Spatial Mental Models in Counterfactual Thinking About What Might Have Been

Transcription

1 Kognitionswissenschaft (1998) 7: 19±26 Ó Springer-Verlag 1998 Spatial Mental Models in Counterfactual Thinking About What Might Have Been Ruth M. J. Byrne Psychology Department, University of Dublin, Trinity College, Dublin 2, Ireland ( Räumliche mentale Modelle beim kontrafaktischen Denken über das, was sein hätte können Zusammenfassung. Die Theorie mentaler Modelle sagt vorher, daû deduktive Schlüsse, bei denen mehrere Modelle mental repräsentiert werden müssen, schwieriger sind als solche, die nur ein einziges Modell erfordern. Diese Theorie konnte durch Untersuchungen in den Kernbereichen des deduktiven Schlieûens einschlieûlich des räumlichen Schlieûens gestützt werden. Der vorliegende Beitrag wendet diese Theorie nun auch auf kontrafaktische Schlüsse an, also auf Denken über das, was sein hätte können. Diese Ausweitung der Theorie beruht auf der Annahme, daû dem Denken über Tatsächliches und Mögliches dieselben mentalen Repräsentationen und Prozessen zugrundeliegen. Daraus ergibt sich die Vorhersage, daû kontrafaktische Szenarien schwieriger zu generieren sind, wenn bereits die faktische Situation es erfordert, mehrere mentale Modelle gleichzeitig präsent zu halten, als wenn ein einziges mentales Modell dafür ausreicht. Hierzu werden experimentelle Ergebnisse berichtet. Das Experiment untersucht, wie Menschen räumliche Aspekte von Szenarien verändern, wenn sie über kontrafaktische Alternativen nachdenken. Die Ergebnisse zeigen, daû im Ein-Modell-Fall reichhaltigere Variationen des einen (faktischen) Modells bei der Generierung kontrafaktischer Alternativen vorkommen als im Fall mehrerer mentaler Modelle. Abschlieûend werden die sich daraus ergebenden Folgerungen für eine allgemeine Theorie des räumlichen Schlieûens diskutiert. Summary. The mental model theory predicts that deductions that require multiple models to be kept in mind are more difficult than deductions that require a single model. The model theory has been corroborated in the primary domains of deduction, including spatial inference. I will describe an extension of the model theory from factual thinking to counterfactual thinking about what might have been. The extension of the model theory is based on the premise that thinking about matters of fact and thinking about matters of possibility are based on the same sorts of mental representations and processes. The model theory of counterfactual thinking therefore predicts that the generation of counterfactual scenarios is more difficult when the factual situation requires multiple models to be kept in mind than when it requires a single model. I will report the results of an experiment that tests this model theory of counterfactual thinking. The experiment examines the way in which people alter spatial aspects of scenarios when they think about counterfactual alternatives. The results show that people make richer mutations to the single factual model required for a determinate description when they generate a counterfactual alternative to it. In contrast, they make less rich mutations to the multiple factual models required for an indeterminate description when they generate a counterfactual alternative to it. The implications of these results are discussed for a general theory of spatial thinking. 1 Introduction Everyday thinking is often based on matters of possibility and impossibility as well as matters of fact. One common way in which people think about possibilities and impossibilities is when they mentally undo situations, particularly situations that have turned out badly. People spontaneously alter a factual situation to generate an alternative counterfactual situation. For example, if you trip over a bag that you left lying in the middle of the room when you came in, you may think, ªif only I had put the bag on the table when I first came inº. Counterfactual thoughts about what might have been may help us to learn from mistakes (e. g. Roese 1994; see also Roese and Olson 1995) and to experience emotions such as regret, guilt and relief (e. g. Gilovich and Medvec 1994; Miller and McFarland 1987). It is important to account for the mental representations and cognitive processes that underlie counterfactual thinking,

2 20 Ruth M.J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been because it plays a central role in many aspects of higherorder cognition, such as deduction (e. g. Johnson-Laird and Byrne 1991), causal inference (e. g. Kahneman and Miller 1986; Wells and Gavanski 1989), problem-solving (e. g. Ginsberg 1986; see also Keane, 1997), and creativity (e. g. Hofstadter 1979). As the example about tripping over the bag illustrates, counterfactual alternatives may focus on spatial aspects of the factual situation, such as a change of the location of an object. In this article, I will examine some of the ways in which spatial aspects of situations ± such as the location of objects and the relations of objects to one another ± are changed when people generate a counterfactual alternative to think about the way in which a factual situation could have been different. Is space a natural ªjointº in reality to mutate when thinking about what might have been? The answer to the question requires an account of why some parts of a factual situation seem to be more mutable than others, and this goal has driven much of the research on the psychology of counterfactual thinking (e. g. Kahneman and Miller 1986) as well as its philosophy (e.g. Lewis 1973; Stalnaker 1968). I wish to suggest that the ªfault linesº of reality may correspond to core categories of mental life, such as space, time, causality and intentionality (Miller and Johnson-Laird 1976). Indeed, people seem to mutate their representations of reality along the joints of time (e. g. Miller and Gunasegaram 1990), causality (e.g. Wells et al. 1987) and intentionality (e. g. Kahneman and Tversky 1982; Girotto et al. 1991). However, relatively little is known about spatial mutability. I will present experimental evidence to show not only that space is mutable, but also that the number of alternatives that must be kept in mind of the spatial relations in a factual situation affects the nature of the counterfactual alternatives that people generate. My starting point is the proposal that people may think about matters of possibility and impossibility in the same was as they think about matters of fact (e. g. Byrne 1997; Johnson-Laird and Byrne 1991). Suppose the facts of the situation are as follows: 1. When she comes in, Molly leaves her bag lying in the middle of the room. Everyday thinking may focus on the factual situation, either in the present or the past. It may also focus on possible situations (that could happen given the actual situation), e. g.: 2. When she trips over the bag, Molly moves it to the table. either in the present, as in the example in 2, or in the past (a possibility that could have happened given the actual state but did not), e.g.: 3. When she came in, Molly put her bag on the table. (see Johnson-Laird and Byrne 1991, Chap. 4). Everyday thinking about non-factual states of affairs may also be based on impossibilities (that could never happen in the past or present), such as: 4. Molly's bag moved out of the way when it saw her coming. When people think about what might have been, their counterfactual alternatives examine past possibilities, such as 3, or impossibilities, such as 4. The mental representations and cognitive processes that underlie thinking about factual situations may also underlie thinking about possibilities and probabilities (e. g. Johnson-Laird and Bell 1997) and thinking about counterfactual situations (Johnson-Laird and Byrne 1991). I wish to suggest that to understand counterfactual thinking requires first an understanding of factual thinking, and I will sketch this claim for spatial thinking. First, I will outline the mental representations and cognitive processes that underlie thinking about spatial aspects of factual situations; next I will outline the mental representations and cognitive processes that underlie thinking about spatial aspects of counterfactual situations, and I will describe the results of an experiment on spatial counterfactual thinking which supports these claims. 2 Spatial mental models People may think about spatial aspects of situations by constructing mental models (e. g. Byrne and Johnson- Laird 1989). Mental models are mental representations that correspond to the structure of the world rather than to the language used to describe the world (Johnson-Laird 1983). Consider the following scenario: 5. Joanne drove home from work one cold wintry night. She was listening to the radio as she drove along a familiar stretch of road. As she scanned the bend ahead, she saw a post-box on the left-hand side of the road. There was a large tree behind the post-box. The tree was in front of a silver lamp-post. She slowed approaching the bend and it was then that the accident happened. The layout of objects on the road ahead of Joanne can be captured in a single model: Joanne's car where the diagram also represents the location of Joanne and her car when she scans the bend ahead and sees the three objects. The objects are represented by the words ªlamp-postº, ªtreeº and ªpost-boxº, although in real mental models in individuals' minds these objects may be visually imaged, or partially sketched, or represented by symbols such as letters, and so on. The relations between the objects are represented by the horizontal layout in the model. People tend to envisage de-

3 Ruth M. J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been scriptions such as the one in 5 as essentially symmetric with equal distances between the objects (Ehrlich and Johnson-Laird 1982). The content of the models may make explicit who Joanne is, where she is driving to, the sort of tree, the colour of the post-box, and so on; however, the content of the models is not my primary interest here, but rather their structure. The description of the layout of the objects in the scenario is a determinate description which gives rise to a single mental model. Descriptions of the layout of objects can also be indeterminate and give rise to more than one model. Consider the following scenario: 6. Joanne drove home from work one cold wintry night. She was listening to the radio as she drove along a familiar stretch of road. As she scanned the bend ahead, she saw a post-box on the left-hand side of the road. There was a large tree behind the post-box. The post-box was in front of a silver lamp-post. She slowed approaching the bend and it was then that the accident happened. The description in 6 differs from the one in 5 only in the fifth sentence (which in 6 above describes the relation between the post-box and the lamp-post). The indeterminacy in the description in 6 renders it compatible with at least two alternative models: Descriptions with an indeterminacy such as the one in 6 are compatible with more than one model, and keeping multiple models in mind is difficult, perhaps because of the constraints of working memory. People have a better gist memory for single-model descriptions than for multiple-model descriptions, and conversely, they have a better verbatim memory for multiple-model descriptions than for single-model descriptions (Mani and Johnson-Laird 1982). The finding is consistent with the idea that individuals readily construct the single model of the determinate description, but fail to keep in mind the multiple models of the indeterminate description (see also Payne 1993). The nature of a relational description can have a large impact on the nature of the inferences people make (see Evans et al. 1993, Chap. 6). People are reasonably good at making valid deductions from determinate descriptions which are consistent with a single model (Byrne and Johnson-Laird, 1989). They make 69 % correct conclusions to determinate problems such as: 7. The tree is behind the post-box. The tree is in front of the lamp-post. What is the relation between the post-box and the lamp-post? which readily yields the conclusion: 8. The post-box is in front of the lamp-post. or equivalently, 9. The lamp-post is behind the post-box. They find it much more difficult to make the correct inference to indeterminate descriptions which are consistent with multiple models. They make only 19 % correct responses that there is no valid conclusion to the following indeterminate problem: 10. The tree is behind the post-box. The post-box is in front of the lamp-post. What is the relation between the tree and the lamppost? (Byrne and Johnson-Laird 1989). It seems that many participants construct just one of the two possible models corresponding to the description: and some participants make the erroneous conclusion: 11. The tree is in front of the lamp-post. and other participants make the erroneous conclusion: 12. The lamp-post is in front of the tree. The difference in difficulty between the two sorts of problems does not depend solely on the availability of a valid conclusion for the determinate problems and no valid conclusion for the indeterminate problems. For these two-premise problems with three objects (or ªthreeterm seriesº problems, as they are often called), determinacy and validity are confounded: the determinate descriptions have a valid conclusion relating the two endterms (the two non-repeated objects in the premises), whereas for the indeterminate descriptions, there is no valid conclusion relating the two end-terms. However, four-premise problems with five objects can be devised that do not suffer from this confound (Byrne and Johnson-Laird 1989). It remains the case that people are reasonably good at making valid deductions from determinate descriptions which are consistent with a single model even for four-premise problems. They make 61 % correct conclusions to determinate problems such as: 21 (Byrne and Johnson-Laird 1989). It seems they construct the single model corresponding to the description, as I have suggested above: 13. A is on the right of B C is on the left of B D is in front of C

4 22 Ruth M.J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been E is in front of B What is the relation between D and E? (where for clarity I have replaced the concrete objects used in the description with the letters ªAº, ªBº and so on). Participants seem to construct the single model consistent with the description: C B A D E which readily yields the conclusion: 14. D is on the left of E They find it much more difficult to make the correct inference to indeterminate descriptions which are consistent with multiple models. They make only 18 % correct responses that there is no valid conclusion to the following indeterminate problem: 15. B is on the right of A C is on the left of B D is in front of C E is in front of A What is the relation between D and E? It seems that many participants construct just one of the two possible models corresponding to the description: C A B A C B D E E D and some participants make the erroneous conclusion: 16. D is on the left of E. and other participants make the erroneous conclusion: 17. E is on the left of D. However, there is a third type of problem for these four premise problems. The description is indeterminate and it is consistent with multiple models, yet it nonetheless yields a valid conclusion. Consider the following problem: 18. B is on the right of A C is on the left of B D is in front of C E is in front of B What is the relation between D and E? The description is consistent with two alternative models: C A B A C B D E D E In each model, the same relation holds between D and E and the valid conclusion is: 19. D is on the left of E and 50% of participants make this correct deduction (see Byrne and Johnson-Laird 1989). The results rule out an alternative account of spatial inference based on inference rules, but they are consistent with an account based on rules that construct mental models (see also Johnson-Laird and Byrne 1991). Effects of the number of models that people must keep in mind on the inferences they make have also been shown for other relations (e. g. Knauff et al. 1995; Schaeken et al. 1996). Inferences based on a single mental model are easier than inferences that require multiple models, as has been shown for a range of deductions, including not only spatial inference but also quantificational inference (e. g. Johnson-Laird and Byrne 1989; Johnson-Laird et al. 1989), suppositional inference (e. g. Byrne and Handley 1997; Byrne et al a) and propositional inference (e. g. Johnson-Laird et al. 1992), including conditional inference (e.g. Byrne 1989 a, b; Byrne and Johnson-Laird 1992). For factual descriptions of the spatial layout of objects, relational inferences based on a determinate description are easier than inferences based on an indeterminate description. The explanation for this difference is that determinate descriptions require a single model to be kept in mind, whereas indeterminate descriptions require multiple models to be kept in mind. I wish to suggest that counterfactual thinking about the spatial layout of objects may be equally sensitive to the determinacy of the description. In particular, counterfactual alternatives generated to a factual situation with a determinate spatial layout that requires a single model may be quite different to counterfactual alternatives generated to a factual situation with an indeterminate spatial layout that requires multiple models to be kept in mind. 3 Spatial counterfactual thinking Research on counterfactual thinking has provided some clues to the mutability of space. The spatial proximity to a goal has an effect on the mutability of the events, e. g. it is easier to imagine someone being saved when they died just 5 miles from help rather than when they died 75 miles from help (e. g. Miller and McFarland 1987; Kahneman and Varey 1990). Spatial aspects of reality seem to be particularly mutable when they are exceptional (e. g. Kahneman and Tversky 1982). For example, people undo the route a person took before a fatal car crash when the route was not their usual one. Consider the following scenario: 20. Mr. Jones was 47 years old, the father of three and a successful banking executive. His wife had been ill at home for several months. On the day of the accident, Mr. Jones left his office at the regular time. He sometimes left early to take care of home chores at his wife's request, but this was not necessary on that day. Mr. Jones did not drive home by his regular route. The day was exceptionally clear, and Mr.

5 Ruth M. J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been Jones told his friends at the office that he would drive along the shore to enjoy the view. The accident occurred at a major intersection. The light turned amber as Mr. Jones approached. Witnesses noted that he braked hard to stop at the crossing, although he could easily have gone through. His family recognized this as a common occurrence in Mr. Jones' driving. As he began to cross after the light changed, a light truck charged into the intersection at top speed and rammed Mr. Jones' car from the left. Mr. Jones was killed instantly. It was later ascertained that the truck was driven by a teenage boy who was under the influence of drugs. As commonly happens in such situations, the Jones family and their friends often thought and often said, if only...' during the days that followed the accident. How did they continue this thought? As Kahneman and Tversky (1982) showed, 53% of the participants who were given this exceptional-route version of the scenario undid this spatial aspect of the scenario, compared to only 13% of the participants who were given a normal-route version of the scenario (in which the time at which Mr. Jones had left the office was varied instead). Space is clearly mutable in some circumstances, and my aim now is to show that the mutability of space in the generation of counterfactual scenarios depends on the mental representation of the factual spatial information. For spatial deductions, the model theory predicts that inferences that require multiple models to be kept in mind are more difficult than inferences that require single models to be kept in mind, and this prediction has been corroborated (Byrne and Johnson-Laird 1989). I have suggested that reasoning about matters of fact and matters of possibility and impossibility may depend on the same sorts of mental representations and cognitive processes (e. g. Byrne 1996, 1997; see also Johnson-Laird and Byrne 1991). Consider the following scenario: 21. Joanne drove home from work one cold wintry night. She was listening to the radio as she drove along a familiar stretch of road. As she scanned the bend ahead, she saw a post-box on the left-hand side of the road. There was a large tree behind the post-box. The tree was in front of a silver lamppost. She slowed approaching the bend and it was then that the accident happened. She hit a large patch of black ice and lost control of the car. She hit the post-box first. By an unlucky coincidence, more ice caused the car to spin and she hit the tree. Once again by a freak coincidence, she spun on more ice and hit the lamp-post. She sustained multiple injuries, including a broken leg and a fractured collarbone. In the weeks she spent recovering in hospital, she often became upset thinking about the accident and thinking about how things could have turned out differently. She often thought ªthe accident wouldn't have been so bad if only...º How do you think Joanne completed this thought? The layout of obstacles into which Joanne crashed can be captured in a single model, as I illustrated earlier: People generate counterfactual alternatives by making changes to the model of the factual situation (Byrne 1997). Because of the constraints of working memory, they are unable to keep all possible counterfactual alternatives in mind. The counterfactual alternative they flesh out explicitly may be based on the layout of objects. Their counterfactual alternative may consist of a simple alteration to the layout, such as the removal of an object: Factual: Counterfactual: and the models may be annotated to keep track of their epistemic status (Johnson-Laird and Byrne 1991). The counterfactual model gives rise to completions of Joanne's ªif only...º thoughts such as ªthe accident wouldn't have been so bad if only the post-box hadn't been there.º Multiple possible models of the counterfactual alternatives can be constructed by deleting one or more of the three objects: Factual: Counterfactual: L L L L T T T T P P P P (where ªLº stands for lamp-post, ªTº stands for tree and ªPº stands for post-box). Each model gives rise to a different completion, e. g. the counterfactual model in 6 gives rise to the thought ªthe accident wouldn't have been so bad if only the lamp-post and the tree hadn't been there.º However, working memory limitations constrain the number of counterfactual alternatives that people can construct. Alternatively, the counterfactual alternative may consist of a more complex alteration to the layout, such as alterations to the relations between the objects: Factual: Counterfactual: and the counterfactual model gives rise to completions of Joanne's ªif only...º thoughts such as ªthe accident wouldn't have been so bad if only the post-box had been behind the tree.º Once again, multiple possible models of the counterfactual alternatives can be constructed by altering the relations between two or more of the three objects: 23

6 24 Ruth M.J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been Factual: Counterfactual: L L T P P T T P L T L P P T P L T L and each model gives rise to a different completion. Once again, because of working memory limitations, it is unlikely that people flesh out all of the counterfactual models. If counterfactual thinking depends on mental models just as factual thinking does, then there should be similar effects of the number of models on the ease with which people generate alternatives. For example, counterfactual alternatives to a factual situation that requires multiple models to be kept in mind may be harder to construct than counterfactual alternatives to a factual situation that requires a single model. To test this prediction, I constructed two sorts of scenarios: one contained the determinate description of a spatial layout which is consistent with a single model outlined in the example in 21 earlier, and the other contained an indeterminate description of a spatial layout which was consistent with multiple models. A determinate spatial scenario requires a single model of the layout to be kept in mind. To generate a counterfactual alternative to a determinate spatial scenario, individuals must keep the single model of the factual situation in mind, make alterations to it and generate a counterfactual alternative on the basis of these alterations. An indeterminate spatial scenario requires multiple models of the layout to be kept in mind. To generate a counterfactual alternative to an indeterminate spatial scenario, individuals must keep multiple alternative models of the factual situation in mind. The limits of working memory may make it difficult to make alterations to the multiple models and to generate an alternative model. For a determinate spatial description, there is a single model of the factual situation and multiple models of the counterfactual possibilities (i. e. 11 counterfactual models, based on deleting one or more objects or on altering the relation between two or more objects). For an indeterminate spatial description, there are multiple models of the factual situation (two factual models), and there are also multiple models of the counterfactual possibilities (ten counterfactual models). As a result, I predicted that counterfactual alterations to a spatial description that required a single model would be richer than counterfactual alterations to a spatial description that required multiple models. The experiment relied on two sorts of vignettes, one with a determinate spatial layout outlined in 21 earlier, and one with an indeterminate spatial layout. I gave one group of undergraduates from Dublin University the determinate scenario in 21 earlier. The experiment used three versions of the vignette, which differed only in which one of the three objects was assigned to which one of the three positions, to control for any tendency participants may have to more readily alter the position of, say, a tree than a lamp-post. Crashing into one object does not directly cause the individual to crash into another object in these vignettes, and so the scenario separates the spatiality of the objects from the causality of the sequence. The description of the layout of the objects in the scenario in 21 is a determinate description which gives rise to a single mental model. I gave a second group of undergraduates the same sort of scenario for which the description of the spatial layout was indeterminate: 22. Joanne drove home from work one cold wintry night. She was listening to the radio as she drove along a familiar stretch of road. As she scanned the bend ahead, she saw a post-box on the left-hand side of the road. There was a large tree behind the post-box. The post-box was in front of a silver lamp-post. She slowed approaching the bend and it was then that the accident happened. She hit a large patch of black ice and lost control of the car. She hit the post-box first. By an unlucky coincidence, more ice caused the car to spin and she hit the tree. Once again by a freak coincidence, she spun on more ice and hit the lamp-post. She sustained multiple injuries, including a broken leg and a fractured collarbone. In the weeks she spent recovering in hospital, she often became upset thinking about the accident and thinking about how things could have turned out differently. She often thought ªthe accident wouldn't have been so bad if only...º How do you think Joanne completed this thought? Please list six possible ways. The indeterminacy in the description renders it compatible with at least two alternative models of the factual situation: In both the determinate and the indeterminate scenario, the order in which Joanne crashed into the three objects was described in the same way: post-box first, tree second and lamp-post third. Could this crash description be construed to disambiguate the indeterminacy of the spatial layout? If so, the multiple-model problem is reduced to a single-model problem, and no differences between the two scenarios would be expected. In fact, the crash description is consistent with either layout and so it does not necessarily disambiguate the indeterminacy: the indeterminate problem supports multiple models. The aim of the experiment was to examine, firstly, how frequently participants focused on aspects of the spatial layout to mutate, and secondly, to examine the richness of the counterfactual scenarios they generated to the determinate and the indeterminate scenarios. I expected that when the factual scenario was consistent with a single model, participants would generate a richer counterfactual scenario, i. e. the counterfactual scenario would alter more than one of the objects, changing the location or relation of two or more of the objects. In contrast, when the factual scenario was consistent with multiple models, I expected that participants

7 Ruth M. J. Byrne: Spatial Mental Models in Counterfactual Thinking About What Might Have Been 25 Table 1. The percentages of different categories of ºif only...º completions Categories of undoings Spatial description Single model (n = 21) Multiple model (n = 20) Total Spatial Ice Control Radio The percentages are based on the responses of participants to list six ways in which Joanne could have completed the thought ªthe accident wouldn't have been so bad if only...º. Table 2. The percentages of undoings of one object (indicated by A, B or C) and two or more objects within the undoings of spatial aspects overall Spatial description Single model (n = 21) Multiple model (n = 20) Undo single object (e. g. ªif only the tree hadn't been thereº) A B C Total Undo multiple objects (e. g. ªif only the tree hadn't been behind the post-boxº) ABC AB BC 18 0 AC 0 5 Total The percentages are based on the responses of participants to list six ways in which Joanne could have completed the thought ªthe accident wouldn't have been so bad if only...º. A (B, C), answer mentioned one object only (A, B or C only); AB (AC, BC), answer mentioned two objects; ABC, answer mentioned all three objects. would generate a less rich counterfactual scenario, i. e. the counterfactual scenario would alter just one of the objects. The participants, task was to generate six counterfactual scenarios and, as Table 1 shows, they tended to focus on spatial aspects of the scenario in about one third of their counterfactual mutations (i. e. their completions of the ªif only...º sentence stem referred to the objects or their layout). Over the two versions of the scenario, a major category of mutations (33 %) concerned the spatial aspects of the scenario. The remaining mutations included 28 % of mutations that mentioned instead the ice and associated factors, such as the weather, winter-time and night-time; 16 % mentioned factors associated with Joanne's control of the car, including skid control and driving expertise; and 13% mentioned attentiveness, especially listening to the radio. As Table 1 shows, the frequency of mutations within each of these categories is similar for both the determinate and the indeterminate scenario. As Table 2 shows, the nature of the mutations in the 33% of counterfactual alternatives that undid the spatial aspects of the scenario corroborates the prediction about the differences between single-model and multiple-model spatial scenarios. I categorized the sentence completions that mentioned the objects or their locations into two groups: ªsimpleº mutations mentioned just a single object, while ªcomplexº mutations mentioned two or more objects. As expected, counterfactual mutations to multiple-model factual situations were minimal: 73% of the counterfactual alternatives were simple mutations that mentioned just a single object (e. g. simple deletions of an object: ªif only the tree hadn't been thereº), whereas 27% of the alternatives were more complex mutations that mentioned two or more of the objects (e. g. altering their relations: ªif only the tree hadn't been behind the post-boxº). However, for the determinate single-model descriptions, counterfactual mutations were richer: 53% of the counterfactual alternatives were simple mutations that mentioned just a single object, but just as many (47 % of the counterfactual alternatives) were more complex mutations that mentioned two or more of the objects. The results show that counterfactual alternatives to a factual situation that requires a single model to be kept in mind are richer than counterfactual alternatives to a factual situation that requires multiple models to be kept in mind. 4 Conclusions When people think about the spatial relations between objects, they construct mental models (Johnson-Laird and Byrne 1991). The number of models that people must keep in mind affects the ease with which they can think about the spatial relations. Experiments on spatial deductions have shown that the number of models of a spatial layout influences people's ability to think about it factually: people make more correct deductions from determinate descriptions which require a single model to be kept in mind than from indeterminate descriptions which require multiple models to be kept in mind (Byrne and Johnson-Laird 1989). The experiment reported here shows that the number of models of a spatial layout also influences people's ability to think about counterfactual alternatives to it: people construct richer counterfactual scenarios to determinate descriptions which require a single model to be kept in mind than to indeterminate descriptions which require multiple models to be kept in mind. The number of models that must be kept in mind of the factual situation affects the ease with which individuals can construct counterfactual scenarios. This finding supports the general suggestion that reasoning about matters of fact and matters of possibility and impossibility rely on the same sorts of representations and processes (e.g. Byrne and Tasso 1994; Byrne et al b). It also supports the more specific suggestion that these representations and processes are procedures that construct and revise mental models.

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