Page 436 - Deep Learning

Notes to Pages 101–103 419

type are called linear syllogisms or three-term series problems, began with Hunter
(1957) and was continued by Clark (1969), DeSoto, London and Handel (1965), and
Huttenlocher (1968), all trying to account for the differential difficulty of various
three-term series problems. Johnson-Laird (1983, pp. 111–112) and Ohlsson (1984c)
concluded independently that people process series problems by building mental
models of the series and reading off answers by inspecting them in the mind’s eye.
Johnson-Laird went on to develop the idea of mental models into a general theory
of thinking (Johnson-Laird, 2006, pp. 122–126). The concept of a mental model
used in these works is closely related to the notion of a situation model in theories
of language comprehension (Kintsch, 1998) and to the notion of a problem state in
theories of problem solving (Newell & Simon, 1972a).
33. Although everyone agrees that people are not logical, researchers disagree on the
reason for this. Henle (1962) argued that people reach conclusions from given
premises that differ from those dictated by logic because they often understand
those premises differently than logicians. Others have argued that people operate
with a “paralogic” or “psycho-logic” that includes fallacious inference rules such
as the conversion of if p, then q into if q, then p (Wason & Johnson-Laird, 1972,
Chap. 6) or all A’s are B’s into all B’s are A’s (Griggs & Osterman, 1980; Revlin &
Leirer, 1978). The notion of invalid inference rules has been applied in clinical
psychology to explain pathologies of thought but with only limited success (von
Domarus, 1944/1964; Mujica-Parodi, Mataspina & Sackeim, 2000). An alternative
type of explanation is that reasoning is primarily determined by nonlogical factors
such as attitudes (e.g., Abelson & Rosenberg, 1958). Cheng and Holyoak (1985)
have proposed that people reason with pragmatic schemas, patterns of reasoning
that are derived from, and hence specific to, an area of everyday experience, e.g.,
cause-effect relations, obligations or permissions. Cosmides (1989) has attempted
to ground particular versions of such schemas in human evolution rather than
everyday experience, not without controversy (Buller, 2005). Johnson-Laird (1983,
2006) have proposed that people reason with mental models instead of inference
rules or schemas. With the exception of the idea that people do not reason but
respond to reasoning problems on the basis of attitudes, these four hypotheses –
people understand the premises differently; they reason with a psycho-logic that
includes domain-general but logically invalid inference rules; they reason with
domain-specific schemas; they reason with mental models – share the goal of
describing a mechanism of reasoning that can explain the pattern of errors in
human reasoning while also explaining the power of human reasoning.
34. One source of evidence for subgoaling is the scalloped reaction time curves
that result when people perform hierarchically organized tasks; see Anderson,
Kushmerick and Lebiere (1993, Figure 6.3), Greeno (1974, Figures 3 and 4), and
Corrigan-Halpern and Ohlsson (2002, Figure 2). Another type of evidence is
that teaching explicit subgoals to students affects how and what they learn from
problem-solving practice; see, e.g., Catrambone (1998).
35. Woodworth (1938, p. 823).
36. The modern study of heuristics, rules of thumb that usefully bias choices during
search, began with George Polya, a mathematician who tried to codify patterns of
reasoning in mathematics for the benefit of students (Polya, 1962, 1968). Newell