Deductive Reasoning: Syllogisms and Logic • 361Deductive Reasoning: Syllogisms and Logic
Aristotle is considered the father of deductive reasoning because he introduced the
basic form of deductive reasoning called the syllogism. A syllogism includes two state-
ments, called premises, followed by a third statement, called the conclusion. We will
fi rst consider categorical syllogisms, in which the premises and conclusion describe the
relation between two categories by using statements that begin with all, no, or some.
An example of a categorical syllogism is the following:Syllogism 1
Premise 1: All birds are animals.
Premise 2: All animals eat food.
Conclusion: Therefore, all birds eat food.If you were asked to evaluate this syllogism, would you decide it is an example of
good reasoning? If you answered “yes,” you would be correct. But what does it mean
to say that “good reasoning” is involved here? The answer to this question involves
considering the difference between validity and truth in syllogisms.VALIDITY AND TRUTH IN SYLLOGISMS
The word valid is often used in everyday conversation to mean that something is true or
might be true. For example, saying “Susan has a valid point” could mean that what Susan
is saying is true, or possibly that it should be considered further. However, when used in
conjunction with categorical syllogisms, the term validity has a very specifi c meaning: A
syllogism is valid when its conclusion follows logically from its two premises.
Let’s now consider another syllogism, that has exactly the same form as the fi rst one:Syllogism 2
All birds are animals. (All A are B)
All animals have four legs. (All B are C)
All birds have four legs. (All A are C)In this example, the form of the premises and the conclusion is indicated in parenthe-
ses, using A, B, and C instead of birds, animals, and legs. From this, you can see that
Syllogism 2 has the same form as Syllogism 1. Both syllogisms are therefore valid,
because the conclusion follows from the two premises.
At this point you may feel that something is wrong. How can Syllogism 2 be valid
when it is obvious that the conclusion is wrong, because birds don’t have four legs?
The answer is that validity and truth are two different things. Validity depends on the
form of the syllogism, which determines whether the conclusion follows from the two
premises. Truth, on the other hand, refers to the content of the premises, which have to
be evaluated to determine whether they are consistent with the facts. The problem with
Syllogism 2 is that the statement “All animals have four legs” is not true; that is, it is not
consistent with what we know about the world. It is no coincidence, then, that the con-
clusion, “All birds have four legs,” is not true either, even though the syllogism is valid.
The difference between validity and truth can make it diffi cult to judge whether
reasoning is “logical” or not. Not only can valid syllogisms result in false conclusions,
but syllogisms can be invalid even though each of the premises and the conclusion seem
reasonable. For example, consider the following syllogism, in which each of the prem-
ises could be true and the conclusion could be true:Syllogism 3
All of the students are tired.
Some tired people are irritable.
Some of the students are irritable.Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.