90 SMART THINKING: SKILLS FOR CRITICAL UNDERSTANDING & WRITING
stage. It is often claimed that deduction is a form of reasoning from general rules
to specific premises and that induction is the reverse, that is, reasoning from
specific cases to a general conclusion. Now, no matter what you might see or read
elsewhere, this is wrong. The difference between deduction and induction has
nothing to do with general or specific reasoning, but has everything to do with
what the conclusion does on the basis of the premises.
We will explore this genuine difference in a moment but let me reassure you
that, if the distinction seems hard to grasp, you are not alone. Philosophers
have generally sought to retreat to those examples and cases of reasoning which
are clearly deductive and clearly inductive: they have not engaged with the
muddy mass of indistinct cases which are, by and large, the everyday reasoning
we use.Deduction
In deductive reasoning, your conclusion states with certainty a relationship
between two or more premises. It has to be certain, because it simply makes explicit
a relationship that is already there (but not directly obvious) in the combination of
the claims that are serving as premises. You will remember this aspect from the
discussion of claims in chapters 2 to 4. Let us look at an example:
I am under 18; people under 18 in Australia cannot vote. Therefore I
cannot vote.
There are three key terms in this argument. One is age (under 18); the other is
voting; and the last is T. The conclusion simply re-expresses the implicit relation-
ship of the premises which can be expressed, in a formula way, like this:
A is one of B; B can't do C; therefore A can't do C.
The certainty with which (in this argument) the conclusion is stated relates not
to the truth or otherwise of the premises but to the logical form of the argument.
If it turns out that the premises are indeed true, then the conclusion is guaranteed
both by the truth of the premises and by the form of the reasoning.
The key test for a deductive argument is to ask yourself, being absolutely
trusting, 'can you deny the conclusion, if it is that you previously have no doubt or
deny the premises'. For example:
African swallows are migratory birds; all migratory birds fly long distances
and therefore I conclude African swallows fly long distances.
Now, let us assume absolutely and without doubt that the premises are true.
Can you deny (refuse to accept) the conclusion now? No! Do not be confused
and think 'Ah, but maybe African swallows are not migratory birds'; if you have
this doubt then you have not accepted the first premise. Deductive thinking is
something of a mind game (an important one, nevertheless): checking for
deductive entailment (where the conclusion is guaranteed by the premises) first