Conclusions

Modern logic has developed both proof theory and model theory for systems powerful enough to cope with all the deductive inferences that human beings make. What is lacking is a systematic method for translating such inferences into formal logic. Psychologists continue to investigate deductive reasoning. Their two main theoretical accounts are based on rules of inference and on mental models, respectively—a distinction that parallels the one between proof theory and model theory in logic. Rule theorists emphasize the automatic nature of simple deductions and postulate rules corresponding to them. More complex inferences, they assume, call for sequences of simple deductions. In contrast, model theorists emphasize that reasoning is the continuation of comprehension by other means. The system for implicit inferences based on knowledge aids the process of constructing models of discourse. In deliberative reasoning, individuals tend to focus on possibilities in which the premises are true. However, they can grasp the force of counterexamples. The evidence suggests that people have a modicum of deductive competence based on mental models. Rules of inference and mental models, however, are not incompatible. Advanced reasoners may construct formal rules for themselves—a process that ultimately leads to the discipline of logic.

See Also the Following Articles

ARTIFICIAL INTELLIGENCE • CATEGORIZATION • CREATIVITY • INFORMATION PROCESSING • INTELLIGENCE • LANGUAGE AND LEXICAL PROCESSING • PROBLEM SOLVING

Suggested Reading

Baron, J. (1994). Thinking and Deciding, 2nd ed. Cambridge Univ.

Press, New York. Braine, M. D. S., and O'Brien, D. P. (Eds.) (1998). Mental Logic.

Erlbaum, Mahwah, NJ. Brewka, G., Dix, J., and Konolige, K. (1997). Nonmonotonic Reasoning: An Overview. CLSI Stanford Univ. Press, Stanford, CA.

Evans, J. St. B. T., and Over, D. E. (1996). Rationality and Reasoning.

Psychology Press, Hove, UK. Garnham, A., and Oakhill, J. (1994). Thinking and Reasoning.

Blackwell, Cambridge, MA. Jeffrey, R. (1981). Formal Logic: Its Scope and Limits, 2nd ed.

McGraw-Hill, New York. Johnson-Laird, P. N. (2001). Mental Models and deduction. Trends in Cognitive Scien. 5, 434-442. Johnson-Laird, P. N., and Byrne, R. M. J. (1991). Deduction.

Erlbaum, Hillsdale, NJ. Johnson-Laird, P. N., Legrenzi, P., Girotto, V., Legrenzi, M., and Caverni, J.-P. (1999). Naive probability: A mental model theory of extensional reasoning. Psychol. Rev. 106, 62-88. Kahneman, D., Slovic, P., and Tversky, A. (Eds.) (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge Univ. Press, New York.

Oaksford, M., and Chater, N. (1998). Rationality in an Uncertain World: Essays on the Cognitive Science of Human Reasoning. Psychology Press, Hove, UK. Rips, L. J. (1994). The Psychology ofProof. MIT Press, Cambridge, MA.

Schaeken, W., De Vooght, G., Vandierendonck, A., and d'Ydewalle, G. (2000). Deductive Reasoning and Strategies. Erlbaum, Mahwah, NJ.

Stanovich, K. E. (1999). Who Is Rational? Studies of Individual

Differences in Reasoning. Erlbaum, Mahwah, NJ. Wharton, C. M., and Grafman, J. (1998). Deductive reasoning and the brain. Trends Cognitive Sci. 2, 54-59.

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