7.3 Non-deductive reasoning 263
because every swan that had ever been
observed was white. That was until a species of
black swan was discovered in Australia.
The premise that only white swans had been
observed up to that date was true, and remains
so. But the inference that therefore all swans
are white was then seen to be false. The great
Scottish philosopher David Hume pointed out
the general problem with induction. The
problem, put very simply, is that to argue in
the way that [1] does, one has to assume that
the future will be like the past. But the only
real evidence that we can have for this
assumption is that the future has always
been like the past, in the past! So the argument
is circular, and we are back where we started.
But although inductive reasoning does not
guarantee the truth of its conclusions, and
sometimes yields false ones, we still draw
inferences from repeated experiences and
observations. Indeed, scientific reasoning is
routinely based on such evidence, and proves
to be highly reliable. Also, the problem of
induction is not really a practical problem.
Rational people, including scientists, do not
make a habit of making such crude inductive
arguments as the one above. There is no need
to say that candles in sealed jars will always
go out. It is enough to say that they always
have, and that there is no reason to think
that this will change. The problem can be
avoided by simply not overstating
conclusions, and recognising that good
inductive arguments increase the probability
of the conclusion up to and beyond any
reasonable doubt.Argument to the best explanation
Anyway, what is of interest scientifically is
not whether candles will always go out in
sealed containers, but why they go out. It has
not always been known that burning, or
combustion, involves the absorption of
oxygen (oxidation). From classical times untilpossible worlds. Again, you could argue that
possible worlds don’t count; only the real
world counts. But in logic, and to many
scientists as well, possible worlds do count. We
human beings are quite intelligent, but our
knowledge is still restricted to a tiny bubble of
space-time. Using words like ‘always’ and
‘everywhere’ literally in our reasoning cannot
be justified by evidence or experience. So,
although [1] may seem a safe bet, it is not a safe
inference in any deductive sense.
Induction
You should have noticed that the first
question was about the form of reasoning in
[1]. Even if you were satisfied that [1] itself
made a good case and justified its conclusion
beyond reasonable doubt, that does not mean
that every argument with the same form as [1]
would be as reliable or as persuasive.
We call arguments like [1] ‘inductive’, to
distinguish them from deductive arguments.
Induction does not establish certainty. Instead
its conclusions come with varying degrees of
probability. In strictly logical terms an
inductive argument is invalid, because it is
theoretically possible for the premises to be
true and the conclusion false, however
unlikely this may be. Inductive arguments are
therefore judged not by their validity or
invalidity, but by the strength of the evidence
that they provide and the degree of probability
it gives to the conclusion.
One problem with induction is that
evidence for any general hypothesis is always
limited to a finite number of experiments or
observations or examples. No matter how
many times a hypothesis is confirmed by an
observation, there is always the possibility that
the next one will be the exception. One of the
best-known examples of this weakness in
inductive reasoning is the case of the black
swan. For many centuries it was believed –
with good reason – that all swans were white,