The Problem of Induction
The problem
of induction is among the most widely discussed epistemological problems
brought up by David Hume. It is taken by many to show that induction is not rational. This
conclusion was inferred by Hume at the end of his investigation on how we can
acquire knowledge of matters of fact that go beyond our present and past sense
experience, i.e., those of future and distant present matters of fact.
For
induction to be rational, it must be justified either by a priori or a posteriori
reasoning. Hume argues that none of these reasonings
can do the job.
To begin
with, there are two kinds of objects of human inquiry according to Hume[1]:
relations of ideas and matters of fact. Among relations of ideas there are
mathematical and logical propositions such as, for instance, that two plus
three equals five or that all bachelors are unmarried adult males. These
propositions are demonstratively (deductively) justifiable; one need not appeal
to sense experience to prove the truth of such propositions. This happens
because it is impossible for one to conceive even in his wildest imagination
that two plus three does not equal five, or that there is a married bachelor.
As for the matters of fact, Hume claims, the contrary to each of them is possible
to conceive:
That the sun
will not rise to-morrow is no less intelligible a proposition, and implies no
more contradiction, than the affirmation, that it will rise. We should in vain,
therefore, attempt to demonstrate its falsehood. Were it demonstratively false,
it would imply contradiction, and could be distinctly conceived by the mind.
(26)
Whereas the present matters of fact can be justified by
direct sense experience, how can we know about the matters of fact that have
not yet been experienced? What kind of reasoning authorizes our anticipation
that the sun will rise tomorrow?
Our
expectations of the future matters of fact lies in the relation of cause and
effect, say both Hume and common sense. “By means of that relation alone,” Hume
continues, “we can go beyond the evidence of our memory and senses”[2].
But how do
we know about this relation? Hume denies that knowledge of this relation can be
obtained by a priori reasoning,
since, should we be given an entirely new object, we would never find out from
it alone what cause produced this object and what effect it would bring about.
Thus, knowledge of causal relations can be acquired only through sense
experience of actual relations between objects. But we do not perceive causal
relation between objects. All we can see is that they are constantly connected
to each other. So, the only way we could obtain knowledge of causality would be
to infer it from our past and present observations of regularities.
What kind of
reasoning underlies our thinking that since in all our previous observations
B-events have followed A-events, it will always be this way? Since matters of
fact imply no contradiction, to suppose that next time B-like event will follow
right after A-like event is no better than to suppose that it will not. Thus,
to legitimately expand the past observations of regularities to the future
times we need an intermediate premise, i.e., some principle that states that
the future will resemble the past.
This
principle of the uniformity of nature, in its turn, must be justified. Hume
argues that it can be done in two ways, either deductively or by inference from
the previous observations.[*] We
cannot prove it demonstratively (deductively) because it is conceivable that
the course of nature can change. As for inference from our past observations,
the argument for the resemblance of the future to the past is doomed to be
circular “since all these arguments are founded on the supposition of that
resemblance”.[3] In other words, as said above every inductive
argument should include the principle of uniformity of nature among its
premises. Thus, to infer uniformity of nature from the previous observations
and legitimately expand it to the future times we have to presuppose this
principle in the premises. This makes the argument circular.
Since our
attempts to justify the uniformity principle have failed, we have to conclude
that there is no legitimate method which would let us infer a general rule
about regularities and predict such regularities in the future based on the
limited scope of observations of regularities in the past and the present.
Because there is no such method, our prediction of future events based on the
past observations is not a rational activity, but just a matter of habit.
Responses
and solutions to the problem of induction:
1. Strawson’s response
According
to Peter Strawson[4],
the problem of induction does not need to be solved, but rather dissolved
because there is no such problem.
Strawson claims that the
problem of induction as described by Hume arises from the misconception of
induction. Induction is unjustifiable if we impose deductive standards on it.
But induction by definition is not deductively valid, and, therefore, we should
not expect induction to meet deductive standards. Thus, the principle of
uniformity of nature mentioned by Hume as an intermediate premise is no longer
needed. Induction should satisfy inductive, but not deductive, standards if it
is to be considered rational.
“Induction”
means inference of a general rule from the observations of regularities. Strawson argues that it is rational to suppose that there
is a common pattern that underlies regularities, while not to make such an
assumption is not rational. At the same time, there can be no solid standard
for inductive arguments as there is for deductive ones because conclusions of
inductive arguments by definition go beyond the content of their premises,
whereas in deductively valid arguments there is nothing in their conclusions
that cannot be found in their premises.
Since true inductive premises do not generally guarantee the truth of a
correspondent inductive conclusion, every inductive argument should be
considered and judged separately. This, however, does not imply that inductive
inference is not rational, Strawson claims. The major
mistake is to think that rationality of an argument should require its
validity. Once we understand this mistake, the problem of induction disappears.
The main
objection to Strawson’s dissolution of the problem of
induction is that while defending the rationality of using inductive rule of
inference, he does not tell us anything about the reliability of this rule.
However, since reasonableness of a rule of inference does not necessarily imply
its validity, it also does not seem to entail reliability.
2. Inductive justification of induction
Max Black
proposes inductive justification of induction claiming that since induction was
reliable in the past, therefore, it will probably be reliable in the future.
Black argues that an argument for induction stated in such a way avoids the
problem of circularity since the conclusion does not repeat the premise as it
is in circular arguments. Nevertheless, there are several serious objections to
this argument.
First, it is
still not clear on what basis we can assume that induction will be reliable in
the future (even with some probability) unless we presuppose that the future
will resemble the past. Even though this presupposition is not expressed in the
above argument, it is intuitively assumed. And if we try to justify our
intuitive presupposition of uniformity of nature we will meet Hume’s problem
set above. To this Black can argue that by involving the principle of
uniformity we make the mistake of imposing deductive standards upon induction.
But without the presupposition that the future will resemble the past the
inductive justification of induction encounters the following problem stated by
Elliot Sober (? - cannot find the origin).
Elliot Sober
comes up with a “new” method of inference called counterinduction[5]. Counterinductive inference, he supposes, is opposite to
inductive one, i.e., it tells us to expect that past and present regularities
are not likely to continue in the future. The counterinductive
argument for counterinduction goes as follows: since counterinduction was unreliable in the past, it probably
will be reliable in the future. Thus, if induction can be inductively
justified, counterinduction, in its turn, can be
authorized counterinductively.
Of course, Sober’s fictitious method is counterintuitive. But what he
tries to show us by this analogy is that if we consider counterinductive
justification of counterinduction as bad, then we
should treat the inductive justification of induction the same.
In fact, the above presentation of Black’s argument is
the simplified version. Inductive justification of induction as described by
Brian Skyrms[6]
can be presented as a multi-level system. On the first level there are
inductive arguments about individual things and logical rules that assign
degrees of inductive strength to these arguments depending on the size and representativeness of their premises. For instance: All the
emeralds which have been observed since the beginning of history until now were
green. Therefore, the next emerald to be observed will be green. To this
argument the rules of the first level assign a very high probability, i.e.,
based on the premises of the argument, it is highly probable that the next
emerald will be green. On this level there are also arguments to which the
first level rules can assign lesser probability depending on a scope of
observations and a proportion of As that are Bs.
The second-level arguments provide justification for the
arguments and logical rules of the first level, whereas logical rules of the
second level assign probability for inductive second-level arguments. For
instance, for the argument about emeralds the second level contains an argument
stating that since the first-level argument about emeralds has always led to
true conclusion in the past, it will likely lead to true conclusion with regard
to the next observation (prediction). The second-level arguments, in their
turn, are authorized by arguments of the next third level, etc.
The same
goes with justification of inductive rules which assign probability to
inductive arguments. The second-level arguments provide justification for why
one should rely on the rules of the first-level. These arguments say that since
the first-level arguments for which the first-level rules assign high
probability yielded true conclusions most of the time in the past, it is very
likely that with regard to the next prediction first-level inductively strong
arguments will be highly reliable. In their turn, third-level arguments justify
the rules of the second level and so on.
While
avoiding problem of circularity the adherent of the foregoing complex argument
is at risk of getting into trouble with an infinite regress. Moreover, a counterinductivist may provide the same multi-layered
system for justification of counterinduction, which
proves that this method of justification works for induction no better than for
its counterinductive rival.
3. Non-epistemic response to the problem of
induction: Pragmatic Vindication
This response is non-epistemic in the same sense as the
Pascal’s wager is; it is not as much about justification of induction as a
legitimate rule of inference leading to true conclusions as it is about
practical value of sticking to this rule as far as it works.[7]
Pragmatists
agree with Hume that there is no epistemic justification for induction.
Instead, they come up with pragmatic explanation of why one is justified in
using this method of inference. Actually, the future is unknown (it has not
come to be yet!). But even though it is unknown, we cannot avoid having
expectations about it. In our expectations it is reasonable, or prudent, for us
to stick to the method which would, among other alternative methods, lead to
success.
What can
this optimal method be?
Nature is
either uniform (the future will resemble the past) or nature is not uniform.
For each of these possibilities let us consider outcomes for using and not
using the inductive principle of inference for the above two options. If nature
is, in fact, uniform, induction is a highly reliable method for predicting
future events. If nature is not uniform, induction, alas, is of no help. If
nature is uniform, non-inductive predicting of future events is just a shot in
the dark – we can hit or we can miss. Non-inductive inference is the same wild
guess if the future will not resemble the past. Thus, the non-inductive method
is not reliable no matter whether nature is uniform or chaotic. As for induction, it will certainly be
helpful at least in the case when nature is uniform. Thus, it is rational for
us to prefer this method of inference.
The
following table sums up the outcomes for using and not using induction in cases
of uniformity and non-uniformity of nature:
|
|
Nature is Uniform (The Future Resembles the Past) |
Nature is not Uniform (The Future Does Not Resemble The Past) |
|
using induction |
Successful in predicting the future |
Fails in predicting the future |
|
not using induction |
Fails in predicting the future (since we do not even try to use it) |
Fails in predicting the future |
One may
claim that there can be some other way to predict the future besides induction
and pure guess though we have not found it yet. To this a pragmatist can answer
that if there was any third option, the outcome for it would be like this:
i.
If nature is uniform,
this method would either be successful or unsuccessful (since we do not know
what the method is like). In charity we can assume that this method would
succeed.
ii.
If the nature is
not uniform, then this or any other method would fail - chaotic character of
nature would refute any systematic method.
If we assume
that there can be some method other than induction that works in irregular
nature, this means that the nature is uniform at least in one aspect - it
conforms to this method. Pragmatists claim that if it were so, it is induction
that would find this method.
Thus, this
alternative undiscovered method would be no better that induction. Pragmatists
conclude that if there are methods that lead us to success in predicting the
future, inductive rule of inference is among them. Pragmatists provide a
pragmatic reason for why it is better for us to cling to induction. However,
they do not solve the main problem of Hume: what kind of epistemic reason there
is for expecting the future to resemble the past.
4. Sir Karl Popper’s response
Popper[8]
accepts Hume’s skeptical conclusions about induction, but is not a bit
sorrowful about it. What makes him optimistic about these conclusions is “the
conjectural character of human knowledge”. By this Popper means that none of
our best scientific theories can ever be proven to be true. They always remain
hypothetical in the sense that they are open for revision and can be refuted
should evidence to their falsehood occur. The way of science is approximation
to the truth. And this approximation is fulfilled not by acceptance of true
theories (there is no legitimate way to do this), but by refutation of the
false ones and by retaining those which were not refuted. Thus, there is no
need for induction, Popper says. “Induction simply does not exist, and the
opposite view is a straightforward mistake.”
The method
that we use in science, Popper claims, resembles induction, but is not
induction should we take a closer look. Suppose that we develop a theory that
should yield a certain observation. If the expected observation really occurs,
we cannot validly conclude that the theory is true[†].
However, we can state that the theory has passed the test and can be retained
for further verification. A chain of similar experiments may look like
inductive premises, but we are not about to infer a general rule from them.
Instead of inferring the general rule that is true for all times, we claim that
the theory is “corroborated”, which means that it has survived our most severe
tests and we can make practical use of it so far. If, however, the observation
expected under certain theory fails to occur, we may validly conclude that the
theory is false and should be refuted. Popper called this method “the method of
trial and elimination of error” as well as “the method of conjectures and
refutations”.
Popper
concludes that rationally we should not accept any theory as true even if it
survived any amount of “eliminative criticism”. However, we can make a
practical use of it, being at the same time ready to refute this theory upon
appearance of disqualifying evidence.
The main
objection to Popper’s method of conjectures and refutations is Duhem’s thesis that theories, in fact, are never being
falsified by an experiment[9].
This happens because theories are never tested (put on test) in isolation, all
by themselves. Besides a theory, its testing includes initial conditions under
which a test is provided and a bunch of auxiliary assumptions. Thus, if a
supposed observation does not occur, we cannot tell which one among a theory,
auxiliary hypotheses or initial conditions should be rejected as false. We can
always save a theory by refutation of some of background assumptions.
5. A priori
justification of induction - Laurence BonJour’s
Response
A recent answer to the problem of induction is provided by Laurence BonJour[10].
Since a posteriori justification of
inductive inference proved to be unsatisfactory due to begging the question or
infinite regress problem, the only way to save induction would be in justifying
it a priori. The proposed a priori justification is not what Hume
meant by demonstrative reasoning (deduction). BonJour
proposes to justify induction using inference to the best explanation.
The first
issue he is concerned with is how among many observations we pick those that
can serve as premises for an inductive argument such that it is likely to lead
to a true conclusion (either concerning a general rule or the next
prediction). BonJour claims that such series of
observations are those in which the observed value of As that are Bs converges
to some particular value over time. For instance, if we observe people who wear
pink shirts on Tuesdays, and the proportion of such people does not converge to
any particular value with time no matter how many observations have been
provided, we have no reason to infer a general rule or to predict the number of
such people for the next observation. If, however, in some series of
observations a value of As that are Bs converges to some particular limit (even
with some insignificant fluctuations), such convergent series require an
explanation. There can be two possible explanations: either they are matter of
pure chance or they reflect a real regularity in the world. BonJour
claims that though chance is still logically possible, it becomes less likely
as a certain convergence persists. So, the best explanation of such convergent
series is that they are evidence to the regularities that actually exist due to
the nature of objects involved. For instance, since in all our observations of
emeralds they have always been green, the best explanation of these
observations is that they reflect the actual relations between “emeraldness” and “greenness”. There must be something in
the nature of light, the molecular structure of emeralds and the constitution
of human eye that makes the latter perceive emeralds as green. Given this, it
is rational to expect that the next emerald will be green.
Thus, the
inductive premises representing a convergent series of observations are very
likely to lead to a true inductive conclusion.
There are
two problems with this response. The first problem concerns the uniformity of
nature. Hume claims that the possibility that the course of nature will change
is no less conceivable that it will not. BonJour does
not respond to the question directly, saying that the issue of uniformity of
nature is more of a metaphysical question. He only states that since
regularities that persist through time cannot be counted as a mere coincidence,
but happen somehow due to the nature of As and Bs, these regularities will
likely persist as long as As and Bs exist.
Second, BonJour’s answer seems to be rather “on the surface”. To
suppose that convergent series of observations are the evidence of actual
regularities in nature, but not just a matter of pure chance is what strikes
everybody first. The reason why the inference to the best explanation was not
previously used to justify induction is that abduction has not yet been
justified as a legitimate principle of inference. Before we can use the
inference to the best explanation to justify induction we have to prove
abduction to be rational. The
justification of the inference to the best explanation is likely to encounter
the same rationality and reliability problems as raised for induction, since in
this type of reasoning the conclusion also goes beyond the scope of premises
(it is the explanation of premises), thus being at risk to be false.
Conclusion
It is
difficult to say whether we can consider any of the above responses to be a
satisfactory solution to the traditional problem of induction. At least it is
obvious that there can never be any epistemically
infallible justification of the inductive principle of inference since the
definition of induction presupposes that there cannot be such infallible
justification. So either we should agree with Hume and Popper that there is no
such legitimate rule of inference as induction and take seriously Popper’s
method of “conjectures and refutations” or we should revise our approach
towards knowledge and accept a lower justification standard, at least with
regard to the matter of facts that transcend our direct experience.
BIBLIOGRAPHY:
1. Duhem, Pierre. “Physical Theory and Experiment.” In Readings
in the Philosophy of Science (From Positivism to Postmodernism), Theodore
Schick, Jr., Mayfield Publishing Company, Mountain View, California.
2. Hume,
David. Enquiries concerning human understanding and concerning the
principals of morals. 3rd ed. With text revised and notes by P.
H. Nidditch. Clarendon Press.
3. Popper,
Karl. “The problem of Induction (1953, 1974)”, Popper Selections. ed.
David Miller.
4. Skyrms, Brian. Choice and Chance: an introduction to inductive
logic. 4th ed.
5. Sober,
Elliot. Core Questions in Philosophy. 3rd ed.
References: