Thinking and Deciding

WHAT IS LOGIC? 79
validity of syllogisms depends on their form, not on the specific terms used in them.
We can use letters such as P, Q, L, or M to stand for specific terms. If the syllogism
is valid, no matter how we replace the letters with actual terms, it will be impossible
for the conclusion to be false if the premises are true.
Consider another example:
An L can be an M.
An M can be an N.
Therefore an L can be an N.
Is this a valid syllogism? Is the conclusion always true whenever the premises are
true? How can you tell? Try to think of examples. “A man can be a scientist”; “A
scientist can be a New Yorker”; “A man can be a New Yorker.” So far, so good; but
remember (from ch. 3) that good thinkers try to find evidence against a possibility as
well as evidence in its favor. Try to find an example that shows the rule is false — that
is, a counterexample. What about substituting “men,” “scientists,” and “women,” for
L, M, and N, respectively, just as we did before? “A man can be a woman.” Aha!
The syllogism is invalid; the proposed rule is false. Did you know that before? Was
it part of your knowledge of the word can? Hmm.
Let us try another one:
A is a blood relative of B.
B is a blood relative of C.
Therefore A is a blood relative of C.
Sounds good. But now try to think of a counterexample. 1 We discover that this rule
is wrong by constructing what Johnson-Laird calls a mental model of a situation.
The mental model serves as a counterexample. This example makes it much more
plausible (to me, anyway) that when we reflect on the laws of logic we are not simply
discovering what we already know. Most college students think that this rule is
true, until they are pushed to think of counterexamples, or given one (Goodwin and
Johnson-Laird, 2005).
As a final example, let us consider a syllogism that is one of the bugaboos of
logic students:
If A then B.
B.
Therefore A.
(In the shorthand form used by philosophers, here “A” means “A is true”; “B” means
“B is true”; and so forth.) What happens if we substitute words for the letters?
If it rains, Judy takes the train.
Judy took the train today.
Therefore it rained.
1You are a blood relative of both of your biological parents, yet they are probably not blood relatives
of each other.