Psychological Review Copyright 2002 by the American Psychological Association, Inc. 2002, Vol. 109, No. 4, 646–678 0033-295X/02/$5.00 DOI: 10.1037//0033-295X.109.4.646 Conditionals: A Theory of Meaning, Pragmatics, and Inference P. N. Johnson-Laird Ruth M. J. Byrne Princeton University University of Dublin The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. You reason about conditional relations because much of your If the TCE in the wells had been drawn from out of the river, knowledge is conditional. If you get caught speeding, then you pay then there’d be TCE in the riverbed. a fine. If you have an operation, then you need time to recuperate. But there isn’t any TCE in the riverbed. If you have money in the bank, then you can cash a check. Conditional reasoning is a central part of thinking, yet people do Schlictmann then argued that these premises were consistent with not always reason correctly. The lawyer Jan Schlictmann in a the proposition that no contamination came from the river. What celebrated trial (see Harr, 1995, pp. 361–362) elicited the follow- he overlooked is that the conclusion is not merely consistent with ing information from an expert witness about the source of a the premises but follows necessarily from them. Psychologists chemical pollutant trichloroethylene (TCE): disagree about the cause of such oversights and about conditional reasoning in general (e.g., Braine & O’Brien, 1998; Cheng & Holyoak, 1985; Johnson-Laird, 1986; Rips, 1983). Philosophers, P. N. Johnson-Laird, Department of Psychology, Princeton University; logicians, and linguists also disagree about the meaning of condi- Ruth M. J. Byrne, Department of Psychology, University of Dublin, tionals (Adams, 1975; Lewis, 1973; Stalnaker, 1968). No consen- Dublin, Ireland. sus exists about if. This research was made possible in part by a grant to P. N. Johnson- Our concern is everyday conditionals, including all sentences of Laird from the National Science Foundation (Grant BCS 0076287) to study the form If A then C or CifA,where A and C are declarative strategies in reasoning. We thank Jon Baron and Ray Nickerson for their clauses. Naive individuals can grasp the meaning of such asser- helpful criticisms of an earlier version of this article. We thank Yingrui tions, and they can use it to reason. The term naive refers here Yang for providing technical help and advice, Patricia Barres for carrying merely to people who have not studied logic in any depth. In the out Experiment 2, Rachel McCloy for carrying out a study of modus 1970s, psychologists assumed that such individuals reason using tollens, Dan Zook for writing a preliminary version of the program for pragmatic modulation, and David Over for engaging in many discussions formal rules of inference like those of a logical calculus. The of philosophical theories of conditionals. We are also grateful to many challenge was to pin down the particular rules (e.g., Braine, 1978; people: Peter Wason, now in retirement, for pioneering the psychological Johnson-Laird, 1975; Osherson, 1974–1976). Such theorizing ne- study of conditionals; Jonathan Evans and David Over for a critique of our glected a discovery made by Wason (1966). Intelligent adults in account, which they presented at the Workshop on Mental Models in his selection task regularly committed a logical error. He laid out Brussels, March 2001, and also for many discussions of conditionals; Luca four cards in front of them: Bonatti, the late Martin Braine, Keith Holyoak, Howard Margolis, David O’Brien, and Lance Rips for their vigorous criticisms of the model theory; AB23 Monica Bucciarelli, Orlando Espino, Vittorio Girotto, Eugenia Goldvarg, Paolo Legrenzi, Maria Sonino Legrenzi, Juan Garcı´a Madruga, Henry They knew that each card had a letter on one side and a number on Markovits, Mary Newsome, Cristina Quelhas, Sergio Moreno Rios, Carlos the other side. He showed them a conditional: If a card has the Santamarı´a, Fabien Savary, Walter Schaeken, Walter Schroyens, Alessan- letter A on one side then it has the number 2 on the other side. dra Tasso, and Valerie Thompson for their collaboration in studies of Their task was to select those cards that had to be turned over to conditional reasoning. We are also grateful to the following individuals for discover whether the conditional was true or false about the four many useful ideas: Bruno Bara, Victoria Bell, David Green, Uri Hasson, cards. Most people selected the A and 2 cards, or the A card alone. Mark Keane, Markus Knauff, Jim Kroger, Robert Mackiewicz, Hans- Georg Neth, Tom Ormerod, Rosemary Stevenson, Dan Sperber, Vladimir They failed to select the 3 card. However, if the 3 has an A on its Sloutsky, and Jean-Baptiste van der Henst. other side, the conditional is false. Indeed, nearly everyone judges Correspondence concerning this article should be addressed to P. N. it to be false in this case. Individuals also generate this case when Johnson-Laird, Department of Psychology, Princeton University, Green they are asked to make a conditional false (Oaksford & Stenning, Hall, Princeton, New Jersey 08544. E-mail: [email protected] 1992), and they judge that the probability of this case is zero given 646 CONDITIONALS 647 the truth of the conditional (Johnson-Laird, Legrenzi, Girotto, model theory) run in parallel for many aspects of reasoning. Legrenzi, & Caverni, 1999). When Wason and Shapiro (1971) Insofar as both sorts of theory reflect logical principles, however, changed the assertion to a sensible everyday conditional, many they have potential limitations (cf. Sloman, 1996). And at the heart people made the correct selection. Theories based on formal rules of these limitations is the vexed question of conditionals. Are they have difficulty in explaining both the error with neutral condition- truth functional or not? The answer is not clear. Some theorists als and its correction with sensible content. have argued that conditionals have the same meaning as the Our theory is not formal. It assumes instead that reasoners use truth-functional connective of material implication (e.g., Grice, the meaning of premises, and general knowledge, to imagine the 1975; Wilson, 1975), which is shown in Table 2. Other theorists possibilities under consideration—that is, to construct mental mod- have rejected this analysis (e.g., Gazdar, 1979; O’Brien, 1999). els of them (see Johnson-Laird & Byrne, 1991; Polk & Newell, The profundity of the puzzle correlates with the length of its 1995). Mental models can be constructed from perception, imag- literature. One aim of the present article is to resolve this puzzle. ination, or the comprehension of discourse. They underlie visual Simple inferences from conditionals are of four main sorts: images, but they can also be abstract, representing situations that 1. Modus ponens: cannot be visualized. Each mental model represents a possibility. It is akin to a diagram in that its structure is analogous to the If there is a circle then there is a triangle. If A then C. structure of the situation that it represents, unlike, say, the structure There is a circle. A. of logical forms used in formal rule theories. І There is a triangle. І C. Some sentential connectives such as and and or have logical 2. Modus tollens: meanings that are easy to define. For example, consider the fol- lowing: If there is a circle then there is a triangle. If A then C. There is not a triangle. Not C. Either the printer is broken or else the cable is disconnected, І There is not a circle. І Not A. but not both. 3. Denial of the antecedent: The truth of an exclusive disjunction such as this one is a function of the truth of its constituent atomic propositions, that is, those If there is a circle then there is a triangle. If A then C. propositions that contain neither not nor connectives (the printer is There is not a circle. Not A. broken, the cable is disconnected). The exclusive disjunction is І There is not a triangle. І Not C. true in two cases: first, where it is true that the printer is broken but false that the cable is disconnected, and, second, where it is false 4. Affirmation of the consequent: that the printer is broken but true that the cable is disconnected. Logicians lay out these conditions in a truth table, as shown in If there is a circle then there is a triangle. If A then C. Table 1, in which we abbreviate the atomic propositions. Each row There is a triangle. C. І І in the truth table represents a different possibility. Thus, the first There is a circle. A. row represents the possibility in which both the printer is broken Modus ponens and modus tollens are valid for both conditionals and the cable is disconnected; in this possibility, the exclusive and biconditionals (If and only if there is a circle then there is a disjunction is false. The connective and can be defined in an triangle), whereas the other two inferences are valid only for analogous way.