Illusions in modal reasoning

According to the mental model theory, models represent what is true, but not what is false. One unexpected consequence is that certain inferences should have compelling, but invalid, conclusions. Three experiments corroborated the occurrence of such illusions in reasoning about possibilities. When problems had the heading "Only one of the premises is true," the participants considered the truth of each premise in turn, but neglected the fact that when one premise is true, the others are false. When two-premise problems had the heading "One of the premises is true and one is false," the participants still neglected the falsity of one of the premises. As predicted, however, the illusions were reduced when reasoners were told to check their conclusions against the constraint that only one of the premises was true. We discuss alternative explanations for illusory inferences and their implications for current theories of reasoning.     

How to eliminate illusions in quantified reasoning

The mental model theory postulates that reasoners build models of situations described in premises. These models normally make explicit only what is true according to the premises. The theory has an unexpected consequence. It predicts the existence ofillusions in inferences: Certain inferences should have compelling but erroneous conclusions. Previous studies have corroborated the existence of such illusions. The present study reports the first effective antidote to them. For example, most people incorrectly answer “yes” to the following problem:Only one of the following statements is true . . . /At least some of the plastic beads are not red. /None of the plastic beads are red. /Is it possible that none of the red beads are plastic? In two experiments, we progressively eliminated this fallacy and others by using instructions designed to overcome the bias toward truth. The difference between the illusory and the control problems disappeared when the participants were instructed to work out both the case in which the first premise was true and the second premise was false and the case in which the second premise was true and the first premise was false.     

An antidote to illusory inferences

The mental model theory predicts that reasoners normally represent what is true, but not what is false. One consequence is that reasoners should make “illusory” inferences, which are compelling but invalid. Three experiments confirmed the existence of such illusions based on disjunctions of disjunctions. They also established a successful antidote to them: Reasoners are much less likely to succumb to illusions if the inferences concern disjunctions of physical objects (alternative newspaper advertisements) rather disjunctions of the truth values of assertions. The results shed light both on the cause of the illusions and on the current controversy among different theories of reasoning.     

Book review

Bruner, J., Cole, M. and Lloyd, B. (Eds.). The Developing Child. London: Fontana/Open Books. 1977. (1) MacFarlane, A. The Psychology of Childbirth. Pp. 128. £1.00. (2) Garvey, C. Play. Pp. 128. £1.00. (3) Schaffer, R. Mothering. Pp. 128. £103. (4) Dunn, J. Distress and Comfort Pp. 128. £1.00. (5) Bower, T. The Perceptual World of the Child. Pp. 128. £1.00. (6) Goodnow, J. Children'sDrawing. Pp. 128. £1.00. (7) Tucker, N. What is a Child? Pp. 128. £1.00. (8) Stern, D. The First Relationship. Pp. 128. £1.00.

Mandler, G. Mind and Emotion. New york: Wiley. 1975. Pp. 280. Hardback £7.65; paperback £3.70. ISBN 0471 56690 X.

Elcock, E. W. and Michie, D. (Eds). Machine Intelligence 8. Chichester: Ellis Horwood. 1977. Pp. 630. £24.00. ISBN 85312 058 7.

Griffin, D. R. The Question of Animal Awareness: Evolutionary Continuity of Mental Experience. New York: The Rockefeller University Press, 1976. Pp. viii + 133. $8.95. ISBN 87470 020 5.

Drucker-Colin, R. R. and McGaugh, J. L. (Eds). Neurobiology of Sleep and Memory. New York: Academic Press. 1977. Pp. 456. £13.85. ISBN 0 12 222350 0.

Elkind, D. Child Development and Education: A Piagetian Perspective. New York: Oxford University Press. 1977. Pp. 274. HArdback £8.95. ISBN 0 19 502068 5; paperback £3.75. ISBN 0 19 502069 3.

Tyrer, P. The Role of Bodily Feelings in Anxiety. Londn: Oxford University Press. 1976. Pp. 128. £6.50. ISBN 0 1971 2145 4.

Desmedt, J. E. (Ed.). Progress in Clinical Neurophysiology. Vol. 2. Auditiory Evoked Potentials in Man. Psychopharmacology. Correlates of Evoked Potentials. Basle: KArger. 1977. £37.75. ISBN 3 8055 2629 6.

Snow, C. E. and Ferguson, C. A. (Eds). Talking to Children. Cambridge.: Cambridge University Press. 1977. Pp. 369. £8.00. ISBN 0 521 21318 5.

Lerner, R. M. Concepts and Theories of Human Development. Reading, Mass.: Addison-Wesley. 1976. Pp. 324. £9.10. ISBN 0 2010 4342 4.

Gesell, A., Ilg, F. and Ames, L. The Child from Five to Ten. Revised edition. New York: Harper & Row. 1977. Pp. 461. £7.95. ISBN 06 011501 7.

Bergling, K. The Development of Hypothetico Deductive Reasoning in Children. IEA Monograph studies No. 3. New York: John Wiley. 1975. Pp. 127. £7.50. ISBN 0470 06972 2.     

Mental simulation and argument

When a quantified premise such as: Everyone loves anyone who loves someone, occurs with a premise such as: Anne loves Beth, it follows immediately that everyone loves Anne. It also follows that Carol loves Diane, where these two individuals are in the domain of discourse. According to the theory of mental models, this inference requires the quantified premise to be used again to update a model of specific individuals. The paper reports four experiments examining such iterative inferences. Experiment 1 confirmed that they are harder than immediate inferences. Experiment 2 extended the finding to negative inferences, i.e., granted that Anne does not love Beth, it follows from the quantified premise that Carol does not love Diane. Experiment 3 established that intermediate steps referring to specific individuals are accepted more readily than intermediate steps referring to quantified variables. Experiment 4 showed that the participants' written justifications corroborated the model theory.     

The psychological puzzle of Sudoku

Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 × 9 array according to the general rule that every digit from 1 to 9 must occur once in each row, in each column, and in each of the 3-by-3 boxes in the array. We present a theory of how individuals solve these puzzles. It postulates that they rely solely on pure deductions, and that they spontaneously acquire various deductive tactics, which differ in their difficulty depending on their “relational complexity”, i.e., the number of constraints on which they depend. A major strategic shift is necessary to acquire tactics for more difficult puzzles: solvers have to keep track of possible digits in a cell. We report three experiments corroborating this theory. We also discuss their implications for theories of reasoning that downplay the role of deduction in everyday reasoning.