Reason and Experience:
Is there a ‘Problem’ of Induction?
Stephen Mumford, Department of Philosophy, University of Nottingham
1. Reasoning from our experience
Are we entitled to reason from our experience to something that is
outside of our experience?
There is no contradiction in all observed ravens being black but there
also being a white raven that is unobserved.
The example of All swans are white is frequently used by philosophers
because it was believed to be true, on the basis of inductive
E.g.:
From the observed to the unobserved?
From the past to the future?
From the front of objects to the backs of objects?
inference, but eventually found to be false. There is a sub-species
of black swan: cygnus atratus.
The general problem is that we are attempting to infer from particular
Inferences of this broad kind are usually called inductive, in contrast to
deductive inferences.
instances to the general case. All our experience is of particulars,
e.g. individual swans, but in science we frequently want to find
general truths about all swans.
2. Deduction and induction
In a valid deductive argument, if the premises are true, the conclusion
must also be true, as a matter of certainty: it is not logically
Scientific laws, for instance, concern general truths, e.g. that all
unsupported objects fall to the ground, all electrons have negative
charge.
possible for the premises to be true and the conclusion false.
There is a broader sense of induction in which it means any nonE.g.
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
In contrast, inductive arguments are never a matter of logical
certainty. But it is nevertheless alleged that there are ‘good’
inductive arguments.
deductive inference. I see the fronts of people, for instance, and
assume they have backs as well. I have sometimes walked around
people and seen that they have backs so I infer that others do as
well. This is again inferring the unobserved from the observed.
Inferences that the future will be like the past are also inductive. I have
seen, for instance, that hitherto when rain freezes it turns to snow.
I infer that it will always do so. I assume that when the sun goes
3. What is an inductive inference?
down at night, it will be back up the next day.
There is both a narrow, technical sense of inductive argument, and a
broader sense.
In the technical sense, an inductive argument is usually taken to have
the following form:
All observed Fs are G
Therefore, all Fs are G
For instance:
All observed swans are white
Therefore all swans are white
Or perhaps:
a is a swan and is white
b is a swan and is white
c is a swan and is white
…..
Therefore, all swans are white
4. Why is induction a problem?
Inductive inferences are not reliable. We can form an expectation
based on our experience but it may be disappointed. Bertrand
Russell illustrated such disappointment:
The man who has fed the chicken every day throughout its
life at last wrings its neck instead, showing that more refined
views as to the uniformity of nature would have been useful to
the chicken (Russell, The Problems of Philosophy, chapter
IV)
We cannot, therefore, assume that the future will be like the past or,
in general, that the unobserved cases will be like the observed
cases. Perhaps this is a problem with the whole of empirical
As this is an inference from all observed Fs to all Fs, both observed and
unobserved, it is clearly not deductively valid.
science. How far does science get if it only records particular facts
and can never ascend to general theories? Science would be
impoverished.
The constant conjunction view says that for a to be a cause of b, a
must be of a kind A that is always followed something of the same
kind B, as b.
5. Some fixes, and why they don’t work
David Hume (A Treatise of Human Nature) considered, and rejected,
Water causes salt to dissolve, for instance, only if every time salt is put
in water, it dissolves.
one possible solution to the problem of induction. Could one
Hume also thinks that necessity is part of the idea of cause (even
invoke a uniformity of nature principle as an additional premise so
though he ultimately says this idea is groundless), so we think that
as to make an inductive argument deductively valid?
a causes b only if a necessitates b.
Perhaps one could reason:
All observed Fs are G
Nature is uniform
Therefore, all Fs are G
But no natural causal process, I argue, is ever necessitated or
guaranteed (see Stephen Mumford and Rani Lill Anjum, Getting
Causes from Powers, forthcoming Oxford University Press).
Striking a match may cause it to light, but it didn’t guarantee it lighting.
But Hume immediately see that this does not work. To take as a
Some struck matches fail to light. There might be a gust of wind at
premise that nature is uniform is merely to assume the very thesis
just the wrong moment. And even if the light did in fact light, it
that is under examination: induction. For the uniformity of nature
might not if a gust of wind had come.
principle is just the claim that that future will be like the past, or
that unobserved cases will be like observed ones.
The principle’s only justification is itself inductive, and one cannot, on
pain of circularity, assume induction to justify induction.
In confirmation of this, we see that we can have general causal truths
that clearly do not involve constant conjunctions. Smoking causes
cancer, for instance, but not everyone who smokes gets cancer.
Hume’s uniformity of nature principle, therefore, will not just make the
justification of induction circular, it is also a false principle. Nature,
Francis Bacon had a different kind of approach (Novum Organum). We
or at least that part of it that concerns causal laws, is not entirely
can make our inductive inferences as safe as possible just through
uniform: some ravens are not black but albino, and even an albino
gathering the right kind of evidence. One should prefer inductive
black swan might be white!
inference from a large number of observations over an inference
The problem of induction is not, therefore, a genuine problem. We
from a few. One should look in different places and in different
cannot infer from the observed to the unobserved because we
circumstance. One should look also for exceptions. If one follows
should not. It is false to assume the rest of the cases will be like the
the rules of the new organ, one will generate general conclusions
ones you have sampled.
as if mechanically.
But the problem is that although these measures may make the
This view applies to natural causal processes. There are, however,
inference more robust, it will never reach the point of certainty.
some cases of absolute uniformity. Every electron, for instance, is
We thought we had followed the new method in inferring that all
indeed negatively charged and every object with mass attracts
swans were white, but we were still wrong. The black swans were
every other object with mass.
in some hitherto undiscovered country.
Could these be reasonable cases for inductive inference? No. The
reason they are absolute uniformities is because they are not
Peter Strawson (Introduction to Logical Theory) warns in general that it
is foolish to try to turn an inductive argument into a deductive one.
We have to accept that inductive arguments will always be short of
deduction: that is what makes them distinctive.
causal at all. And the truth ‘All electrons are negatively charged’
has not come from an inductive inference.
Essentialism is the view that these claims are not causal/inductive
inference at all but instead name an essential property of the
objects in question.
6. Is there any problem of induction at all?
There is another kind of response that has so far been neglected. The
reason for this neglect is because of a faulty philosophy of nature.
Hume had argued that causal laws consisted in regularities or what he
Hence it should be no surprise that all electrons are negatively charged
because if particle were not negatively charged, it could not be an
electron. Being negatively charged is part of what it is to be an
electron.
called constant conjunctions. Many have continued to hold this
assumption: even those who are non-Humeans.
Conclusion: there is no ‘problem of induction’ after all.