Running Head: DETECTING INCONSISTENCY Multiple sources of competence underlying the comprehension of inconsistencies: A developmental investigation

How do children know the sentence the glass is empty and not empty is inconsistent? One possibility is that they are sensitive to the formal structure of the sentences and know that a proposition and its negation cannot be jointly true. Alternatively, they could represent the two state of affairs referred to and realize that these are incommensurate – i.e., that a glass cannot simultaneously be empty and contain something. In two studies we investigated how children (N=186; ages 4 to 8) acquire competence to notice inconsistencies. We found that children could determine that two states of affairs were incommensurate before being able to determine that statements of the form p and not-p were inconsistent. Our results demonstrate that competence in understanding inconsistent relations depends on (a) the ability to represent two states of affairs and (b) the ability to process negation in the context of an inconsistency. We discuss these results in relation to sources of competence that may underlie the assessment of such simple inconsistencies. Detecting Inconsistency 3 Multiple sources of competence underlying the comprehension of inconsistencies: A developmental investigation. An inconsistency is any case in which two states cannot simultaneously hold and are therefore mutually exclusive (e.g., if 2 + 2 = 4, then 2 + 2 cannot also equal 5). Inconsistencies arise when an assertion conflicts with current knowledge, when two statements are mutually exclusive, or more generally, when a set of statements cannot all be true at the same time. The ability to recognize an inconsistency is important in distinguishing true from false information and is critical in scientific, medical, and legal reasoning. Our aim was to understand the sources of competence underlying the ability to understand inconsistencies. Consider a statement such as the water is hot and not hot. Adults can clearly understand that such a statement cannot be literally true and in doing so the may rely on formal knowledge, semantic knowledge or both. Specifically, individuals may (a) recognize the formal property of the statement and know that any statement of the form x and not x is inconsistent, or (b) may represent the meaning of “hot water” and “not hot water” and consequently realize the two states of affairs cannot hold at the same time. Adults’ ability to utilize both semantic and formal knowledge to detect inconsistencies makes it difficult to understand whether both semantic and formal knowledge play a role in the recognition of inconsistencies. Indeed, adults can clearly rely on formal knowledge alone and know that the two statements Wood contains phlogiston and Wood does not contain phlogiston are contradictory without having any knowledge of the domain at hand. To this end, in this work we focused on the developmental trajectory by which such abilities are acquired, and to this end examined two types of inconsistencies: those in which knowledge of syntactic structure is Detecting Inconsistency 4 sufficient for identifying the inconsistency (e.g., the glass is full; the glass is not full; syntaxbased inconsistencies [SBIs]), and those where semantic knowledge is necessary (e.g., the glass is full; the glass is empty; non-syntax-based inconsistencies [NSBIs]). Given a statement such as the glass is full, would children find it easier to identify an inconsistency between this statement and the glass is not full or the glass is empty? We presented such pairs of inconsistent statements (with matched consistent statements as controls) to children between 4 and 8 years of age. If the ability to recognize NSBIs as inconsistent were to develop before the ability to recognize SBIs, this would indicate that the initial cognitive processes used to recognize inconsistencies are based on meaning and emerge prior to recognition of any relation between syntactic structure and logical consistency. If the opposite were to hold, this would suggest that the ability to recognize propositions as inconsistent emerges by noticing formal syntactic relations, which then bootstraps a more general ability. Finally, if competence with both types of inconsistency develops in tandem over time, this would suggest a general unitary ability underlying both. Cognitive Mechanisms While our domain of inquiry has not been examined by prior work, several lines of research suggest that recognizing simple inconsistencies occurs relatively early in development. Children acquire the ability to note a single statement as inaccurate or false between 1.5 and 3 years of age, e.g., they will correct a speaker who refers to dog as a cat or makes other mistaken references (Pea, 1982; Hummer, Wimmer, & Antes, 1993). Thus, children can relate the state of affairs described by a statement to the state of affairs in the world. Yet, this ability is insufficient for recognizing that a proposition and its negation are necessarily incompatible, which develops later. There is some evidence (Vosniadou, Pearson, & Rogers, 1988) that 1 st graders can detect Detecting Inconsistency 5 inconsistencies between a statement and a state of affairs (e.g., the ball is green given a red ball) but that only 9-year old children can detect inconsistencies between two statements (e.g., the ball is green and the ball is not green). However, other work suggests that in certain cases children can detect inconsistencies between certain statements, e.g., between statements in task instructions, beginning at the age of 6 (Jorgenson & Falmagne, 1992; Markman, 1977; Ruffman, 1999; Russell & Hayworth, 1987). The ability to reason about inconsistencies between statements (hereafter inconsistencies) also develops later: Osherson and Markman (1975) presented children with a series of syntaxbased inconsistencies (e.g., “There is a poker chip in my hand and there is no poker chip in my hand”) and found that only starting at the age of seven did children realize that no further evidence was necessary for determining the truth or falsity of the statement. Braine and Rumain (1981) reported that approximately 75% of the 5and 6-year-old children detected inconsistencies between the predictions two puppets made about the contents of a closed box. Prior work therefore indicates that detecting inconsistencies between two statements is more difficult than detecting an inconsistency between a statement and the ongoing state of affairs in the world. However, this prior work is agnostic with respect to how children come to identify inconsistencies between statements and what mechanism underlies this ability. We therefore constructed our studies to examine three types of explanation for the initial detection of inconsistencies: one arguing that children detect the syntactic structure of the inconsistencies (syntax-based account), the second arguing that children acquire the ability to realize that two states of affairs are incompatible (model-based account) and the third arguing that children acquire pragmatic knowledge about the use of negation. Detecting Inconsistency 6 On the syntax-based account, children realize that SBIs of the form p & not-p are inconsistent by detecting that the structure of the statement necessarily indicates that the statement is inconsistent. In pioneering work, Osherson and Markman (1975) noted that SBIs of the form p & not-p are “true or false by virtue of their linguistic form, rather than deriving their truth-value from any extra-linguistic states of affairs” (p. 214; Braine & Rumain, 1981; Braine, 1998 offers similar arguments). On this approach, SBIs are recognized on the basis of the formal structure of the statement: If it matches a certain schematic form such as p & ~p (sometimes referred to as a rule in formal approaches), then it is immediately realized as inconsistent or false. Note that on this approach, the entire form is recognized as a schema and the negation of one constituent is not processed separately and does not incur additional processing costs. On this account then, SBIs are detected when linguistic structure can trigger a matching rule. This account describes the capabilities mediating the comprehension of SBIs but is agnostic about how children develop the ability to understand NSBIs such as the glass is full and the glass is empty, where syntactic form is not diagnostic of an inconsistency. A relatively strong position is that NSBIs are mentally “recoded” in a form similar to that of SBIs (Braine, 1998): i.e., the statement above would be recoded into form the glass is full and the glass is not full thus triggering the recognition mechanism subserving the comprehension of SBIs. For example, Braine (1998) suggests that there is nothing in the box is instantiated as a universal negation because the quantifier nothing “is a signal that the argument set is included in the negation” (pg. 300). On this view, SBIs should be easier to detect than NSBIs since the latter entail transformation or recoding of an affirmative predicate to negated form (e.g., empty not full). The model-based account stems from the premise that while SBIs could indeed be potentially recognized by virtue of their syntactic form, cognitively, it is possible to recognize Detecting Inconsistency 7 them by other means. For example, given the statements “the box contains a sticker” and “the box does not contain a sticker,” one may construct mental representations corresponding to (a) a box with a sticker and (b) a box that is empty (or absent of a sticker), and realize that these two representations cannot hold at the same time. Thus, an inconsistency can be recognized by representing the two states of affairs to which it refers and realizing they cannot jointly hold. On this explanation, the syntactic form of the problem does not play any special role; instead, the representation of semantic content via models is of essence (Johnson-Laird, 1983; Zwaan, 1999). On this approach, a set of propositions is recognized as inconsistent when there is no model in which they all hold (Johnson-Laird, Legrenzi, & Girotto, 2004) and individuals are sensitive to such dis-correspondences (Johnson-Laird & Hasson, 2003). On such “model-based” approaches, inconsistencies will be detected when a person can create veridical models of two predications (e.g., full and not-full), simultaneously hold these two models in mind, and understand they cannot exist at the same time (see Markovits & Barrouillet, 2002 for an extensive discussion). This account would predict a dissociation between the ability to represent NSBI and SBI contradictions because SBIs, which have the form p and not-p are particularly difficult since one of their clauses contains a negation. Negations are considered difficult because their representation necessitates “tagging” or ”annotation” of an affirmative model with an additional bit of information (Bell & Johnson-Laird, 1998; Johnson-Laird, 2001) or a recoding of the negated predicate as an affirmative predicate (e.g., not-above below; Fillenbaum, 1966; Hasson, Simmons, & Todorov, 2005; Mayo, Schul, & Burnstein, 2004; Morris, 2003). Such recoding is expected to increase processing complexity and is more difficult for young children given their limited processing capacities (Halford, Cowan, & Andrews, 2007). Detecting Inconsistency 8 Finally, an account based on the pragmatic aspects of the use of negation (pragmaticbased account henceforth) would hold that children may consider SBIs of the form p and not p as inconsistent by relying not on syntax or semantics, but on their knowledge of situational pragmatics. Specifically, children may treat an ostensible disagreement between two or more speakers as indicative of inconsistency, even if the disagreements are not mutually exclusive. Children may treat situations where one statement as affirmed and the other denied as diagnostic of an inconsistency, because negation may be most felicitously comprehended within a “context of plausible denial” (Wason, 1965). Knowledge of such a discourse principle suggests that an inconsistency exists in any context in which a negated proposition was presupposed or previously introduced. Thus, the presence of a negation may be a particularly salient cue for disagreement. This pragmatic-disagreement explanation makes the unique prediction that children could judge any case where an affirmative and negative statement are presented together as being inconsistent, even when the two statements are consistent. Examining such an account is also important for understanding prior work, as previous investigations (e.g., Braine & Rumain, 1981) utilized only SBI-based problems (potential hits) but did not include in their design consistent statements with similar syntactic form (potential false alarms). Because of this limitation, what appeared to be correct responses in prior work may have been driven not by logical competence but by response biases (e.g., a Yes bias) or pragmatic principles. Thus, to date a pragmatics-based account to what appears to be demonstrated competence with SBIs has not been ruled out. To summarize, the syntax-based, model-based, and pragmatic approaches make divergent predictions on the sources of difficulty underlying contradictions. On the pragmatic approach, Detecting Inconsistency 9 children should either (a) recognize any disagreement between statements as inconsistent or (b) use the presence of a negative as an indication of inconsistency. On the syntax-based approach, processing contradictions of the canonical form p and not-p should be easier than or as easy as processing contradictions that do not contain negations because the syntactic form p and not-p matches an inferential rule sensitive to syntactic structure (Braine, 1998). In contrast, on the model-based approach, both NSBIs and SBIs demand the construction of models, and the presence of negation in SBIs will serve to increase their difficulty. Therefore, contradictions containing negations should be more difficult. While it is likely that both types of processes (relatively simple formal logic and model building) are easy for adults, who have more significant working memory resources (Markovits & Barrouillet, 2002), we hoped that by examining their developmental trajectory we could obtain decisive data regarding the underlying sources of competence and their developmental trajectory. Experiment 1 Experiment 1 consisted of three within-subjects conditions. The participants participated in all 3 conditions across different sessions. Here we provide the common properties across the conditions, and later we detail those aspects on which the conditions differed.