Thinking and Deciding

MENTAL MODELS 87
Some B are A.
All B are C.
many subjects say, “No valid conclusion,” even though “Some B are A” means the
same as “Some A are B.” Those subjects who are correct in the second form are
also more likely to state the conclusion as “Some C are A,” possibly because they
have switched around the “arrows” in their mental model of the second premise. The
figure seems to affect both the difficulty of the problem and the way in which the
conclusion is expressed.
Ability to solve categorical syllogisms is affected both by the tendency to consider
alternative models and by the figural effect. Subjects who have the greatest
difficulty are often unable to put together even a single model, especially when the
premises are not in the most convenient order (that is, A–B, B–C). These subjects
find the problem particularly hard when one of the premises must be turned around.
Other subjects do not find the problem hard when only a single model must be considered,
almost regardless of the figure, but do have trouble with multiple-model
problems.
Galotti, Baron, and Sabini (1986) found support for this analysis. Subjects were
selected according to their scores on a test of syllogistic reasoning. Subjects were
asked to give an initial answer under time pressure, and a final answer without pressure.
It was thought that the initial answer might be based on a single model of
both premises, and that the final answer in good reasoners (high scorers) would result
from consideration of alternative models inconsistent with the initial conclusion.
Good reasoners were in fact more likely to correct answers that were initially incorrect,
especially on problems in which “nothing follows,” which always involved
more than a single model. Good reasoners also took about twice as much time as
poor reasoners between initial and final answers. (The two groups were about equal
in the time spent on initial answers.) Apparently, those who were good at the task
were more thorough in their search, and possibly more self-critical as well. They
seemed (in think-aloud tasks) to search for models that were inconsistent with their
initial conclusion.
The mental-model approach can be extended to both predicate logic and propositional
logic. Consider the following examples of predicate logic:
1. None of the As is in the same place as any of the Bs.
All of the Bs are in the same place as all of the Cs.
2. None of the As is in the same place as any of the Bs.
All of the Bs are in the same place as some of the Cs.
Problem 1 easily leads to the conclusion “None of the As is in the same place as any
of the Cs.” A single model is required for this: AAA / BBBCCC. (The slash separates
the different places.) If a single model of the second problem is constructed, an
incorrect conclusion might be drawn. Specifically, the model AAA / BBBCC / CC
might yield the conclusion “None of the As is in the same place as any of the Cs.” The
correct answer requires consideration of a second model, AAACC / BBBCC. The