Enumerative
Induction
as a Subset of Inference to the Best
Explanation
Laith Al-Shawaf
In his paper The Inference
to the Best Explanation, Gilbert
Harman explains his position on enumerative induction. He first argues
that
inferences that seem to be instances of enumerative induction are
actually
better explained as inferences to the best explanation (IBE). He claims
that
the former are actually “uninteresting special case[s] of the more
general
inference to the best explanation” (Harman, 1965). Indeed, according to
Harman,
all cases of enumerative induction can be explained using IBE, making
the
former redundant as a separate form of inference.
By contrast,
the use of IBE need never be accompanied by enumerative induction, i.e.
there
are no situations that can be explained by the latter but not by the
former.
Enumerative induction is the process whereby a conclusion about, say,
type A,
is drawn based on several examined cases of type A. An often-cited
example is
as follows: if we observe one white swan, and then observe another
white swan,
and then another, up to a very large number of observations of white
swans
(with no exceptions), then we are likely to conclude that all swans are
white.
We have thus extrapolated from observed instances to a general
conclusion that
applies to other cases that are as of yet unobserved. Harman's second
main
argument in favor of his view is that in selecting a hypothesis to
explain
certain evidence, we often make use of certain lemmas. The use of these
lemmas,
according to Harman, is obscured if the process of hypothesis selection
is
described as one of enumerative induction, whereas the use of IBE
appropriately
highlights them as crucial steps in arriving at an explanation.
In
arguing for the necessity of
IBE, Harman begins by explaining the process of the inference to the
best
explanation. The process begins with the existence of several competing
hypotheses, which all purport to explain the same data. The key is to
then
reject all of the alternative hypotheses in favor of the one that
provides the
best explanation for the data, inferring its truth from its superior
explanatory power. Here, Harman admits the existence of a quandary: how
to
define “best”. Unfortunately, he chooses not to tackle the issue,
merely
mentioning in passing a few possible criteria: “which hypothesis is
simpler,
which is more plausible, which explains more, which is less ad
hoc …”
(Harman, 1965). Clearly, the author believes that this issue can be
dealt with
later, after first establishing that there is no need to describe our
inferences as inductive. In setting this task aside for later, Harman
is
assuming something that may prove to be problematic: that the task is
indeed
accomplishable. It may not be possible to objectively define “best”,
which
would pose a serious dilemma for philosophers attempting to use or
explain IBE.
Alternatively, as suggested by Okasha, we often define the “best”
hypothesis as
the one that has gained the most inductive support (Okasha, 2002).
This, too,
may prove to be a conundrum. These problems notwithstanding, many of
Harman’s
points still hold, and must be considered in the following paragraphs.
In
order to convince us of his
first argument, that enumerative induction is superfluous if we
consider IBE,
the author provides several examples that can be explained by IBE and
not by
induction. It is important to note here, though, that although such
examples
may establish the need for IBE, they do not necessarily show that
enumerative
induction is superfluous. The examples Harman gives include the way a
physicist
infers the existence of atoms and sub-atomic particles. He asserts that
the
inference of the existence of sub-atomic particles can only be
explained using
IBE. However, he does not explain why this is the case; he just assumes
it to
be so. Perhaps an explanation can be offered here. There isn’t a
convincing
sense in which inductive reasoning is being used to infer the existence
of
these particles, because there haven’t been any past observations
verifying
this hypothesis. In other words, the first time a
physicist posited the
existence of sub-atomic particles, she could not have been using
enumerative
induction, as induction extrapolates from cases that have already been
fully
observed to cases that are as of yet unobserved. Clearly, this is not
what is
happening here: we are not saying that since all observed things have
had atoms
and sub-atomic particles so far, the rest will too. Rather, we are
making an
entirely new inference about an unobservable entity, something that
seems to be
beyond the scope of induction. In our example, the physicist is looking
at
something for the first time; there exists no buildup of relevant past
observations that can now be inductively used to explain what is
happening in
the present situation. Indeed, this is her first observation, and the
first
time she formulates this hypothesis! Thus, she cannot be extrapolating
from the
already observed to the as of yet unobserved. Rather, the scientist
attempting
to explain a novel phenomenon must be using something other than
enumerative
induction. The most sensible answer here is that the physicist selected
the
best explanation of the data: a hypothesis postulating the existence of
such
particles. There is a sense in which induction can then
be used for many
other unobservable entities in the future, after IBE
has been used to
speculate the existence of atoms and sub-atomic particles in the first
place.
In this sense, after the original claim has been advanced, similar
findings in
experiments may inductively suggest that all objects are made of atoms
and
sub-atomic particles. However, it seems inescapable that the original
claim was made using IBE. In fact, it is tempting to say that this is
usually
the case with first-time discoveries, especially concerning
unobservable
entities. Certainly, it seems that the first time scientists suggested
the
existence of magnetic fields, quarks, and many other unobservable
entities,
they were using IBE. No other explanation provided a better fit for the
data,
and so the hypotheses were accepted. It seems impossible to construct a
convincing argument for the use of induction in such cases. Again, it
may be
argued that from then on, inductive reasoning can
be used to claim that
because previous A’s were said to have magnetic fields, and because a
new
object appeared to be an A as well (was similar in all relevant
respects); this
object should have a magnetic field. We will see in a moment whether it
is
indeed the case that we then use induction for future cases. For now,
we can
content ourselves with our demonstration that the original speculation
seems to
have necessarily been a product of IBE.
Now,
let’s move on to examine
whether after the initial IBE inference, we might still be using IBE in
future
encounters with unobservable bodies, for it deserves greater
elaboration. This
point can be made in two different senses, and taken together, they may
suggest
that induction is actually just a special form of IBE. The first sense
in which
we are still using IBE at a later stage in the scientific process (as
described
above) is as follows: when trying to explain a phenomenon, it may make
more
sense (given the trouble with assuming uniformity of nature) to
consider the
particular phenomenon itself, excluding past observations of similar
situations. So, for instance, if we want to argue that we have located
an
electron, it may make more sense to argue for this claim only on the
basis of
the evidence we have discovered in the present experiment, without
resorting to
the use of past experiments that supposedly produced similar
discoveries. This
is because, as David Hume pointed out, we have no reason to assume that
the
present and the future will be like the past. And, as he noted, it does
not
help to argue that we know that nature is uniform because it has been
uniform
in the past, since this is circular reasoning. Given this difficulty,
if we
simply consider the evidence of the present experiment itself, as
outlined
above, then we are unlikely to be using induction. Instead, each and
every case
(or experiment) becomes identical to the original inference, in which
IBE was
used to select the best explanation for the data.
The
second sense in which induction
is a subset of IBE may seem even more robust. In using induction, we
extrapolate from the observed to the unobserved, assuming that
(roughly) the
future will conform to the past. Why do we assume this? The answer
seems to be
that we infer its truth from the fact that it is the best
explanation.
We seem to think that when something has applied so many times in the
past, the
best explanation for a similar situation in the future will be the same
explanation used in the past. We reject the alternative hypothesis,
finding it
less plausible that (for example) our world will radically change and
the Earth
will stop orbiting the sun. This, then, is an instance of IBE: the
rejection of
seemingly inferior alternative hypotheses in favor of the one we regard
as
supplying the best explanation. In the sense outlined above, IBE is
more
fundamental than induction. Indeed, the latter seems to depend on the
former,
making it a special case of IBE. This is what Harman meant when he said
that
all cases of induction can be explained using IBE. In fact, Harman
makes this
second point – though without clearly articulating that induction is systematically
dependent on IBE, as shown above. It is precisely this fact
that suggests
that it is impossible to think of a situation in which inductive
reasoning
could not be replaced by IBE. This would serve as a rejoinder to those
who
claim that induction is more fundamental than IBE, as the "best"
explanation is the one that has the greatest amount of inductive
support.
Instead, this analysis suggests that inductive support is only ever
accumulated
because we use IBE to arrive at the conclusion that the future will
likely have
the same laws as the past.
For
a final example of a situation
in which we can only be using IBE, consider the following. Suppose we
are
trying to explain a particular phenomenon, and have had several past
observations, leading to a buildup of relevant information.
Unfortunately,
about half of our previous observations and information point to
explanation X
for this phenomenon, and half of our previous observations suggest
explanation
Y for this same phenomenon. Or alternatively, all of our information
points
equally to both explanation X and explanation Y. That is, the two
explanations
do not differ in their predictions of the phenomenon under
investigation.
Either explanation would account for all of the evidence at hand. What
should
we do here? In picking between explanation X and explanation Y, we need
to use
IBE. We are clearly not using induction, since, as we've said, our
inductive
reasoning makes us completely undecided about which is better,
explanation X or
explanation Y. Given that they have the same amount of inductive
support, we
must use some other method to discriminate between them and decide
which is a
better explanation. What we would do in such a situation is as follows:
reject
the seemingly inferior explanation in favor of the "better" one. We
may use such criteria as parsimony or which explanation is less ad hoc.
This
method of choosing between competing explanations by choosing the
superior one
is a process of Inference to the Best Explanation.
Harman’s
second main argument is
that in explaining the evidence at hand, we often make use of certain
lemmas.
The crucial role that these lemmas play is obscured if we describe the
inferential process as inductive. If we describe it as IBE, however,
then their
role is properly established. In order to clarify his point about
exposing or
obscuring lemmas, Harman presents us with two examples. The first is
that when
we hear someone say something, “the inference which we make from
testimony to truth
must contain as a lemma the proposition that the utterance is there
because it
is believed and not because of a slip of the tongue” (Harman, 1965).
Similarly,
if we see somebody quickly withdrawing his hand from a hot oven he has
just
touched, we infer that his hand hurts. In this case, our lemma is that
it is
the pain that caused the withdrawal.
According
to Harman, describing
such inferences as instances of enumerative induction masks the lemmas
involved. Indeed, the implication of this for the first example, as
Harman
points out, is that we would be able to find all the past correlations
between
a person’s utterance of something (and the circumstances surrounding
it) and
its truth. Then, using induction, we would say that the inference is
simply
from the past relationship between utterance and truth to the present
case. The
same process applies to the second example, with correlations between
such a
behavior and pain. As Harman asserts, these accounts hide the
“essential
relevance” (Harman, 1965) of the lemmas that the speaker believed the
statement, and that the pain was responsible for the withdrawal,
respectively.
Here, a possible response to Harman would be that if indeed, all past
instances/correlations showed that people do not pull their hands away
because
of pain, but rather because of fury (for example), then perhaps we
would be
inclined to say that this person is furious, not in pain. In such an
instance,
it would seem that we used enumerative induction. However, Harman could
counter
this response in one of two ways. He could say that we are still using
IBE,
because given all the past correlations, the assumption that the same
explanation holds in the present is indeed the better explanation. This
is an
instance of the previous explanation of why induction may be seen to be
systematically dependent on IBE. Alternatively, he could say that we
are still
using IBE, but a different lemma is playing a part: the idea that the
person’s
fury is responsible for the withdrawal of his hand. Perhaps he would
opt for
the second reply, as it highlights the lemma involved.
Although
this may seem like a novel
idea, it shouldn’t strike us as too surprising. It should be relatively
uncontroversial to hear that we have intermediate beliefs that help us
to
arrive at an explanation of a given phenomenon. After all, the
suggested
alternative is that we use enumerative induction and simply project the
correlation from past into the present and future. Perhaps a final
example can
elucidate the idea further. Suppose I notice that Jack is soaking wet,
and I
explain this by saying that it is currently raining. If I have done
this
through a simple examination of past correlations (i.e. usually someone
is wet
because it has rained on them), then I obscure the roles of some very
important
lemmas. These lemmas include that Jack was outside in the first place,
and did
not have an umbrella or a trench coat. Clearly, these intermediate
lemmas did
play a role in my explanation, because I would not have postulated rain
as the
cause of Jack's wetness had I thought that he was equipped with an
umbrella. It
is clear, then, that describing the inferential process as one of IBE -
as
opposed to one of enumerative induction - highlights our use of lemmas.
Perhaps
a much bigger potential
problem for Harman is not whether we use lemmas, but rather where our
lemmas
come from. What if the lemmas themselves are based on enumerative
induction?
This reply would suggest that the reason we think pain is responsible
for the
withdrawal, or that the utterance was made because the speaker
genuinely
believes it to be true, is because it has been so in the past. This
would be a
predicament, because given Harman’s assertion that the lemmas are an
ineliminable part of IBE, it would make IBE dependent on enumerative
induction.
It seems, however, that this objection is escapable, as Harman could
respond by
saying that our lemmas are based on intuitive reasoning, not
enumerative
induction. Perhaps this would be a plausible reply, as it does seem as
though
we attribute withdrawal to pain because it is intuitively satisfying.
However,
Harman would probably need to account for why we
find this
explanation intuitively acceptable. Alternatively, we may be
attributing
withdrawal to pain because we have had similar experiences, and are
using IBE
to arrive at the conclusion that other minds exist and operate in
roughly the
same way as ours. However, there are special cases that do not seem to
conform
to this model. If we have witnessed someone accidentally touch an oven
several
times and quickly withdraw his hand each time, explaining that he
didn’t feel
any pain (maybe he has a faulty nervous system), then perhaps we would
not be
inclined to attribute withdrawal to pain the next time we witness such
behavior. Our lemma might instead be the reason he cited in the past,
such as
fear of an ugly burn on his hand.
This may show that there are certain instances in which it is harder to
rule
out the use of enumerative induction in establishing lemmas.
Nonetheless, it
may still be possible to rebut such an argument by claiming that the
lemma in
use would be that the person is likely to stay the same, or maintain
the same
faulty nervous system.
In
essence, Harman’s claim that
enumerative induction masks the vital roles played by lemmas in our
inferences
is a solid one. Though there may be certain instances in which the
lemmas may
appear to be partly induction-based, the claim holds for most cases and
the
objection is avoidable. Further, his argument that enumerative
induction should
not be viewed as a separate form of reasoning is also powerful,
although he
does not articulate the full slew of reasons why this is so, as this
paper has
attempted.
American University of Beirut
Beirut, Lebanon
About the Author
References
Harman, G. (1965).The inference to
the best explanation. The
Philosophical Review. 74, 88-95.
Okasha, S. (2002). Philosophy
of science: A very short
introduction. United Kingdom: Oxford University Press.