Annu. Rev. Psychol. 1999. 50:109–35Copyright © 1999 by Annual Reviews. All rights reservedDEDUCTIVE REASONINGP. N. Johnson-LairdDepartment of Psychology, Princeton University, Princeton, New Jersey 08544;e-mail: [email protected] WORDS: deduction, logic, rules of inference, mental models, thinkingABSTRACTThis chapter describes the main accounts of deductive competence, whichexplain what is computed in carrying out deductions. It argues that peoplehave a modicum of competence, which is useful in daily life and a prerequi-site for acquiring logical expertise. It outlines the three main sorts of theoryof deductive performance, which explain how people make deductions: Theyrely on factual knowledge, formal rules, or mental models. It reviews recentexperimental studies of deductive reasoning in order to help readers to assessthese theories of performance.CONTENTSINTRODUCTION .......................................................... 110RATIONALITY AND DEDUCTIVE COMPETENCE ............................. 111THEORIES OF DEDUCTIVE PERFORMANCE ................................. 113Deduction as a Process Based on Factual Knowledge........................... 113Deduction as a Formal, Syntactic Process .................................... 114Deduction as a Semantic Process Based on Mental Models ...................... 115THE PHENOMENA OF DEDUCTIVE REASONING ............................. 118Reasoning with Sentential Connectives ....................................... 118Conditional Reasoning .................................................... 119Reasoning About Relations ................................................ 122Syllogisms and Reasoning with Quantifiers ................................... 123The Effects of Content on Deduction ......................................... 126The Selection Task ....................................................... 127Systematic Fallacies in Reasoning........................................... 128CONCLUSIONS ........................ ................................... 1300084-6570/99/0201-0109$08.00109Annu. Rev. Psychol. 1999.50:109-135. Downloaded from arjournals.annualreviews.orgby University of Colorado - Boulder on 08/31/08. For personal use only.INTRODUCTIONReasoning is a process of thought that yields a conclusion from percepts,thoughts, or assertions. The process may be one of which reasoners are pain-fully aware or of which they are almost unconscious. But it is a systematicprocess if it is reasoning, as opposed to, say, daydreaming.This chapter is concerned with one sort of reasoning, deduction. By defini-tion, deduction yields valid conclusions, which must be true given that theirpremises are true, e.g.:If the test is to continue, then the turbine must be rotating fast enough.The turbine is not rotating fast enough.Therefore the test is not to continue.Some deductions are difficult, and the failure to draw this particular valid con-clusion probably contributed to the Chernobyl disaster. Despite such mistakes,the business of life depends on the ability to make deductions. Individuals dif-fer in this ability, and those who are better at it—at least as measured by intelli-gence tests—appear to be more successful. If so, it is not surprising. A personwho is poor at reasoning is liable to blunder in daily life. Conversely, withoutdeduction, there would be no logic, no mathematics, and no Annual Review ar-ticles.Psychologists have studied reasoning for a century. Not until Piaget, how-ever, did anyone purport to explain how people were able to make deductions.In his account of the genesis of knowledge, he argued that children spontane-ously recapitulate the history of mathematics and arrive at formal reasoning inearly adolescence (e.g. Beth & Piaget 1966). By the mid-1970s, researchers as-sumed that even though Piaget’s theory might not be viable in detail, it wasright on the grand scale. People were equipped with a mental logic. The taskfor psychologists—so they thought—was to delineate its principles. This ap-proach ignored an unsettling discovery made by Wason (1966). Intelligentadults in his “selection” task regularly committed a logical error. He laid outfour cards in front of them:AB23They knew that each card had a letter on one side and a number on the otherside. He showed them a conditional rule: If a card has the letter A on one side,then it has the number 2 on the other side. He then asked them to select thosecards that had to be turned over to discover whether the rule was true or falseabout the four cards. Most people selected the A card alone, or the A and 2cards. What was puzzling was their failure to select the 3 card: If it has an A onits other side, the rule is false. Indeed, nearly everyone judges it to be false inthat case. Yet when Wason changed the content to a sensible everyday gener-110 JOHNSON-LAIRDAnnu. Rev. Psychol. 1999.50:109-135. Downloaded from arjournals.annualreviews.orgby University of Colorado - Boulder on 08/31/08. For personal use only.alization, many people made the correct selections (Wason & Johnson-Laird1972). Insofar as the task is deductive, mental logic is stymied by these effectsof content, which have no bearing on its logic.So much for the historical introduction to the present review. Its plan is sim-ple. It begins with accounts of what the mind is computing when it makes de-ductions, that is, accounts of deductive competence. It then describes theoriesof how the mind carries out these computations, that is, theories of deductiveperformance. The controversy among these theories is hot, so the chapter re-views recent experiments to enable readers to make up their own minds aboutdeduction.RATIONALITY AND DEDUCTIVE COMPETENCENaive individuals, who have no training in logic, may err in tests of deductivereasoning yet achieve their goals in daily life. This discrepancy is the funda-mental paradox of rationality. Psychologists react to it in several differentways, each of which yields a different account of logical competence (for aphilosophical analysis, see Engel 1991). This section reviews these accounts,which are couched at the “computational” level—they characterize what iscomputed but not how the process is carried out.One reaction to the paradox is that people are wholly rational but the psy-chological tests do not reflect their competence. “I have never found errors,”Henle (1978) wrote, “which could unambiguously be attributed to faulty rea-soning.” The