legitimate
reason, because any reason for fixing one's priors counts as
legitimate by Bayesian standards. According to mainstream Bayesian
epistemology, priors (and sometimes likelihoods) are up for grabs,
meaning that one assignment of priors is as good as another, provided
both are coherent (that is, they obey the axioms of probability
theory). Lipton's recommendation to the Bayesian to be an
explanationist is meant to be entirely general. But what should your
neighbor do differently if he wants to follow the recommendation?
Should he give the same prior to any best explanation that you, his
explanationist neighbor, give to it, that is, *lower* his
priors for best explanations? Or rather should he give even
*higher* priors to best explanations than those he already
gives?



Perhaps Lipton's proposal is not intended to address those who
already assign highest priors to best explanations, even if they do so
on grounds that have nothing to do with explanation. The idea might be
that, as long as one does assign highest priors to those hypotheses,
everything is fine, or at least finer than if one does not do so,
regardless of one's reasons for assigning those priors. The
answer to the question of how explanatory considerations are to guide
one's choice of priors would then presumably be that one ought
to assign a higher prior to the best explanation than to its rivals,
if this is not what one already does. If it is, one should just keep
doing what one is doing.



(As an aside, it should be noticed that, according to standard
Bayesian usage, the term "priors" does not necessarily
refer to the degrees of belief a person assigns before the receipt of
*any* data. If there are already data in, then, clearly, one
may assign higher priors to hypotheses that best explain the
then-available data. However, one can sensibly speak of "best
explanations" even before any data are known. For example, one
hypothesis may be judged to be a better explanation than any of its
rivals because the former requires less complicated mathematics, or
because it is stated in terms of familiar concepts only, which is not
true of the others. More generally, such judgments may be based on
what Kosso (1992, 30) calls *internal features* of hypotheses
or theories, that is, features that "can be evaluated without
having to observe the world.")



A more interesting answer to the above question of how explanation is
to guide one's choice of priors has been given by Jonathan
Weisberg (2009). We said that mainstream Bayesians regard one
assignment of prior probabilities as being as good as any other.
So-called objective Bayesians do not do so, however. These Bayesians
think priors must obey principles beyond the probability axioms in
order to be admissible. Objective Bayesians are divided among
themselves over exactly which further principles are to be obeyed, but
at least for a while they agreed that the Principle of Indifference is
among them. Roughly stated, this principle counsels that, absent a
reason to the contrary, we give equal priors to competing hypotheses.
As is well known, however, in its original form the Principle of
Indifference may lead to inconsistent assignments of probabilities and
so can hardly be advertised as a principle of rationality. The problem
is that there are typically various ways to partition logical space
that appear plausible given the problem at hand, and that not all of
them lead to the same prior probability assignment, even assuming the
Principle of Indifference. Weisberg's proposal amounts to the
claim that explanatory considerations may favor some of those
partitions over others. Perhaps we will not always end up with a
unique partition to which the Principle of Indifference is to be
applied, but it would already be progress if we ended up with only a
handful of partitions. For we could then still arrive in a motivated
way at our prior probabilities, by proceeding in two steps, namely, by
first applying the Principle of Indifference to the partitions
separately, thereby possibly obtaining different assignments of
priors, and by then taking a weighted average of the thus obtained
priors, where the weights, too, are to depend on explanatory
considerations. The result would again be a probability
function--the uniquely correct prior probability function,
according to Weisberg.



The proposal is intriguing as far as it goes but, as Weisberg admits,
in its current form, it does not go very far. For one thing, it is
unclear how exactly explanatory considerations are to determine the
weights required for the second step of the proposal. For another, it
may be idle to hope that taking explanatory considerations into
account will in general leave us with a manageable set of partitions,
or that, even if it does, this will not be due merely to the fact that
we are overlooking a great many prima facie plausible ways of
partitioning logical space to begin with. (The latter point echoes the
argument of the bad lot, of course.)



Another suggestion about the connection between abduction and Bayesian
reasoning--to be found in Okasha 2000, McGrew 2003, Lipton 2004
(Ch. 7), and Dellsen 2018--is that the explanatory
considerations may serve as a heuristic to determine, even if only
roughly, priors and likelihoods in cases in which we would otherwise
be clueless and could do no better than guessing. This suggestion is
sensitive to the well-recognized fact that we are not always able to
assign a prior to every hypothesis of interest, or to say how probable
a given piece of evidence is conditional on a given hypothesis.
Consideration of that hypothesis' explanatory power might then
help us to figure out, if perhaps only within certain bounds, what
prior to assign to it, or what likelihood to assign to it on the given
evidence.



Bayesians, especially the more modest ones, might want to retort that
the Bayesian procedure is to be followed if, and only if, either (a)
priors and likelihoods can be determined with some precision and
objectivity, or (b) likelihoods can be determined with some precision
and priors can be expected to "wash out" as more and more
evidence accumulates, or (c) priors and likelihoods can both be
expected to wash out. In the remaining cases--they might
say--we should simply refrain from applying Bayesian reasoning. A
fortiori, then, there is no need for an abduction-enhanced Bayesianism
in these cases. And some incontrovertible mathematical results
indicate that, in the cases that fall under (a), (b), or (c), our
probabilities will converge to the truth anyhow. Consequently, in
those cases there is no need for the kind of abductive heuristics that
the above-mentioned authors suggest, either. (Weisberg 2009, Sect.
3.2, raises similar concerns.)



Psillos (2000) proposes yet another way in which abduction might
supplement Bayesian confirmation theory, one that is very much in the
spirit of Peirce's conception of abduction. The idea is that
abduction may assist us in selecting plausible candidates for testing,
where the actual testing then is to follow Bayesian lines. However,
Psillos concedes (2004) that this proposal assigns a role to abduction
that will strike committed explanationists as being too limited.



Finally, a possibility that has so far not been considered in the
literature is that abduction and Bayesianism do not so much work in
tandem--as they do on the above proposals--as operate in
different modes of reasoning; the Bayesian and the explanationist are
characters that feature in different plays, so to speak. It is widely
accepted that sometimes we speak and think about our beliefs in a
categorical manner, while at other times we speak and think about them
in a graded way. It is far from clear how these different ways of
speaking and thinking about beliefs--the epistemology of belief
and the epistemology of degrees of belief, to use Richard
Foley's (1992) terminology--are related to one another. In
fact, it is an open question whether there is any straightforward
connection between the two, or even whether there is a connection at
all. Be that as it may, given that the distinction is undeniable, it
is a plausible suggestion that, just as there are different ways of
talking and thinking about beliefs, there are different ways of
talking and thinking about the *revision* of beliefs. In
particular, abduction could well have its home in the epistemology of
belief, and be called upon whenever we reason about our beliefs in a
categorical mode, while at the same time Bayes' rule could have
its home in the epistemology of degrees of belief. Hard-nosed
Bayesians may insist that whatever reasoning goes on in the
categorical mode must eventually be justifiable in Bayesian terms, but
this presupposes the existence of bridge principles connecting the
epistemology of belief with the epistemology of degrees of
belief--and, as mentioned, whether such principles exist is
presently unclear.