Running Head:  BEYOND REALLY AND TRULY

Beyond really and truly:  
Children's counterfactual thinking about pretend and possible worlds
Eric Amsel and J. David Smalley
Weber State University
Department of Psychology
1202 University Circle
Ogden UT 84408-1202, USA

Acknowledgments
Collection of the data described in this chapter was partially supported by a Weber State University Research, Scholarship & Professional Growth grant to the first author. We would like to thank Judi Amsel, Michael Chandler, Nick DeLeeuw, Tamara Ferguson, Paul Harris, Chris Lalonde, Angeline Lillard, Bill McVaugh  Peter Mitchell, Kevin Riggs, and Cecilia Wainryb for many very helpful comments and discussions.

To appear In K. Riggs & P. Mitchell (Eds.), Children’s reasoning and the mind. Brighton, UK: Psychology Press.

Introduction
	By way of introduction to this chapter, consider the reasoning of two people. First imagine a child pretending that a banana is a telephone. The child holds the banana like a telephone, talks into it, and then hands it off to her mother saying, "You talk to Daddy!" Now think about a parent whose child is throwing a temper tantrum in a toy store.  The exasperated parent considers ways in which the day could have been different so as to have avoided the scene now playing out in front of her (e.g., if only the parent had been more patient, if only the child had had a longer nap, if only the parent had just driven past the toy store).  
	At first glance, it would seem that the child who is playing pretend and the parent who is pondering possibilities are engaged in very different forms of reasoning. Maybe because playing pretend is a fanciful distortion of reality and pondering possibilities is a serious examination of reality (see Kahneman and Tversky (1982) for an account of the ‘simulation heuristic’), the two forms of reasoning appear to be different (Woolley, 1995). Moreover, if we are to believe Piaget (1970), pretense is, well, child's play, requiring no more demanding cognitive processes than the symbolic assimilation of the world to desired mental schemes. In contrast, pondering possibilities is a formal operational stage accomplishment involving thoughts about hypothetical rather than actual states of affairs.
     One goal of this chapter is to convince the reader that, contrary to Piaget and others, playing pretend and pondering possibilities are close relatives in the reasoning family. The analogy is that the two forms of reasoning are like siblings, who may be different but nonetheless share a common underlying (genetic) nature. We will argue that the cognitive processes underlying both playing pretend and pondering possibilities, the processes which give them their common underlying (computational) nature, are those associated with counterfactual thinking, defined as reasoning about states of affairs which are contrary to known facts (Roese, 1997). We will propose a simple counterfactual model of pretense which involves such counterfactual reasoning skills as representing true and false states of affairs, marking them as such, and reasoning on the basis of the false state of affairs. Evidence will be presented demonstrating the importance of children’s capacity to coordinate separate representations of true and false states of affairs in their development of pretend play. A similar model of counterfactual reasoning that also focuses on the growth of the capacity to coordinate separate true and false representations will be proposed to explain the nature and development of children’s ability to ponder possibilities.  
	As a part of the argument supporting our claim, a distinction will be drawn between children’s lower-level processes involved in playing pretend and pondering possibilities (e.g., representing and managing relevant information) and higher-order understanding of such activities (e.g., conceptualizing the mind as a representational and interpretative entity). The distinction introduces a second goal of the chapter, that of considering the proper relation between children’s development of lower-level processing and higher-order understanding of mental phenomena. We will review traditional accounts of the development of children’s understanding of mind (i.e., simulation theory and the Theory theory), which propose different views of the relation between the lower-level processing and higher-order understanding of mental phenomena.  We will conclude the chapter with an alternative to the traditional views of the development of children’s knowledge of the mind.
Counterfactual reasoning and playing pretend

	A central question regarding pretend play is how children do it without becoming confused.  Pretending that a banana is a telephone, Leslie (1987) points out, is an activity that young children perform without dire consequences for their concept of bananas or telephones. Yet such dire consequences (what Leslie calls “representational abuse”) seem to be an outcome of, or at least are not prohibited by, other accounts of pretense notably Piaget’s (1962). Piaget’s model proposes that a real and true state of affairs (an event or object) is symbolically assimilated by a scheme other than the one to which the state of affairs is habitually or typically assimilated. Thus, there is no mechanism stopping a child who pretends that a banana is a telephone from again assimilating bananas to her telephone scheme in contexts where a telephone is actually desired. The problem according to Leslie is that we cannot have a theory of pretense which supposes that children employ cognitive structures in the service of pretense that are the same ones used to understand the real world in non-pretend contexts.
	As a solution to the problem, which has been widely acknowledged and accepted, Leslie (1987) proposed that children in pretend contexts (whether observing or participating) reason counterfactually; that is, they create a reality that is an alternative to the one known or believed to be true (Amsel et al., 1996; Bretherton & Beeghly, 1989; Harris, 1991; Harris & Kavanaugh, 1993; Lillard, 1993a; Perner, 1991; Woolley, 1995). So a child pretending a banana is a telephone reasons counterfactually by representing two identities for the same physical object: A true identity in the real world (i.e., a real banana) and a false identity in the pretend world (i.e., a pretend telephone). This resolves the problem of representational abuse because the child in a pretend context can now distinguish between and keep track of both states of affairs. 
	Beyond solving the problem of representational abuse, a counterfactual model of pretend play can explain the ease with which children pretend and their success at it. A child who failed to distinguish between or lost track of the false states of affairs in the pretend world and true states in the real one would behave in a manner which could hardly be appropriate in pretend contexts. For example, a child who loses track of the fact that she is really and truly holding a block while pretending that it is a cookie may bite down on the block when “eating the cookie” (Lillard, 1993a) or start building a house with the block, forgetting about the pretend scenario she was just playing. Generally speaking, children do not show such inappropriate behavior in pretend contexts. Indeed, the evidence suggests that young children are competent at distinguishing between and keeping track of the true states of affairs in the real world and their false ones in the pretend world, even when false states in the pretend world change (Gopnik & Slaughter, 1991; Harris & Kavanaugh, 1993; Harris, Kavanaugh, & Meredith, 1994; Leslie, 1994; Walker-Andrews & Harris, 1994).  Even evidence of periodic apparent confusion of pretend and real states of affairs (see reviews by Lillard, 1994; Woolley, 1995, 1997) does not deny that children are usually successful pretenders who act appropriately in most pretend contexts and show no signs of representational abuse (Lillard, 1993a; Woolley, 1995, 1997). 

	Despite wide acceptance for general aspects of Leslie’s analysis, there is still much debate and discussion about how children reason counterfactually in pretend contexts; that is, how it is that they successfully distinguish between and keep track of true states of affairs in the real world and false ones in the pretend world.  What follows is a review of two theoretical issues about the nature and development of children’s counterfactual reasoning in pretend contexts.  The first issue concerns lower-level processing of pretend information, specifically, the manner by which information regarding true and false states of affairs is represented and managed.  On the one hand, some theories propose that information about true and false states of affairs are represented together by forming a single “counterfactual” proposition which encodes both types of states of affairs (Harris & Kavanaugh, 1993; Leslie, 1987, 1994).  This contrasts with other theories, which propose that information about true and false states of affairs in pretend contexts are represented separately and so need to be managed by other means because there is no proposition relating them (Lillard, 1993a, 1996; Perner, 1991).  The second way of dividing the theoretical pie addresses children’s higher-order understanding of pretense as a mental activity. The issue addresses when or if young children conceive of pretense in terms of the thoughts of a pretender.  The issue pits those who deny that children ever conceive of pretense representationally, as a mental activity, for the purposes of understanding the goings-on in pretend contexts, against those who have sought to explain when and how children arrive at such a conceptual insight.
	Lower-level processing of pretend information
	At the level of representing and managing information in pretend contexts, some theorists suppose that children represent true and false states of affairs in pretend contexts by actually encoding each of the states and the relation between them in a counterfactual proposition. For example, according to Leslie (1987, 1988, 1994; Leslie & Roth, 1993), to pretend a banana is a comb, children would have to compute the M-representation I pretend (of) the banana that “it is a comb”.  Similarly, for Harris (1991, 1994; Harris & Kavanaugh, 1993; Harris, Kavanaugh, & Meredith, 1994) the same child would form the “flagged” representation  “In this episode, this banana is a (make-believe) comb”.  While there are important differences between these mental structures, each of them specify that, in a pretend context, true states of affairs are redefined as false ones.  These structures are thought to guide children’s understanding of, actions in, and memory for pretend contexts.  
	In contrast, other theorists deny that young children represent the relation between the true and false states of affairs as part of their counterfactual reasoning competence. Perner (1991; Perner, Baker & Hutton, 1994) likens the cognitive demands of pretending to remembering, where true (or current) and false (or past) states of affairs are represented separately as distinct models, with young children needing only to monitor which state is being attended to, not form a relation between them. Lillard (1993a,b, 1994; 1996) suggests that the true and false states of affairs may be represented at different cognitive levels, with the true state of affairs “cognitively backgrounded” relative to the false state of affairs. Children may simply shift attention between the different representations in much the same way someone shifts attention between figures in a reversing figures stimulus. Since the true and false states of affairs are represented at different cognitive levels, each can influence young children’s activities in pretend contexts, without children understanding the role of the mind, knowledge, or intention in pretending.
	To assess whether young children in pretend contexts encode true and false states of affairs together as a counterfactual proposition or separately as distinct representations, Amsel, Bobadilla, Coch, and Remy (1996) examined 3- and 4-year-olds’ memory for each state of affairs.  In Study 1, 16 three- and 19 four-year-olds initially pretended that a banana was a comb and “combed” a white teddy bear, then immediately afterwards pretended that the banana was a spoon and “fed” a brown teddy bear.  After the pretense was completed (and a 5 minute delay), children were asked two questions about the first pretend scenario: a question about the identity of the object in the real world (When you played with the white teddy bear, what did you really and truly have in your hand? Did you have a spoon, banana, stick, or comb?) and one about its identity in the pretend world (When you played with the white teddy bear, what did you pretend to have in your hand? Did you have a spoon, banana, stick, or comb?). After the last pair of questions was asked, children were asked to reconstruct their actions (Show me exactly what you did when you played with the white teddy bear) with an array of objects and the white teddy bear in front of them.
	With regard to their memory for actions, a majority of children in each age group (63% of 3- and 87% of 4-year-olds) correctly remembered that they picked up a banana and “combed” the white teddy bear. Only 2 children (a 3- and a 4-year-old) confused the true identity of the object with its pretend identity by picking up the comb and "combing" the white teddy bear. Such errors would be expected if young children were confused about the contents of the real and pretend world (DiLalla & Watson, 1988) or believed that their mental representations correspond to reality (Woolley & Wellman, 1993). 
	If a counterfactual proposition formed in a pretend context was retrieved when remembering what had happened in that context, then children who correctly remembered their actions should also have identified the banana as the true identity of the object and the comb as its pretend identity.  However, this was not the case. Overall, 3-year-olds correctly identified both identities only 19% of the time, whereas for 4-year-olds the corresponding figure was 61%. More generally, children’s performance remembering actions and an object’s identities in a pretend context appears to be unrelated: 77% of the children who correctly identified both identities of the object also successfully remembered their actions whereas a surprisingly similar 72% who never successfully remembered both identities correctly remembered their action. Thus, there were many children (largely 3-year-olds) who remembered picking up a banana and combing the white teddy bear but who could not correctly identify the banana as what they really had in their hand and the comb as what they pretended to have in their hand. 
	Three further findings additionally challenge the proposal that children form and retrieve a counterfactual proposition.  
	1.  Children’s tendency to correctly remember one identity of the object was unrelated to their tendency to correctly remember the other identity. A positive relation was expected if children in object-substitution pretend contexts encode the true and pretend identities of the object together into a single counterfactual proposition:  Either children successfully retrieve the proposition and correctly remember both identities or they fail to successfully retrieve it and have to guess, probably incorrectly, which is the true and which is the pretend identity.  	
	2.  There was an unexpected asymmetry in young children's memory performance, with more 3-year-olds correctly naming the object's true than pretend identity. Again, such an asymmetry was not expected since it was supposed that children would either retrieve the counterfactual proposition and remember both identities or fail to retrieve it and likely remember neither one.
	3.   When children erred, they showed an unexpected perseveration, tending to give the same response to both questions. Indeed, on 66% of the trials on which an error was made identifying an object’s true or pretend identity, children gave the same response to both questions.  On 70% of these trials children responded that both identities of the object were the true identity (banana), on 26% of them they responded that both were the initial pretend identity (comb), and on 3% of the trials both were the final pretend identity (spoon). Such response perseveration was also found by Flavell, Flavell, & Green (1987), who characterized it as an “apparent tendency to select a single representation of an object and stick with it”. These perseveration errors are difficult to explain if both identities are encoded together in the same counterfactual proposition.
	These findings were replicated in Study 2 of Amsel et al. (1996), in which 42 preschoolers (37-54 months) were asked to specify the true and pretend identities of an object used by an experimenter in a pretend scenario. In an extension of this work, Amsel, Foulkes, Gilmore, Smalley, and Volpe (1998) had 20 3- and 4-year-olds pretend one object was another and then placed the object they played with in an opaque jar.  Children were then asked whether the true and the pretend object were in the jar (in counterbalanced order). For example, children pretended a straw was a comb by “combing” the fur of  a white teddy bear.  The straw was placed in an opaque jar and children were asked whether there was a comb in the jar and whether there was a straw in the jar.  Despite the different procedure and type of question posed in this study than in Amsel et al. (1996), children’s performance still showed 1) non-contingency (correctly judging the presence of the true identity was unrelated to correctly identifying the absence of the pretend identity); 2) asymmetry (more children correctly identified the true identity of the object than the pretend identity); and 3) perseveration (children erred by claiming that both identities were in the jar, rather than by claiming that only the pretend identity was in the jar).
	A model
	The results of the study suggested that children do not reason counterfactually regarding pretend contexts by forming and retrieving a counterfactual proposition. This was made clear by the fact that children specified the true and pretend identities of an object noncontingently, asymmetrically, and they erred by persevering on one identity. The data were more consistent with those who claim that the two identities are represented separately, with the true identity of the object encoded into a representation of a true state of affairs and the pretend identity encoded into a distinct representation of a false one.
	The evidence that 3-year-olds have difficulty remembering both identities can be explained by their poor cognitive management abilities (see Harris, 1993, for a related discussion).  That is, rather than easily shifting between representations of the true and false states of affairs when they were both activated by questioning, young children tended to adopt Flavell et al.’s (1987) “select and stick with one representation” strategy. Moreover, children had a rich multi-modal experience (visual, proprioceptive, verbal) of the actual objects but not of the pretend (verbal) objects in otherwise mundane and affectively-neutral pretend play scenarios. As a result, children responded to both questions by reference to the better elaborated and more strongly activated representations of true states of affairs, failing to shift to the less salient representations of the false states.  
	Perhaps if the pretend context were such that the false state of affairs were more elaborated and strongly activated than the true one, children would have difficulty disengaging from pretend identity.  Such a claim is supported by Lillard (1994) and Woolley (1995), who reviewed the literature and suggested that young children are susceptible to acting as if the pretend world is in fact real if they have a strong emotional response to the pretend world.  For example, as the pretend monster or “bad guy” becomes better elaborated and more strongly activated than the mundane perceptions out of which it was created, children will be increasingly likely to fail to disengage from and to be frightened by their pretend creation.  Thus, cases in which children appear to confuse fantasy and reality may be best interpreted as the result of limitation in children’s management of the multiple representations formed during pretend play, rather than due to a profound conceptual or ontological confusion.
	Children’s actions in pretend contexts may serve as a means to concretize and externalize the problem of  managing the separate representations of the true and false states of affairs. That is, actions in pretend contexts may serve to help children to monitor the relation between true states of affairs, which are being manipulated, and false ones, which are being simulated. Previous research has demonstrated an age-related decrease in preschoolers’ preference for actual objects that are similar in form and function to pretend ones (Elder & Pederson, 1978; Jackowitz & Watson, 1980; Overton & Jackson, 1973; Pederson, Rook-Green, & Elder, 1981; Ungerer, Zelazo, Kearsley, & O’Leary, 1981). Such preferences may exist initially because young children have no other means to manage the multiple representations formed when pretending so they seek out objects that afford actions manipulating the true and simulating the false states of affairs. 
	Older children may rely less on a similarity between the true and false states of affairs in order to engage in pretense as they find mental means of managing the representations. Such an argument regarding children’s progression away from relying on externalized and concretized information as a means of relating true (i.e., referent) and false (symbol) states of affairs has been demonstrated in children’s production and comprehension of pantomimes. O’Reilly (1995) found that children’s reasoning about pantomimes was supported by the use of concretized and externalized body part information (e.g., brushing teeth using a finger as a toothbrush) relative to the same actions with an imaginary object (e.g., brushing teeth with an imaginary toothbrush) for 3- but not 5-year-olds. Young pretenders’ vocalizations may also serve as a concretized means for them to manage the separate representations of true and false states of affairs. Young children may use different voices when talking about the true and pretend world and make supportive sounds (e.g., saying “vroom” when pretending a block is a car) to aid them in selectively activating and/or attending to a target represented state of affairs. 
	A model of the proposed representations children formed during (object-substitution) pretense is presented in Figure 1. Children encode the physical object’s true and pretend identities as separate representations of the true and false states of affairs, depicted in Figure 1 by different shapes for the representations. It is further proposed that the representations are unequally activated in memory, which is depicted by the different sizes for the representations in Figure 1. Finally, the representations are related by actions performed in pretend contexts (depicted by an arrow). When asked to reconstruct their actions, children retrieve the entire structure, including the represented true identity of the object as the thing being manipulated and the represented pretend identity as the thing being simulated by actions. However, when asked about each object independently of the other and the action performed, the action link between the models is not activated and young children are left to (unsuccessfully) attend selectively to the appropriate representation. Older children, it is assumed, can perform the appropriate mental management to correctly attend to the appropriate representation.
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Place Figure 1 here. 
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	Higher-level understanding of pretense 
	Beyond the manner by which children process information in pretend contexts, the theories of how children reason counterfactually about pretense differ in how pretense is understood. As mentioned, the issue hinges on when or if children understand pretense representationally, as a mental activity in which pretenders represent false states of affairs. Three aspects of children’s conceptualization of pretense has been examined: their appreciation of 1) the role of knowledge in pretending, 2) the diversity of pretense, and 3) the difference between pretense and false belief.
	Lillard (1993a, 1996) challenged the claim that children in pretend contexts appreciate that the same state of affairs is represented in multiple ways  (e.g., Flavell, Flavell, & Green, 1987; Gopnik & Forguson, 1988; Leslie, 1987). Lillard (1993a) argued that although children are aware and keep track of true and false states of affairs, that is not the same as saying that they understand pretense in terms of the representations that pretenders form. In experimental tests of these ideas, Lillard (1993b, 1996, 1998) found that a majority of preschool-aged children assert that a protagonist who is hopping like a rabbit is pretending to be a rabbit despite the protagonist having been described as having no knowledge of or desire to act like rabbits. Young children miss critical points about the representational nature of pretense: Pretending involves knowledge of the pretend object and an intention to pretend. According to Lillard, rather than conceiving of pretense as based on intentionally created mental representations of false states of affairs, young children conceived of it in terms of the actions which simulate false states.
	A number of researchers have attempted to detect any insight children may have about the role of knowledge in pretense on Lillard’s task by a) minimizing the salience of protagonists’ actions (Aronson, Golomb, & Kirkpatrick, 1997), b) making mental state information more salient (Custer, 1996), or c) both (Bruell & Woolley, in press). The general finding is that children as young as 3 years of age understand that pretenders have thoughts of the false states of affairs they represent. Such evidence though, does not detract from the fact that children’s representational understanding of pretense is fragile and can be easily overwhelmed in normal pretend contexts where actions and verbalizations are salient. The claim that children have at least a fragile understanding of pretense as representational (although see Lillard, 1996) is supported by evidence that they appreciate the diversity of pretense: That two people may be pretending that a particular true state of affairs are different false ones (Davis, Woolley, & Bruell, 1998; Hickling, Wellman, & Gottfried, 1997). For example, Hickling et al. found that 3-year-olds judge that a puppet will continue to believe that a glass contains pretend milk even though the child has since pretended that the milk was emptied out behind the puppet’s back. 
	Thus, even young children appear to understand that the same true state of affairs may be responded to by pretenders as different false ones. However, this may be a relatively superficial appreciation which contrasts pretenders’ expectations about what to do and say in response to different pretend stipulations for the same true state of affairs. This is in comparison with the conceptually deeper appreciation which contrasts pretenders’ interpretations of same true states of affairs as different false ones. While expectations and interpretations both refer to a pretender’s subjective state, the latter entails understanding pretenders as actively creating different pretend worlds, whereas the former involves understanding pretenders as merely responding as they should to distinct pretend stipulations. 
	Perner, Baker, and Hutton (1994) tested the claim that young children initially have, at best, a superficial understanding of the relation between pretenders and the false states of affairs they represent, if they have any understanding of it at all. They argued that young children appreciate that an agent may act with respect to false states of affairs but not understand the difference between pretending false states of affairs are true and falsely believing false states of affairs are true. As evidence, Perner et al. demonstrated that children younger than 4-year-olds could not distinguish between whether a protagonist was pretending or (falsely) believing to feed a rabbit, despite being told the protagonist saw or did not see the rabbit being removed from its cage prior to feeding it.
	Thus, there appears to be growth in children’s understanding of the relationship between a pretender and the false state of affairs being represented.  Initially, children have little or perhaps no insight into the nature of the relationship.  By 4 years, children appreciate that a pretender knows the false state of affairs is false, and later grasp more fully that the false state of affairs is a product of and so constrained by the pretender’s knowledge base.
	Representing pretend information and understanding pretend contexts
	The distinction between lower-level processing and higher-order understanding of pretend contexts leaves open the question of the developmental relation between them. Theoretical accounts of the relation between changes in lower-level processing and higher-order understanding of pretense come from the two major theories of the development of a theory of mind. On the one hand, and consistent with the Theory theory, the emergence of a representational understanding of pretense may influence how information in pretend contexts is processed. The Theory theory proposes that young children form and revise intuitive theories (of mind in this case) which have the same function for children that formal theories have for scientists: as a basis to encode, explain, predict, and understand relevant phenomena (Gopnik & Meltzoff, 1997; Wellman & Gelman, 1992).  The idea is that children’s misunderstanding of a phenomenon (e.g., whether someone is pretending) can be traced back to their domain-specific theory of the phenomenon (e.g., non-representational theory of mind) rather than to them having a domain-general limitation (e.g., lacking a general reasoning capacity)
.  Thus, as a consequence of children replacing their behavioral understanding of pretense (i.e., pretense as acting “as if”) with a representational one, they would acquire the means to better represent and manage information in pretend contexts.  
	On the other hand, and consistent with the simulation theory, developmental changes in children’s higher-order understanding of pretense as a mental state may be irrelevant to and thus independent of changes in lower-level processes involved in encoding and managing true and false states of affairs. The simulation theory (c.f., Harris, 1991, 1994) proposes that children and adults alike understand behavior in a particular context by mentally simulating the context and “seeing” what they (and by implication others) would say, feel, and do in the same circumstances. Harris proposes that with the growth of children’s  information processing system (i.e., the central executive), they can run more complex simulations; from ones that alter only states of affairs (i.e., creating simulations of false states of affairs), to those that additionally alter children’s attitude that the simulations are false (i.e., creating simulations of false states of affairs that are taken to be true for an agent). So the development of children’s representations of information in pretend contexts and their discrimination of pretend from false belief contexts results from their being able to form more complex simulations, and their understanding of pretense has its source elsewhere.
	To summarize, children reason counterfactually about pretense by forming distinct representations of true and false states of affairs. Although children have some difficulties managing these representations outside the immediate pretend context, their competence managing the representations within a pretend context may be related to the pretend information being largely externalized and concretized through actions and verbalizations. The actions and verbalizations allow children to monitor both and selectively attend to each of the multiple representations. It is interesting to note that another function of pretenders’ externalizing and concretizing information is in order to share the pretense with others (Goncu, 1993).  Perhaps because externalized and concretized information is so socially and psychologically significant for children’s pretense, such information is taken by children to define what it means to pretend. Young children show only a fragile understanding of pretense as involving pretenders’ reinterpretation of the true states of affairs as false ones.  
	The developmental changes in children’s counterfactual reasoning about pretense involve changes not only  in the lower-level processes for representing and managing the true and false states of affairs but also in the higher-order understanding of pretenders’ relations to representations.  Over age children rely less on externalized and concertized information as a means of managing the information represented from pretend contexts and acquire deeper insight into pretenders’ thoughts about the representations they form. Ironically, by the time children achieve full control over and a stable representational understanding of pretense (i.e., at 6 or 7 years), their tendency to spontaneously engage in the activity begins to dwindle (Rubin, Fein, & Vandenberg, 1983).
Counterfactual thinking and pondering possibilities
	Our interest in comparing the cognitive processes involved in playing pretend and pondering possibilities is that we think by mastering the former, children become better able to do the latter.  They begin to competently “play” with a particularly interesting set of false states of affairs -- possible ones. By possibilities we mean unactualized states of affairs that are capable of happening, existing, or being true without contradicting proven facts, laws, or circumstances. Typically, possibilities are contrasted to actualities which are states of affairs that are known or believed to be real and true. 
	There are a number of ways in which children can reason about the relation between possibilities and actualities (Amsel, Foulkes, & Smalley, 1997). First, an actual state of affairs can be interpreted as one among a set of possible states. Exhaustively enumerating the set of possible states of affairs involves combinatorial reasoning, wherein all logically possible combinations of actual elements in a set (without regard to their order) are generated (Inhelder & Piaget, 1958; Pitt, 1983). Second, features of actual states of affairs in a context can be interpreted as possible conditions or causes in accounting for some other state of affairs in the context. Modal logical reasoning about possibility and necessity underlies the appreciation that multiply sufficient features are individually and in combination possible causes or conditions of some other state of affairs (Fay & Klahr, 1996; Piaget, 1987). Third, features of actual states of affairs in a context can be mentally altered, thereby creating a possible state of affairs with which actual ones can be compared and contrasted. Creating such a possible state of affairs and comparing and contrasting it to an actual one involves counterfactual reasoning  (Amsel et al., 1991; Roese, 1997). 
	Counterfactual reasoning about possibilities
	The parent pondering possibilities who was introduced at the beginning of this chapter, is perhaps best described as engaged in the third form of reasoning about possibilities, where possible states of affairs are created in order to be compared with and contrasted to actual ones. The parent is pondering those possible states of affairs as a means to understand why the child threw a temper tantrum and to prevent it in the future. By determining the event sequence which would have led to the child not throwing the temper tantrum, the events in the actual sequence which are causally relevant would be discovered. Of course this process of identifying alternative sequences which would undo the undesirable outcome is based on the parent’s knowledge and experience with the child.  For example, having dressed the child differently would likely be dismissed by the parent as undoing the tantrum but having had a longer nap may be accepted. With a longer nap, the parent imagines, the child would have been better able to control herself in the late afternoon.
	Counterfactual reasoning about possibilities and emotions
	There are other uses of counterfactual reasoning about possibilities than making causal attributions. One line of research we have been pursuing concerns the development of counterfactual reasoning about possibilities in the domain of emotions (Amsel, Robbins, Tumarkin, Foulkes, Janit, & Smalley, submitted). What is the connection between emotions and counterfactual reasoning about possibilities? Our feelings about actual states of affairs are often influenced by states that could have but do not occur.  For example, consider a contestant on the TV game show, "Let's Make a Deal". Contestants select one of two gift boxes and keep whatever they find inside. How a contestant feels about what is in the selected gift box is typically influenced by what is in the box they could have but did not select. On the one hand, if the contestant gets a refrigerator but could have had a brand new car, they feel sad, regretting the choice they made. Like the pondering parent, the contestant appreciates that a more desirable outcome could have been realized if another course of action had been followed. On the other hand, if the contestant gets a refrigerator but could have had a case of cat food, they are happy, satisfied that they chose the best gift possible. The contestant appreciates that if another course of action had been taken, a less desirable outcome would have been realized.  
	The influence of the possible gift on contestants’ feelings about the actual gift is appreciated not only by the contestant but also by the audience.  For both, a true state of affairs (i.e., the contestant opens the “selected” box and reacts to its contents) is represented.  In addition, a false state of affairs (i.e., the contestant opening the “unselected” box) is represented, reasoned about (i.e.,  the reaction is imagined) and compared to the true state (i.e., the false state is judged to be more desirable, less desirable, or no different than the true state of affairs). 
	Amsel et al. (submitted)  assessed preschoolers’ ability to reason counterfactually about possibilities in the domain of emotions; that is, whether false states of affairs are represented, reasoned about, and compared to true ones. In each of three studies, preschool and college students judged their own or a protagonist's feelings about an actual state of affairs (i.e., a gift) before and after being presented with information about a possible one (i.e., the gift the protagonist could have but did not receive) which varied in desirability from the actual state. Study 1 examined whether preschoolers’ judgments of protagonists’ emotions would be influenced by information regarding counterfactual possibilities. Sixteen preschoolers (38-68 months, 8 females and 8 males) and 7 college students (4 females and 3 males) were introduced to two protagonists (dolls of the same sex as the subject) who were each associated with two gift boxes.  Participants were told that each protagonist selected one of the two gift boxes and, upon opening the selected box, the child-participants were told that each protagonist found the same toy figurine whereas the adult-participants were told that each protagonist found $5.00. Children and adults were then asked the Initial Question for each protagonist:  “How happy is (naming one protagonist) with the gift she (he) received: Not happy or sad, a little happy, pretty happy, or very happy?” 
	Next, each protagonist's unselected gift box was opened and found to contain either a high valued gift for one protagonist, whom we will designate as protagonist+ (stickers or $20.00), and a low valued gift for the other protagonist, designated as protagonist- (a block or $0.50).  Children and adults were then asked the same Counterfactual Question for each protagonist: How happy would (naming one protagonist) have been if she (he) had taken the other gift box: “Not happy or sad, a little happy, pretty happy, or very happy?”
	The children and adults performed no differently in response to the Initial and Counterfactual Questions (Figure 2). All participants recognized that the two protagonists were equally happy initially, but that protagonist+ would have been happier and that protagonist- would have been less happy with the gift they could have but did not receive, compared to the one that they did receive. From these data it seems that preschoolers have adults’ abilities to represent a false state of affairs (i.e., the protagonists opening an “unselected” gift box)  and reason about it (i.e., imagine the protagonists’ feelings discovering what is inside). _______________________________

Place Figure 2 about here.
_______________________________	 At this point in the procedure, the participants had assessed the protagonists' feelings about the gift each actually received and the one they could have had. The issue of whether participants appreciate the influence of the possible gift on the protagonists’ feelings about the actual one was assessed by asking the Final Question which was the same as the initial one:  “How happy is (naming one protagonist) with the gift she (he) received: Not happy or sad, a little happy, pretty happy, or very happy?” Adults judged protagonist+ as less happy and -protagonist as happier in response to the Final Question compared to the Initial Question (Figure 3) and so were influenced by the counterfactual information. As expected, protagonist+ was judged as less happy because she could have got $20 but only got $5, whereas protagonist- was judged as happier because she got $5 instead of only $0.50.  _______________________________

Place Figure 3 about here.
_______________________________
	In contrast, the preschoolers showed no change from the Initial to Final Question (Figure 4), suggesting that they were uninfluenced by the information regarding the possible gift. This lack of influence occurred despite evidence that children were just like adults in knowing how the protagonists would have felt if they had received their possible gifts. Nevertheless, that knowledge had no influence on preschoolers' reassessment of protagonist happiness with their actual gift. The implication of these findings is that preschoolers represent and reason about false states of affairs in the same way that adults do, but they do not compare the true state of affairs to the false ones.
_______________________________

Place Figure 4 about here
_______________________________

	Two other studies in the Amsel et al. paper (submitted) replicated the basic finding of Study 1. In Study 2,  twenty-six preschool and twenty-four college students rated protagonists’ feelings about the contents of a selected box before and after learning about (1) the higher or lower value of the contents in the box that they could have but did not select (counterfactual information) or (2) the fact that the protagonists were satiated with or desired the contents (factual information). Children and adults were influenced in predicted ways by factual information: Compared to their initial judgment of protagonist happiness with contents, those described as satiated with it were judged as less happy and those described as desiring it were judged as happier.  However, only adults were influenced as predicted by counterfactual information. Once again, children did not alter their assessment of protagonist happiness regarding the actual content depending on the value of the possible content.
	In Study 3, 10 preschool and 10 college students blindly turned over one of two face-down playing cards, judged whether or not it ‘beat’ the experimenter’s face-up card, and rated their feelings about the card they selected. On trials where the experimenter and the participant tied, the participants were asked to turn over and rate their feelings about the unselected card, which was either higher or lower than the card they actually turned over. Finally, subjects  re-rated their feeling about the card they actually turned over. The results again replicated those of Study 1: Compared to their feelings about the card they actually turned over which tied the experimenter’s, children and adults judged that they would have been happier having turned over the “unselected” card when it would have won and less happy having turned over the “unselected” card when it would have lost.  However only adults compared true states of affairs to false ones in predicted ways: Compared to their initial judgments, adults were happier about having tied after finding out that they would have lost the hand, and less happy about the tie after finding out that they would have won the hand.  In contrast, the children’s ratings of the selected card were the same before and after learning about the card they did not select. 
	Another model
	Children do not have adults' appreciation of how an agent’s (self or other) feelings about actual states of affairs depend on states that could have but do not occur. In this regard, children live in a different emotional world than adults -- one in which counterfactual possibilities do not bear on how they feel about actualities. Why do preschoolers reason differently than adults about the influence of possibilities on emotions? It seems that preschoolers can successfully represent and reason about false states of affairs, but they do not compare the true states of affairs to false ones in predicted ways. 
	Figure 5 presents a model of counterfactual reasoning about possibilities in the domain of emotions to further unpack our claim about preschoolers’ capability. Actual sequences of events leading up to an agent’s (self or other) emotional reaction are marked as a true states of affairs, depicted in Figure 5 by an event sequence (event 1 to event 4) within the representational structure labeled as “true state of affairs.”  A copied and edited version of the true state of affairs, in which a particular event node is altered, is represented as the false state of affairs. This is depicted in Figure 5 as an event sequence, paralleling the true event sequence except for the altered event node (labeled “E” for “edited”) within a representational structure labeled as “false state of affairs”. The copying and editing function by which the true state of affairs became the false one is depicted as an arrow in Figure 5. Beyond editing a change in an event sequence, the consequences of the edited change must be imagined, depicted here by a broken arrow to an event node labeled “I” for “imagined”.  The imagined event node can now be compared and contrasted with the corresponding event node in the true state of affairs such that the assessment of an actual state of affairs can be evaluated in light of a possible one. This process is depicted in Figure 5 by an arrow going from a false state of affairs to a true one._______________________

Place Figure 5 about here.
_______________________ 	The data from Amsel et al. (submitted) suggest that preschoolers are like adults in their competence to copy an actual sequence of events, edit it by altering a specific event, and then imagine the consequences of the edited change on an agent’s emotional reaction.  However, preschoolers are unlike adults in bringing such possible states of affairs to bear when evaluating (i.e., comparing and contrasting with) true ones:  Adults’ but not children’s assessments of true states of affairs were affected in predicted ways by false ones. Thus, there seems to be an asymmetry in children’s similarity to adults in their ability to reason counterfactually about possibilities.  On the one hand, children and adults are similar in their creation of states of affairs which could have but did not occur and imagining the consequences of those possible states; that is, in their reasoning about possibilities, given actualities. On the other hand, children and adults are dissimilar in their use of information about the states of affairs which could have occurred to evaluate the actual ones; that is, in their reasoning about actualities, given possibilities.
	Extending this analysis of children’s counterfactual reasoning about possibilities in the domain of  emotions are the results from Harris, German, and Mills (1996), who examined young children’s counterfactual reasoning about possibilities in the domain of causality.  In Studies 1 and 2, Harris et al. found that a majority of 3- and 4-year-olds could answer questions about preventing a negative outcome.  In these studies, children were told of an event sequence (i.e., a protagonist paints the floor red with a paint brush) that has an undesirable outcome (the floor is dirty).  They were asked then to imagine the consequence for the outcome (i.e., the floor would still be dirty or would not have gotten dirty) of mentally altering a causally-relevant event (i.e., the protagonist not having painted) or a causally-irrelevant event (the protagonist using his fingers to paint). Children showed a great deal of competence to think counterfactually about the conditions under which negative outcomes could have been avoided. The finding supports the claim that children copy and edit true states of affair, altering particular events, and then imagine whether the altered events can “undo” negative outcomes.  Put differently, the data from Harris et al. suggest that children can readily reason about false states of affairs, given true ones.  
	In Study 3, Harris et al. additionally examined whether children can reason counterfactually to attribute the causal conditions in a real event sequence rather than to identify preventative conditions in an imagined event sequence. To test children’s ability to reason counterfactually about causation children were asked to identify the causes of an undesirable outcome (i.e., inky fingers) befalling a protagonist. Children were told that the protagonist had acted in a certain way (i.e., selecting a black pen with which to draw) after rejecting a course of action which would have led to the same outcome (i.e., drawing with a blue pen: Control condition) or after rejecting a course of action which would have led to a desirable outcome (i.e., drawing with a pencil: Experimental condition). The experimental condition invites children to reason counterfactually about the role of the protagonist’s course of action in producing the undesired outcome whereas the control condition blocks such reasoning. Children answered the causal question by reference to the protagonist’s failure to adopt an appropriate course of action, specifically identifying the rejected option in the experimental condition (e.g., failure to use a pencil) more frequently than in the control condition. Harris et al. claim that their Study 3 finding replicates with children the results of Wells and Gavanski’s (1989)  study with adults. In each study, the differential impact of the experimental condition over the control on children’s and adults’ causal judgments was cited as evidence of the influence of counterfactual reasoning about possible states of affairs (i.e., unselected options which undo outcomes) on the evaluation of actual ones (i.e., attributing events as causal).  
	The findings suggest that children are influenced by possibilities in their assessments of actualities in the domain of causality, which contrasts with Amsel et al.’s finding that children are not so influenced in the domain of emotions. While such domain-specificity in the development of children’s counterfactual reasoning about possibilities may well yet turn out to be the case, the present data, we claim, are insufficient basis to make such a claim. Specifically, we are skeptical of Harris et al.’s finding as evidence of children’s sophistication in reasoning counterfactually about causality because the central finding reported by Harris et al. is different and less compelling than Wells and Gavanski’s finding to which they were compared; a finding which is now under a great deal of criticism.  First, with regard to the nature of the effect, Harris et al. and Wells and Gavanski found that the experimental condition influenced children and adults alike to arrive at different causal attributions than did the control condition.  However, the causal attributions were framed in terms of what the protagonist hadn’t done  (i.e., the alternative actions such as not having used a pencil) for Harris et al.’s children, whereas they were  framed in terms of what the protagonist had done (i.e., the decision of the protagonist such as ordering the meal with wine) for Wells and Gavanski’s adults.  While this difference may be an artifact of the different tasks, procedures, or coding systems used in the two studies, it may also be the case that possibilities have a different influence on children’s than on adults’ causal reasoning.  Second, with respect to how compelling the findings are, Wells and Gavanski found that adults made reference to what the protagonist had done as the cause of the undesirable outcome approximately 67% of the time overall (about 86% of the time in the experimental and 48% of the time in the control condition). In contrast, Harris et al. found that children made reference to what the protagonist had not done as the cause of the undesirable outcome only about 39% of the time overall. This difference, too, may be an artifact of differences in the tasks, but may reflect that adults are more strongly influenced by possibilities than children.  Finally, social psychologiests have criticized Wells and Gavanski’s claims about the role of counterfactual reasoning on causal attribution, suggesting instead that counterfactual reasoning leads to judgments of how to prevent undesired outcomes and typically not to causes of such outcomes (Mandel & Lehman, 1996; N’gbala & Branscombe, 1995).  Such an argument may be too strong given the centrality of the role of counterfactual reasoning as a tool for performing causal analysis in law (Amsel et al., 1991).  Nonetheless, the criticism suggests that Wells and Gavanski’s findings may not be sufficient evidence of the role of counterfactual reasoning in causal attributions, undermining Harris et al.’s appeal to the parallel between the respective findings as evidence of children’s counterfactual reasoning competence.
	In summary, young children have little difficulty in reasoning about possible states of affairs, given actual ones, whether the possibilities reasoned about are alternatives to actual causal sequences (e.g., what would have happened if things were different?) or emotional reactions (e.g., how would an agent have felt if things were different?). However, young children’s ability to reason about actualities in light of possibilities is very much in question. There is no evidence that young children’s assessment of actual emotional reactions is influenced in an adult-like way by possible ones (Amsel et al., submitted); such an influence first appears in early elementary school (Amsel et al., 1998).  Moreover, there is only weak evidence that young children’s
 assessment of the causal status of events in an event sequence is influenced in an adult-like way by possible ones (Harris et al., 1996). While more research is needed, it would nonetheless appear that the source of developmental change in children’s counterfactual reasoning about possibilities lies in their ability to bring information about possibilities to bear on their evaluation of actualities; that is, to compare and contrast true states of affairs with false ones.  
	The growth of the ability to reason counterfactually about possibilities may be explained by one of the two developmental accounts previously discussed for pretense. On one hand, and consistent with the theory-theory, children’s higher-order understanding of mental activities may lead to changes in their lower-level processing of such information. The higher-order understanding in this case may be an appreciation of what Chandler and Lalonde (1996) describe as an “interpretative” theory of mind, where children understand the active nature of mind to construe situations. Chandler and Lalonde point out that standard theory of mind tasks assess whether children appreciate that the same state of affairs can give rise to unique representations in different agents (or in the same agent at different times) due to the different agents’ (or the same agent’s changing) relations (e.g., spatial, temporal, history, or quality) to the state of affairs. Chandler and Lalonde further point out that children sometimes have to make sense of situations where the same actual state of affairs is interpreted differently by different agents, even though the agents’ relationship to the state is identical. Such situations call for an understanding of mind as more than just representational; it calls for an understanding of mind as interpretative.  For example, an interpretative mind is implicated in cases where agents who otherwise have the same relation to a state of affairs, react with different emotions or make different causal attributions. Consistent with an interpretative theory of mind, children may appreciate that the differing emotional reactions and causal attributions are the product of a feature associated with the thoughts of the agents rather than with the state of affairs itself or the relation between the agents and state of affairs. From this perspective, it is only when they understand the mind as interpretative that they will acquire the lower-level cognitive processes required for computing how two agents’ different emotional reactions or causal attributions may be due to each evaluating an actual state of affairs in light of different possible ones.  
	On the other hand, and consistent with simulation theory, the acquisition of a higher-order theory of a constructive mind may be irrelevant to and so independent of changes in lower-level processes involved in children’s managing representations of actual and possible states of affairs.  As previously noted, Harris proposes that over age children can run more complex simulations.  Perhaps they also become better able to compare and contrast simulations with actual sequences, thereby being able not only to create representations of false states of affairs and treat them as true, but also to bring them to bear when evaluating actual sequences. 
Summary, conclusions, and implications
	So in what ways are the processes of playing pretend and pondering possibilities related? We make two broad arguments. The first argument, outlined in the introduction, is that counterfactual thinking underlies both activities. Each form of mental activity involves the creation and analysis of false states of affairs, and coordination of the false states with true ones. When children play pretend and ponder possibilities they create false states of affairs out of true ones as alternatives to them. What differs between the false states of affairs created for each activity are the real world implications assumed for each: False stat es of affairs created as pretend worlds are assumed to have no real world significance, whereas those created as possible worlds are assumed to have such significance. Put differently, when playing pretend, false states of affairs are created from true ones as playful alternatives to them, but when pondering possibilities, the false states of affairs are copied and edited versions of true ones which are to be seriously compared to and contrasted with true ones. 
	Once children create a false state of affairs, whether as a pretend or possible world, they seem to be able to use all their available inference tools to create new false information. For example, children may draw on the same causal knowledge to determine the consequences of an alternative event sequence (Amsel et al., submitted; Harris et al., 1996) or of a pretend action (Harris & Kavanaugh, 1993). Finally, the false states of affairs are coordinated with true ones. In the case of playing pretend, that coordination involves keeping the false states of affairs separate from true ones, whereas in the case of pondering possibilities the coordination involves bringing the false states of affair to bear on true ones. Thus, although the manner by which representations of false states of affairs are created and coordinated with true ones are different when playing pretend and pondering possibilities, the two involve similar kinds of cognitive processes.   
	The second argument regarding the similarity of playing pretend and pondering possibilities is the source of developmental change in each activity. Young children appear to be able to form representations of false states of affairs early on, at least by the time that the word “no” is used to express denial, typically before their second birthday  (Bloom & Lahey, 1978). But in contrast to contexts in which children deny representations of false states of affairs in favor of true ones, those in which children play pretend and ponder possibilities involve managing the true and false states of affairs. It is managing the multiple representations which gives young children the most difficulty in each activity and is the source of development of each.  Just as young children have more difficulty compared to older children appropriately shifting between the representations of true and false states of affairs when playing pretend, so do they have difficulty bringing representations of false states of affairs to bear on true ones when pondering possibilities. Children seem to work out the former management problem (pretense) earlier than the latter (possibilities), at least for the tasks examined here.  
	It remains unclear exactly how children overcome their difficulties managing the represented true and false states of affairs when playing pretend or pondering possibilities. Two accounts have been reviewed here: the Theory theory and simulation theory. The Theory theory supposes that changes in children’s higher-order understanding of mind alters their lower-level management of true and false states of affairs.  Understanding the mind as representational enables children to encode an agent in pretend contexts thinking of true states of affairs as false ones. Understanding the mind as interpretative enables children to bring false states of affairs to bear on true ones. In the alternative simulation theory, change in higher-order understanding of mind is denied to have any role in the development of children’s ability to create simulations, whether they be of a pretend or possible world. The development of children’s ability to appropriately simulate pretend and possible worlds, which reflects more complex forms of counterfactual thinking, may involve the growth of general cognitive capacities and control systems (i.e., the central cognitive executive).  
	We offer, as a concluding statement, a third account of the development of counterfactual reasoning about pretense and possibilities, in the form of an interaction between changes in higher-order conceptual understanding and lower-level information processing. That is, as children develop more powerful cognitive capacities and control systems, more complex forms of counterfactual thinking become possible and will occur under the right circumstances. But such a form of reasoning is not always strategic, that is, under the child’s own control. Nonetheless, the occurrence of such thoughts may serve as a basis for children’s conceptual reorganization of their theory of mind. For example, on certain occasions, children may appreciate that an agent’s thoughts about a false state of affairs is a way to judge whether or not the agent is playing (pretending) or is serious (holding a false belief). Later on, the child may appreciate the role of different possibilities entertained by agents for why they arrived at different conclusions about the same state of affairs. While each insight may not generalize beyond the conditions of the particular context, it was enabled by the child’s developing information processing system. A younger child would simply not have the lower-level processing power necessary for the particular insight. Nonetheless, the insight may be the kind of interesting case which is the basis for a conceptual reorganization. Once the new theory is in place, the once haphazard strategy for managing true and false states of affairs may become more strategic and under the control of the child.  Contrary to simulation theory, this proposal supposes that conceptual reorganizations may serve an important role in the development of counterfactual reasoning: from successful counterfactual reasoning about pretense (based on the acquisition of a representational theory of mind) to possibilities (based on the acquisition of an interpretative theory of mind).  Contrary to the Theory theory, the present proposal claims conceptual development of children is unlike that for scientists, since only for the former is conceptual development tied intimately to the growth of the cognitive system. Future research will determine whether the present proposal belongs to the pretend or possible world. In either case, our point has been to show just how similar it is to reason about these worlds.

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Figures
Figure 1: A model of counterfactual reasoning about pretense
Figure 2: Mean happiness judgments to initial and counterfactual questions, all subjects 
Figure 3: Mean happiness judgments of adults to Initial and Final Questions
Figure 4: Mean happiness judgments of children to Initial and Final Questions.
Figure 5: A model of counterfactual reasoning about possibilities