Thinking and Deciding

86 LOGIC
No A are B.
All B are C.
There are three models to consider here: 2
1. 2. 3.
A A A = (C)
A A = (C) A = (C)
B = C B = C B = C
B = C B = C B = C
(C) (C) (C)
(Here the horizontal line under the As indicates separation, as in the premise “No A
are B.”) In model 3, all of the As are Cs. Subjects often conclude that no A are C. It
is apparent that this conclusion is consistent only with the first of the three models.
The only conclusion consistent with all three models is that some C are not A, and
this is the correct answer.
We see that one reason for mistakes in dealing with syllogisms is that subjects
sometimes draw a conclusion based on a single model, and fail to consider alternative
models, especially models that are inconsistent with their conclusion. If we think of
models as “evidence” and the conclusion as a “possibility,” this kind of error is an
example of failure to seek evidence against a favored possibility, a basic source of
poor thinking. The same can be said when subjects consider two models, but not
a third model, although this error is less extreme. Johnson-Laird and Steedman
(1978) and Johnson-Laird and Bara (1984) were able to predict the relative difficulty
of different syllogisms, and the errors that are made, by assuming that many subjects
fail to consider more than a single model. The most difficult syllogisms tend to be
those that require consideration of three alternative models.
Johnson-Laird (1983) has also found that the models people form seem to be “directed,”
that is, the order of the terms in each premise makes a difference. Syllogisms
are easiest when the first term of the conclusion is the first term in the first premise
and the second term in the conclusion is the second term in the second premise (in
the order: A–B, B–C, therefore A–C). It is as though the premises had to be diagrammed
in left-to-right order, with the Bs of the first premise next to the Bs of the
second premise, before the subject could combine them. When the subject must reverse
one of the premises, the task is more difficult. Because the order of the terms
is called the “figure,” this effect is called the “figural effect.” This effect can be
seen when the difficulty of a syllogism depends on the order in which the terms are
presented. For example, when subjects are given
Some A are B.
All B are C.
almost all of them conclude, correctly, “Some A are C.” However, when given
2 It is assumed here that there is at least one A, one B, and one C.