Thinking and Deciding

EXTENSIONS OF LOGIC 93
with the actual situation, by analogy with a similar known situation, or by a general
rule for reasoning about permissions (Cheng, Holyoak, Nisbett, and Oliver, 1986).
Cheng and her colleagues call such a general rule a “pragmatic inference schema.”
It is in between a rule of formal logic and an analogy to a specific example. We may
think of it as a heuristic that leads to conformity with a formal rule in a certain kind
of situation.
Another possibility is that performance is helped when subjects can understand
the rule testing. (Here I use the word “understand” in the sense discussed in Chapter
3.) When the testing of the rule has a purpose — to detect violators — subjects may
understand better, and discover more easily, the arguments in favor of a certain “design”
for testing the rule. One source of the difficulty of the original task may have
been the subjects’ lack of understanding of the task, which, in turn, resulted from the
lack of a purpose, other than the arbitrary purpose provided by the experimenter.
Exercises on mental models in syllogisms
The purpose of these exercises is to help you understand the strengths and limitations of
Johnson-Laird’s theory as an account of your own performance in solving difficult syllogisms.
A. What conclusion can you draw from each of the following pairs of premises? Remember,
the possible conclusions are:
All A are C.
All C are A.
Some A are C (or, equivalently, some C are A).
No A are C (or no C are A).
Some C are not A.
Some A are not C.
No conclusion possible.
Explain how you reached your answer for each syllogism; use diagrams if you wish. Here are
the syllogisms:
1. No B are A. Some C are B.
2. Some B are not A. Some C are B.
3. No A are B. All B are C.
4. No B are A. Some B are C.
5. Some B are not A. Some B are C.
B. What form(s) did your mental models take? Do you think that it was a form that would
represent “Some A are B” as different from “Some B are A” (and/or “No A are B” as different
from “No B are A”)?
C. On which items, if any, did you consider more than one mental model? Can you count the
models you considered?
Extensions of logic
A limitation of formal logic as a normative model of thinking is that it deals only with
conclusive arguments. Few of the rational conclusions that we draw in daily life can