Mental model theory and pragmatics

Johnson-Laird & Byrne (1991; 1993) present a theory of human deductive reasoning based on the notion of mental models. Unfortunately, the theory is incomplete. The present commentary argues that pragmatic considerations, particularly of the type discussed in Sperber and Wilson (1995), can complement the theory. Johnson-Laird & Byrne (1991) (JL&B) conclude their book by claiming that their theory is incomplete (p. 213; all page references are to the book, not the Précis). The present commentary suggests two ways of complementing the theory with some pragmatics. First, contextual factors accounted for by linguistic pragmatics may help predict which conclusion people will derive from the models they construct. Second, a pragmatic approach may help specify how the search for alternative models is triggered. (1) Even if they do not refer to pragmatics explicitly, JL&B (pp. 21–22) list “extra-logical” constraints governing individuals’ conclusions that are actually of a pragmatic nature. However, these constraints do not permit us to make accurate predictions about which conclusion people will try to infer from a set of premises. For example, the authors claims (p. 35) that after constructing a mental model, individuals try to produce “something” not explicitly stated in the premises. The question one can ask is: What kind of “something” do people try to produce? The question becomes relevant, in particular, when one can draw several conclusions from the same set of premises. For example, from the premises Paul is taller than John, John is taller than Pete, Pete is taller that Bob, one can infer that Paul is taller than Bob, but one can also infer that the four boys are of different heights. Which inference will people make? This is a pragmatic question. The context in which information is processed determines to a great extent which inferences people will make. One can easily assume that individuals will try to draw a conclusion that is the most relevant one in the context of processing (Sperber & Wilson 1995). In the above example, if one is interested in knowing the most important relational contrast, then one will probably infer that Paul is taller than Bob. However, if one wants to know whether some of the boys are of the same height, one will probably infer that the four are of different heights. JL&B argue (p. 93) that indeterminate premises such as “the circle is in front of the triangle; the cross is behind the circle” do not support a valid conclusion because the two models compatible with the premises do not yield a determinate relation between the triangle and the cross. From these premises, people will probably conclude that “nothing follows.” Nevertheless, one logical conclusion is “the circle is in front of the triangle and the cross.” This conclusion is compatible with the two models but is of course trivial, and people will probably be reluctant to draw it. But, drawing a conclusion does not only depend on its “nontriviality.” It can also depend on the further inferences it may allow. The premises: John is ahead of Paul John is ahead of Bob support the trivial inference that John is ahead of Paul and Bob. But when the premises are given in the context “John, Paul, and Bob were the first three finishers of the athletics race last Sunday,” that inference conveys more cognitive effects (Sperber & Wilson 1987; 1995) than in a neutral context, because it allows one to know that John won the race. The experimental results of a production task (van der Henst et al. 2000) show that in the neutral context, participants give significantly more indeterminate answers (31.4%) such as “nothing follows” than they do in the “race” context (11.1%). (2) Relevance considerations can also shed light on the procedure of searching for alternative models. According to JL&B, reasoners draw a putative conclusion from an initial model and then try to construct alternative models of the premises. The search for alternative models is the genuinely deductive stage according to the authors (pp. 36 and 127). JL&B seem to link good reasoning with the procedure of searching exhaustively for counterexamples. Reasoners following this procedure are designated as “prudent” (p. 35). Consider the following problem: 1. B is on the right of A 2. C is on the left of B BEHAVIORAL AND BRAIN SCIENCES (2000) 23, 283–298 Printed in the United States of America © 2000 Cambridge University Press 0140-525X/00 $12.50 283 Continuing Commentary Commentary on Philip N. Johnson-Laird & Ruth M. J. Byrne (1993). Précis of Deduction. BBS 16:323–380. Abstract of the original article: How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system. Deduction argues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on propositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the trueof the original article: How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system. Deduction argues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on propositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. 3. D is in front of C 4. E is in front of B What is the relation between D and E? This problem supports the model: C A B D E But another model is compatible with this problem: A C B D E Only one model is necessary to draw the conclusion that D is on the left of E because the alternative model yields the same conclusion. Nevertheless, this problem is labelled as a multiple-model problem. If the falsification procedure is seen as a necessity, then individuals who construct only one model are not “prudent” reasoners, reaching the correct conclusion accidentally (indeed, the alternative model could have refuted the putative conclusion supported by the first model, in particular if the premise had been “E is in front of A”). However, for the problem presented below the search for all possible models is not seen as a necessity for correct reasoning: All the athletes are bakers All the bakers are canoeists This problem supports the model: [[a] b] c [[a] b] c ... But other models are compatible with this problem, for example: [[a] b] c [[a] b] c [b] c c ... As in the case of the spatial problem, the alternative models do not refute the initial conclusion, that is, “all the athletes are canoeists.” Nevertheless, this time the problem is considered a one-model problem (p. 107) and people constructing only the initial model are not viewed as imprudent. It seems, then, that sometimes the number of models associated with a problem – and consequently its difficulty – depends on the set of possible models, and sometimes it depends on the set of necessary models. So, do subjects attempt to construct the exhaustive set of models or do they attempt to construct only necessary models? One can try to answer by assuming that one will attempt to construct an alternative model if one presumes that this model contains information one considers relevant. That is, the model coveys information that could cause the revision of information reached initially and its construction does not exceed the maximum effort the individual is willing to expend (Sperber & Wilson 1995). Consider the description below: A is taller than B A is taller than C A is taller than D A is taller than E A is taller than F. With these premises, individuals will probably not try to construct any of the 120 possible models, first, because none of these models could express any determinate information other than that A is the tallest, and second, because the construction of all possible models will be very costly. One can then suggest that the falsification procedure is not only limited by working memory, as suggested initially by the authors (pp. 86 and 214), but also by expectations of relevance. This is what van der Henst’s study (1999) tends to show (see also Schaecken et al. 1996). Authors’ Response Mental models and pragmatics P. N. Johnson-Lairda and Ruth M. J. Byrneb aDepartment of Psychology, Princeton University, Princeton, NJ 08544; bDepartment of Psychology, Trinity College, University of Dublin, Dublin 2, Ireland. [email protected] www.tcd.ie/Psychology/People/Ruth_Byrne/ www.cogsci.princeton.edu/~phil/[email protected] Abstract: Van der Henst argues that the theory of mental models lacks a pragmatic component. He fills the gap with the notion that reasoners draw the most relevant conclusions. We agree, but argue that theories need an element of “nondeterminism.” It is often impossible to predict either what will be most relevant or which particular conclusion an individual will draw. Van der Henst argues that the theory of mental models lacks a pragmatic component. He fills the gap with the notion that reasoners draw the most relevant conclusions. We agree, but argue that theories need an element of “nondeterminism.” It is often impossible to predict either what will be most relevant or which particular conclusion an individual will draw. The theory of mental models postulates that individuals reason by envisaging the circumstances in which the premises and any other starting information are true (Johnson-Laird & Byrne 1991; 1993t). Each mental model represents a possibility, and so reasoners infer that a conclusion is possible if it holds in at least one model of the premises, that it is necessary if it holds in all the models of the premises, and that it is impossible if it holds in none of the models of the premises. Our book describing the theory and its corroboratory evidence received a mixed reception in BBS. Some commentators applauded the theory; some thought that it was – to a first approximation – rubbish. Nevertheless, the theory has flourished. Many authors have proposed interesting variants of the theory (e.g., Evans 1993; Polk & Newell 1995; Richardson & Ormerod 1997; Sloutsky & Morris, submitted). It has also been extended to reasoning based on suppositions (e.g., Byrne & Handley 1997), to temporal reasoning (e.g., Schaeken et al. 1996), to reasoning about probabilities (e.g., Johnson-Laird et al. 1999), and to counterfactual and causal reasoning (e.g., Byrne 1997; Goldvarg & Johnson-Laird, submitted). A striking prediction of the theory is that certain inferences should be illusory. They are invalid yet most people should draw them, and they should seem compelling. They follow from the principle that mental models represent only those possibilities that are true given the premises, and a mental model represents the constituent propositions in the premises (affirmative or negative) only when they are true in the corresponding possibility. Consider, for example, the following problem (from Goldvarg & Johnson-Laird, in press): Only one of the following assertions is true about a particular hand of cards: There is a king in the hand or there is an ace in the hand, or both. There is a queen in the hand or there is an ace in the hand, or both. There is a ten in the hand or there is a jack in the hand, or both. Is it possible that there is an ace in the hand? Most people respond: yes (including 99% of the Princeton undergraduates whom we tested). Yet the response is an illusion. If there were an ace in the hand, then the first two assertions in the problem would be true, contrary to the rubric that only one assertion is true. Such illusions are a unique prediction of the model theory. They have been observed to occur in sentential reasoning (Johnson-Laird & Savary 1999), in quantified reasoning (Yang & JohnsonContinuing Commentary 284 BEHAVIORAL AND BRAIN SCIENCES (2000) 23:2 Laird 1999), in probabilistic reasoning (Johnson-Laird et al. 1999), and in causal reasoning (Goldvarg & Johnson-Laird, submitted). Likewise, their predicted antidotes have also been corroborated (e.g., Newsome & Johnson-Laird 1996; Tabossi et al. 1999). If a theory is to be judged by the amount of work it has inspired, the model theory has survived its critique in BBS. The theory is radically incomplete, but other theories of reasoning are no better. Indeed, a complete theory of reasoning would necessarily be a complete theory of the whole of cognitive psychology from perception to action. There are three principal gaps in the model theory. First, it gives no account of how general knowledge is represented in the mind or mobilized in reasoning. Second, the theory provides a semantics of standard connectives, temporal and spatial relations, and quantifiers, but it does not contain a full compositional semantics for a significant fragment of natural language, such as Basic English, or for various quantifiers that are not standard in formal logic, such as “most,” “many,” and “more than half.” Third, the theory recognizes that the pragmatics of communication plays an important part in how people interpret the premises of inferences, and in what conclusions they are likely to draw. The theory, however, offers no account of pragmatics (Evans & Over 1997). Van der Henst makes the same criticism, but he proposes to rectify matters by incorporating the theory of relevance, as formulated by Sperber and Wilson (1995). He points out that the theory of relevance makes powerful predictions about the particular conclusions that reasoners draw from premises. Because infinitely many valid conclusions follow logically from any set of premises, we had argued for several constraints. Reasoners tend to draw conclusions that maintain the semantic information in the premises, that express it parsimoniously, and that make explicit a proposition not explicitly asserted among the premises (Johnson-Laird & Byrne 1991). Van der Henst adds the further principle that reasoners tend to draw the most relevant conclusion in the context of processing. This principle is important, he says, when reasoners could draw several conclusions from the same premises. People are unlikely to reason just for fun, and so their goals – their reasons for reasoning – will be crucial in determining the conclusion that they draw. Van der Henst illustrates his thesis with the following premises: Paul is taller than John. John is taller than Pete. Pete is taller than Bob. You can infer that Paul is the tallest, or Bob is the shortest, or that these individuals differ in height, depending on what is relevant to your goals. Likewise, even with indeterminate premises that support no valid conclusion interrelating the end terms, it may still be relevant to draw a conclusion. When you are interested in who won the race, and know only that Ann, Beth, and Cath were the leaders, you are more likely to draw a conclusion from premises of the form: Ann came in ahead of Beth. Ann came in ahead of Cath. In the experiment that van der Henst describes, more participants drew the conclusion that Ann was the winner in this context than in a neutral context. Van der Henst raises a second point concerning the search for alternative models. Given a spatially indeterminate description, we argued that people need to construct alternative models to reach the correct conclusion for the correct reasons. But, given premises of the form: All the A are B. All the B are C. we postulated only a single mental model: [[a] b] c [[a] b] c, which yields the valid conclusion: All the A are C. But the premises are consistent with other models, such as: [[a] b] c [[a] b] c c Why do we not postulate that individuals construct this model? In fact, we have tinkered with the computer programs of the model theory of syllogistic reasoning, and in the latest version (described in Johnson-Laird & Byrne 1996), it does produce the preceding model. But, as we wrote in this article, our tinkering with the program now strikes us as a vain attempt to capture a highly flexible, if not labile, system within a single deterministic framework. Studies that externalize the search for alternative models suggest that people are indeed biased to construct a single model wherever possible, but the process of searching for counterexamples can be modeled only in a nondeterministic way (see Bucciarelli & Johnson-Laird 1999). We agree with van der Henst on the importance of pragmatic issues. What is more controversial, however, is whether a reasoner’s goals can be fully captured in Sperber and Wilson’s (1995) conception of relevance. As we understand their theory, the relevance of an inference increases with its cognitive consequences and decreases with the amount of cognitive work needed to make the inference. These constraints are plausible, but sometimes difficult to put into practice, that is, to use to derive testable predictions. Moreover, as an unpublished study by van der Henst et al. shows, one person differs from another about what conclusion, if any, is relevant. In our view, theorists are unlikely to improve significantly on the sort of formulation offered by Sperber and Wilson, but they will be forced to allow for a considerable degree of “nondeterminism” in their theories. In many cases, it is impossible to predict which particular conclusion a particular individual will draw from particular premises.