We use deductive reasoning whenever we act on the basis of
general knowledge--knowledge about classes of things and the
properties they share. We acquire that knowledge in various
ways, but primarily by generalizing from our experience--a form
of inductive reasoning.
We cannot support a general proposition by merely appealing to other general propositions. At some point in our reasoning, we have to look at the actual instances
of the general propositions.
However, there are dangers in generalizing from instances to a
general proposition. We often generalize too quickly on the
basis of insufficient evidence, committing the fallacy known as
Hasty generalization is a fallacy because a single instance
doesn't necessarily prove a general rule. Suppose we have a
general proposition of the form "All S are P." Now consider the
individual members of the class of Ss. If an individual S is P,
it is called a positive instance, and it confirms the
generalization. If an individual S is not P, it is a negative instance or counterexample, and it disconfirms the generalization.
There is a logical asymmetry here. A single negative instance
decisively refutes a general statement. If I say that all
athletes are dumb, and you point out that the varsity quarterback
is getting excellent grades, you have proved me wrong.
A single positive instance, however, does not prove that a
generalization is true. The fact that one athlete is a weak
student doesn't prove that all of them are.
If S stands for a small, delimited class of things, we can solve
this problem by examining each member of the class individually
to see whether it is P. This is called the method of induction
by complete enumeration.
However, most of the generalizations we employ in everyday
reasoning do not involve classes that can be completely
enumerated. They involve much larger classes that are open-ended
in the sense that there is no limit on the number of members they
So we have to rely on an incomplete survey of the class, a sample
taken from the class as a whole. Our generalizations rest on
the assumption that the sample is representative of the whole
A sample can provide evidence of a connection between S and P
only if it is representative of the whole class of Ss, but how do
we tell whether a sample is representative?
Three rules will help us decide. These rules are standards for assessing the
strength of the inference from sample to generalization, and they
are analogous to the rules for determining whether a syllogism is
1. The sample should be sufficiently numerous and various.
2. We should look for disconfirming as well as confirming
instances of a generalization.
3. We should consider whether a link between S and P is plausible in light of other knowledge we possess.
Unlike a deductive argument, an inductive one is not self-
contained. Its strength is affected by the context of other
knowledge we possess. The truth of the premises does not
guarantee the truth of the conclusion, and the degree of support
the premises provide for the conclusion depends on factors not
contained in the argument itself.
It is always possible to strengthen an inductive argument further
by finding additional positive instances, especially if they
increase the variety of the sample (Rule #1). However, the
strength of the argument is dependent on our diligence in looking
for disconfirming evidence as well (Rule #2). Its strength also depends on the initial plausibility of the generalization, which is
determined by our theories and basic assumptions (Rule #3).
This is not a defect of induction. It means that inductive
reasoning puts a special premium on integration, on looking
beyond the argument itself to see how it fits with the rest of