Deductive Reasoning: Syllogisms and Logic • 363Syllogism 1 is called affi rming the antecedent because the antecedent, p (If I study),
is affi rmed in the second premise (I studied). The conclusion of this syllogism (I got a
good grade) is valid. Syllogism 2 is called denying the consequent because the conse-
quent, q (I’ll get a good grade) is negated in the second premise (I didn’t get a good
grade). The conclusion of this syllogism (I didn’t study) is valid.
Syllogism 3 is called affi rming the consequent because q is affi rmed in the second
premise (I got a good grade). The conclusion of this syllogism (I studied) is invalid,
because even if you didn’t study, it is still possible that you could have received a good
grade. Perhaps the exam was easy, or maybe you knew the material because it was
about your job experience. If that explanation is not convincing, consider the follow-
ing syllogism, with “studying” and “good grade” in Syllogism 3, replaced by “robin”
and “bird.”If it’s a robin, then it’s a bird.
It’s a bird.
Therefore, it’s a robin.When stated in this way, it becomes more obvious that the affi rming the consequent
form of the syllogism is invalid.
Syllogism 4 is called denying the antecedent because p is negated in the second
premise (I didn’t study). The conclusion of this syllogism (I didn’t get a good grade) is
not valid. As in Syllogism 3, you can probably think of situations that would contradict
the conclusion, in which a good grade was received even though the person didn’t study.
Again, the fact that this syllogism is invalid becomes more obvious when restated in
terms of birds and robins:If it’s a robin, then it’s a bird.
It’s not a robin.
Therefore, it’s not a bird.How well can people judge the validity of these syllogisms? The results of many
experiments, shown in the far right column of Table 13.1, indicate that most people
(close to 100 percent in most experiments) correctly judge that Syllogism 1 is valid,
but performance is lower on Syllogism 2, which is also valid, and 3 and 4, which are
not valid. These percentages are the average results from many studies in which the
syllogisms were stated abstractly, using the letters p and q for the antecedent and the
consequent. In the next section we will describe a reasoning problem that has been
studied both when stated in abstract form and also in terms of specifi c real-world
examples.TABLE 13.1 Four Syllogisms That Begin With the Same First Premise
First premise of all syllogisms:
If p, then q. (abstract version)
If I study, then I’ll get a good grade. (concrete example)Syllogism Second Premise Conclusion Is It Valid? Judged Correctly?Syllogism 1: Affi rming
the antecedentp (abstract)
I studied. (concrete)Therefore, q
Therefore, I’ll get a good grade.Yes 97%Syllogism 2: Denying
the consequentNot q
I didn’t get a good grade.Therefore, not p
Therefore, I didn’t study.Yes 60%Syllogism 3: Affi rming
the consequentq
I got a good grade.Therefore, p
Therefore, I studied.No 40%Syllogism 4: Denying
the antecedentNot p
I didn’t study.Therefore, not q
Therefore, I didn’t get a good grade.No 40%Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.