Thinking and Deciding

82 LOGIC
For each system of logic, we can ask whether people actually make inferences
in a way that is consistent with the rules of logic. When we do think logically, we
can ask how we do it. It is not necessarily by following the rules as stated in logic
textbooks. When we do not, we can ask why not and whether the problem can be
corrected.
For propositional logic, there is considerable evidence that people (at least adults)
have learned to follow many rules that correspond directly to some of the major
argument forms. For example, consider the following syllogisms (from Braine and
Rumain,1983, p. 278):
1. There is a G. There is an S. Therefore there is a G and an S.
2. There is an O and a Z. Therefore there is an O.
3. There is a D or a T. There is not a D. Therefore there is a T.
4. If there is a C or a P, there is an H. There is a C. Therefore there is an H.
These inferences are so obvious (once we understand the words) that no thinking
seems to be required to evaluate their truth. Moreover, we seem to be able to
draw more complex inferences by stringing these simple ones together. For example,
evaluate the argument “If there is an A or a B, there is a C. There is a B or a
D. There is not a D. Therefore there is a C.” This argument combines forms 3 and 4
in the list. Braine and Rumain (1983) and Rips (1983) review and report a number
of studies of such reasoning. It is possible to predict the difficulty of evaluating an
argument by figuring out which of the basic arguments from propositional logic must
be put together in order to make it up. This approach to the study of logic has been
called natural logic or natural deduction. The name reflects the idea that certain
forms of argument are just as easy for most of us to use and understand as speaking.
Researchers have been particularly interested in finding out how we have acquired
these abilities. Studies of children suggest that some of them are slow to appear,
developing only as children mature (Braine and Rumain, 1983).
Difficulties in logical reasoning
The natural-logic approach sometimes works for propositional logic, but it does not
seem to work for categorical logic. First, categorical syllogisms seem to be much
harder. Moreover, the difficulties are of a different sort. In most problems in propositional
logic, we either see an answer right away or we puzzle over the problem,
sometimes solving it, sometimes not. In categorical reasoning, we almost always
come up with an answer, but the answer very often turns out to be wrong. Consider
this very difficult example (from Johnson-Laird and Bara, 1984): Given the
statements
No A are B.
All B are C.