The class inclusion question: a case study in applying pragmatics to the experimental study of cognition

Referential ambiguity and the inclusive versus exclusive comparisons

A classic riddle among school children is “What barks but is not a dog?” Solving it at once may be hard even for adults, for reasons that are cognitively interesting. Readers who have failed to find the answer, “a bitch”, probably feel both that they should have been able to answer and that they have been cheated–indeed both intuitions are correct. The pair dog (generic)—bitch completed with dog (male) is of course an instance of lexical markedness, dog providing an instance of autohyponymy. That lexemes such as dog can refer to the class of all the dogs (dog ₀ ) or to the included class of male dogs (dog ₁ ) is exploited in the riddle and sometimes referred to as privative ambiguity. What barks (a class that uniquely characterises dog₀) and is not a dog₀ belongs to an empty class (barking while not being a dog₀ is contradictory), hence the failure to find a solution. What barks (dog₀) and is not a dog₁ defines the class-solution, bitch. If initially you have the interpretation dog₁, you get it right immediately and there is no riddle proper. Assuming that initially you have the interpretation dog₀, you get it right or not depending on whether or not you shift your interpretation from dog₀ to dog₁. Of course, one could imagine a reverse riddle, in which the initial interpretation is dog₁ but the required construal to get the solution is dog₀: “Are there more bitches or more dogs” would be one such question where in the vicinity of bitch, dog₁ is a more likely interpretation than dog₀. We will say that a comparison of bitch with dog₁ is exclusive (or contrastive) and a comparison of bitch with dog₀ is inclusive.

Now consider the class inclusion question, “Are there more asters or more flowers”. The subclass to superclass structure is identical but there is a lexical difference: Whereas the complementary class dog₁ is not lexicalised, in the class inclusion question the complementary class is lexicalised (the tulips). However, using a hypernym (in the plural) to refer indifferently to a superclass or to one of its subclasses is always correct literally and generally appropriate in ordinary speech (the exceptions stem from a possible distance between the subclass and the basic level: Microbes generally are not felicitously called animals). The hypernym is potentially ambiguous and it is the context of the utterance that guides the interpretation. Coming back to the standard class inclusion question, “Are there more asters or more flowers” it is clear that depending on the context, it may be relevant to give it either interpretation: (i) “Are there more asters or more tulips (flower₁)” or (ii) “Are there more asters or more flowers₀.” In the first case the children make an exclusive comparison and answer that there are more asters, the response that is deemed to be incorrect; in the second case they make an inclusive comparison and answer that there are more flowers, for which they are credited with a correct response.

In sum, the foregoing analysis reveals the nature of the class inclusion question, namely a riddle in an experimental setting. There is something queer in the question which would not be used naturally. A speaker would normally exploit one of the various linguistic devices available to disambiguate the question. To invite an exclusive construal one would use the name of the class B’, or if it is unknown or not lexicalised use a qualifier or a deictic marker. To invite an inclusive construal one would use the quantifier all (which would oblige one to use a different sentence: “What is more, the asters or all the flowers?”).

Interestingly, the triangular structure is often exploited for rhetorical reasons, in particular in advertisements. A commercial slogan (popular in the 1980s) such as “Don’t buy a car, buy a Saab” has a real impact. Here the sentence initially understood as “Don’t buy a car₀… ” yields a contradiction as a Saab is a car₀. Reinterpreted as “Don’t buy a car₁…” (in which car₁ is the class of cars that are not Saab), it gets the exclusive interpretation. The cognitive effort is worthwhile in terms of effect as the hearer ends up with “buy a Saab” and “don’t buy a car that is not a Saab”.

We now turn to the determination of the relevance of the question, which depends on the interaction between the child and the experimenter.

Determining the relevance of the question

Hayes (1972) remarked that the way the class inclusion question is interpreted constitutes a developmental variable. This is a fundamental insight. Once this view is adopted, the disambiguation of the question must be envisaged in relation to the child’s development. From the notion that the children attempt to render the question optimally relevant it follows that the way they do so will vary with their cognitive development. In other words, the interpretation chosen by the children is constrained by their level of development. Therefore, the interpretation can be predicted on the basis of what is likely to be the children’s estimation of the relevance of the question.

To specify what it means for the question to be relevant, we need to analyse the relationship between the child and the experimenter. A question is relevant when it can give rise to an answer that is relevant for the questioner, that is, the answer should satisfy the expectation of relevance attributed by the questionee to the questioner¹. However, experimental settings have (in common with instructional settings) a specific feature characteristic of the testing situations: It was noted long ago (Searle 1969 p. 66) that the question is a higher order question. In testing situations, when a question of the type “Is it the case that S?” is asked, the answer “yes” or “no” is irrelevant to the questioner; what is relevant is to know whether the questionee knows whether it the case that S, which the questionee is aware of. This applies to school age children who are exposed to this kind of questioning through repeated interaction with teachers. In the frame of an experiment, which generally takes place at school, participants cannot fail to identify that the question belongs to this conventional genre.

Now the identification of the kind of knowledge which the child expects the experimenter to wish him or her to exhibit is necessarily bounded by two kinds of limit, which are the child’s own knowledge, and as crucially the child’s meta-knowledge. Obviously the children cannot attribute to the experimenter an interest in knowledge that they do not possess themselves; and not any more to knowledge that they possess but are not aware of. This implies that the children attribute an interest in what they feel is a difficult acquisition (often some skill or piece of knowledge being currently learned), that represents a respectable achievement worthy of consideration. Consider now the younger children who are requested to make a quantitative comparison (more B or more A?). The capability they wish to demonstrate, and in which they will attribute an interest to the experimenter, is that of counting and making additions. This is a fundamental school acquisition, highly valorised. They can achieve this demonstration by making either comparison, but are these equally likely to be chosen?

Consider first the younger children, typically five to seven years old, who are in a situation where they have the choice between an exclusive and an inclusive comparison. There are two main differences between these two possibilities. One, the exclusive comparison is numerically easier as it requires to compare the number of asters with the number of tulips (B and B’) whereas the inclusive comparison requires to compare the number of asters with the number of asters + the number of tulips (B and B + B’). Second, the inclusive comparison does not match the child’s experience (nor the adult’s for that matter) as it hardly has any ecological validity. Indeed comparisons in daily life concern exclusive or, less typically, overlapping classes, and hardly ever included classes. These two differences concur to give the exclusive comparison a definite advantage: It is easier. Because it enables the child to achieve the same result for the least effort, the exclusive comparison has the greatest chance of being chosen.

Consider next the older children, typically 8 years old and above. The elementary arithmetic skills are already an objective of the past (even in case they are not actually attained); their mastery cannot constitute an achievement worth demonstrating to the experimenter. But what is currently emerging is metacognition in the linguistic domain (Gombert 1992) and the logical domain (Moshman 1990; in particular, logical necessity: Cormier and Dagenais 1983; Miller et al. 2000). Significantly, it is from about 8 years onwards that children start to understand riddles based on semantic ambiguity (Bernstein 1986; Kilcher 1991; Shultz 1974; Shultz and Horibe 1974; Sutton-Smith 1976) and about the same age that they start to offer a majority of metalinguistic explanations in response to requests to explain the use of linguistic items (Karmiloff-Smith 1986). The contemporaneous character of the emergence of metacognition (logical and linguistic, including awareness of semantic ambiguity) on one hand, and success on the class inclusion question on the other hand is no coincidence: The former is a condition for the latter.

Essentially, when the logical concept of inclusion has been acquired, this provides the kind of knowledge that the child assumes to be of interest to the experimenter and worth showing her. There is an additional piece of knowledge that the child may wish to exhibit, namely that the hypernym is ambiguous and that it is better to disambiguate by referring to the superclass rather than to the minor subclass B’ because if the experimenter wished to refer to B’ she would have used its name.² In brief, of the two comparisons, the inclusive one now is by far the more relevant. One may add another possible reason to use the inclusive comparison, which concerns children at an intermediate level of development. They might make this choice for exactly the opposite reasons why the younger ones who wished to demonstrate their arithmetic skills opted for the exclusive interpretation. This time, opting for the inclusive interpretation amounts to making the most difficult calculation, but the increase in effort is offset by an important increase in effect (precisely showing their capability of executing the most difficult calculation).

To summarise: depending on their metacognitive development the children can disambiguate the class inclusion question in two ways. The younger make the question relevant by interpreting it as a request for an exclusive comparison of the subclasses; the older, by interpreting it as request for an inclusive comparison of a subclass and the superclass. The choice is constrained both by the cognitive and metacognitive capabilities in the logical or linguistic domains. The standard class inclusion question cannot be a valid test of the simple inclusion judgement because the child is not given a fair opportunity to compare a subclass with the superclass, so that failure does not demonstrate that the child does not possess the knowledge that the part is included in the whole. (On the contrary, the standard class inclusion question, provided it is supplemented with justification, may be a valid test of the knowledge of the necessity that the part is included in the whole, as failure is incompatible with the attainment of the required metacognitive knowledge).

Classes versus collections

The most powerful of the factors that affect performance is the replacement of classes by collections. Markman (1973) used materials such as six dogs (four small, two big) and compared two questions: The class question, “Who would have more pets, someone who owned the baby dogs or someone who owned the dogs?” and the collection question in which the collection name replaced the final occurrence of the hypernym: “Who […..] who owned the family”. The author reports that more than 50 % of 7-year-olds passed the collection question whereas none of them passed the class question. The study was motivated by the observation that it is permissible to designate the subclass by the hypernym, so that if the children are set to make subclass comparisons (for cognitive, linguistic or perceptive reasons), they may be encouraged to misinterpret the question, which cannot occur with collections as it is not possible to designate the subclass by the word “family”. Surprisingly, even though the ambiguity is well noted, its explanatory role is amalgamated with another factor: This is the notion that in a collection such as a family the subparts (parents and children) stand in a specific relation to one another, which could help apprehending the part and the whole simultaneously. This second explanation will be considered in detail and refuted later (“Experimental investigation of the role of collections” section).

Lexical definition

Applying a modified version of a procedure initially used by Smedslund (1964) in a battery of Piagetian tests, Carpendale et al. (1996) asked an exclusive comparison (“more horses or more cows”) as a preliminary question that preceded the class inclusion question proper (“more horses or more animals”). This resulted in a substantial increase in performance which can be explained by disambiguation. Because the initial formulation conveyed a request for an exclusive comparison, the subsequent formulation by contrast was unlikely to be interpreted again as an exclusive request—there must be some relevance in the change in wording—so that the inclusive interpretation was chosen by the children who could remember the first request. In brief, this procedure indirectly attracts the attention to the difference between naming the minority hyponym and the hypernym. It is remarkable that Carpendale et al. (1996) discuss at some length the pragmatic explanation, but in the end reject it on the grounds that they do not see how to account for the developmental trend in the performance on the class inclusion question.

Winer and Falkner (1984) showed a dog to two groups of adults. The first group was asked, “Is it a dog or an animal?” and the second, “Is it a dog or an animal, or both?” following which both groups were asked a class inclusion question (animals, with dogs as a major subclass). This was repeated with four concepts. In the first group more that one half of the participants committed at least one error but in the second group less that 10 % did. This is easily explained under the hypothesis that for the first group the preliminary question at best maintains the ambiguity and at worst invites to an exclusive interpretation (which will be transferred to the class inclusion question); whereas the second group are invited to answer “both”, suggesting an inclusive interpretation which they will transfer to the class inclusion question.

Other investigators have used procedures that help define the vocabulary used in the class inclusion question. This includes naming the classes (Inhelder et al. 1974), or explaining that the members of B’ are also members of A (Bideaud 1981). The disambiguation can be obtained even more explicitly by agreeing with the children to give a new name to the superclass (e.g., “round balls” for a set of blue marbles (B’) and red marbles (B), while asking them to compare the round balls with the red marbles (Sheppard 1973).

The typicality of the minor subclass

Inhelder and Piaget (1959) noticed that performance varies with the concepts used (animals, flowers, fruit…), a phenomenon called “horizontal décalages” in their theory and which received ad hoc explanations in such terms as familiarity or abstraction.

Carson and Abrahamson (1976) manipulated the typicality of the subclasses. For example, they compared questions in which the minor subclass was atypical (e.g., five dogs and three bees: “more dogs or more animals?”) with questions in which the minor subclass was typical (e.g., five flies and three horses: “more flies or more animals?”). The performance was consistently higher in the first case than it was in the second. Similar results were reported by Lane and Hodkin (1985). The ambiguity hypothesis offers a straightforward explanation. In the first case, referring to bees by using “animals” is countermanded by the lack of typicality of bees, whereas in the second case referring to horses by “animals” is invited by the typicality of horses.

Quantifying

To make the question sound more natural, Shipley (1979) presented 6- to 9-year-old children with a modified class inclusion question such as, “Which is more, only the lions or all the animals?” Children tested in a within-participant design improved their performance by one third. This result was confirmed by Hodkin (1981) who asked, “Are there more B or more of all the A?” in a between-participant design. She too attributed the improvement to the conformity of the sentence with natural language. Obviously, this explanation is circular, as the problem is to know why in everyday usage one would modify the superclass in this way. In fact, it is not infrequent that for the standard class inclusion question the older children spontaneously ask “do you mean all the A?” For a speaker who wishes to refer to the superclass and is aware that the hypernym can refer to the subclasses as well, the most economical way to communicate her intended meaning is to mark the union of the subclasses by “all”: The quantifier enables the speaker to refer unambiguously to the union of the subclasses and therefore to contrast the superclass with any one subclass.

Qualifying

Wilkinson (1976) used materials modified as follows. All the members of A (houses) had a common perceptual feature (a window) and all members of B had another common feature (a door). This yielded three houses (A), two with a window and a door (B) and one with a window but no door (B’). The question was, “Are there more houses that have a door or more houses that have a window?” The performance of kindergarten children increased by 50 % when compared to a standard question with usual materials (children: two boys, one girl). Similar results were obtained by Dean et al. (1981) among 5- to 7-year-olds.

Similarly, McGarrigle et al. (1978) gave a qualifier to all the members of A, which introduced a second salient feature that should compete with the first (the one that defines the contrast between B and B’) and thus discourage exclusive comparisons. Six years old children performed better with such a material made of four lying cows, three black, one white (“Are there more black cows or more sleeping cows) than they did with the standard question (more black cows or more cows?”). This effect is explanable if one considers that there is a clue for disambiguating in favour of the superclass. Indeed, it should be noticed that the sleeping property does not appear in the definition of B (black cows). By contrast, the class to which the latter is compared in the question (sleeping cows) is described by the sleeping property so that its denotation as all the cows (because they all are sleeping) is encouraged. A control condition is missing, namely one in which the question would be “more sleeping black cows or more sleeping cows”, which presumably would produce a reduced effect, or even no effect. Generally, the existence of a feature perceptually salient common to all the A should enhance performance by helping to disambiguate in favour of the A when this feature qualifies only the hypernym in the question. The effect of saliency was demonstrated by Tatarski (1974) who presented 5- to 8-year-old children with three kinds of wooden blocks. The first set consisted of six cylinders wholly coloured (four blue, two red: “more wooden blocks or more blue blocks?”); the second set were painted over one half of the surface and the question was the same; the last set were wholly bi-coloured (four blue and yellow, two red and yellow: “more yellow blocks or more blue blocks?”). The rate of success increased significantly from the first set (below 50 %) to the second (below 60 %) to the third set (above 80 %), the increase from the second to the third reflecting nicely the increase in saliency of the common feature.

The level of specificity

McGarrigle et al. (1978) report interesting results with non included classes. For instance, given cows (two black, two white) and horses (three black, one white) most 5-year-old children failed the question, “Are there more black horses or more cows?” Their spontaneous justifications suggest that they consider black horses and black cows. These observations were replicated and extended by Grieve and Garton (1981). They presented 4-year-old children with either equally or unequally specified questions. Instances of the former case are “Are there more black horses or more black cows?” for between-class comparison and “more black horses or more white horses?” for within-class comparison. These yielded near perfect performance. Instances of the latter case are “more black horses or more cows?” for between-class comparison and “more black horses or more horses?” (that is, the standard class inclusion question) for within-class comparison, which both yielded near complete failure. This was linked with exclusive comparisons, as could be inferred from children’s comments. For the between-class comparisons, the children introduced the qualifier when there was none. In brief, children treat the two sub-classes at the same level of specificity.

The results for the between-class comparisons were replicated with even greater accuracy by Gold (1984) who requested 5- to 9-year-old children to justify their responses to similar questions. Among those who failed questions such as “more black horses or more cows”, one third qualified cow by black, one third removed black from horse, 10 % added white to cow. Again, all these transformations amount to choosing comparisons at the same level of specificity. As McGarrigle et al. (1978) remarked, this strongly suggests that the source of the difficulty of the class inclusion question does not lie with inclusion, as the same kind of comparison is made for the between-superclass and the within-superclass cases. Children have expectations for comparisons that do not match the experimenter’s.

Based on these results, Shipley and Kuhn (1983) posited the equality in the level of specificity as an explanatory principle for class comparisons. They hypothesised that there exists a constraint on the selection of the criteria for membership in a class—which they call “target”—which accounts for the formation and consequent comparison of the wrong classes. The constraint, called “equally detailed alternatives” is that the set of targets corresponding to the classes being compared are specified in equal detail. This means, for instance, that if a value for colour appears in one target, some value for colour must appear in the other target(s). If a target is red square, the other target must specify a colour and a shape. If the experimenter’s description does not respect the constraint, the children form a different target by adding or eliminating some criteria, so that the classes that they compare are not those meant by the experimenter. Taking an example with natural kinds, in the request to compare poodles and dogs, the breed is specified in one target; by the constraint it must be specified for the other target, so that the child will compare poodles with a class homogeneous in breed.

The equally detailed alternatives hypothesis has the interest that it applies to comparisons of included and non included classes as well and it seems to be descriptively accurate. However, it is somewhat obscure as an explanatory principle, as it lacks a justification. It also has a limited explanatory power, as it cannot account for a number of effects already mentioned, such as the nouns of collections, counting, quantification, or typicality—indeed the authors acknowledge that the constraint is not the only source of difficulty. Moreover, it seems to lack parcimony as from the present viewpoint this hypothesis is derivable from considerations of relevance. As the authors noted themselves, “specifying ‘red’ for one class has made color relevant to membership in all classes. Essentially, this is the equally detailed alternatives hypothesis” (p. 200). In this quote, they used the expression “relevance” in a pre-theoretical sense. Theoretically, specifying the value of a feature establishes a presumption of relevance of this feature to refer to the classes mentioned in the dialogue or at least in the utterance. If the speaker takes the trouble to specify the value of an attribute for one class, this creates the expectation of being informed about the value of this attribute for the other class; and if this value is not pertinent to refer to the other class, this is normally marked by “all”. For instance, given short and tall green trees and short and tall brown trees, “the short green trees or the brown trees” is less felicitous than “the short green trees or all the brown trees”. In fact, in agreement with this analysis, the five-year-old children tested by the authors did commit more errors in comparing the short green trees and the brown trees given these four classes than they did when they were given short and tall green trees and wide and narrow brown trees. We conclude that the equally detailed alternatives hypothesis can be considered as an accurate description of phenomena that are explanable within the pragmatic framework.

Mentioning both hyponyms in the question

Winer (1978) asked pairs of questions of 8- to 10-year-old children. These combined a request for an exclusive comparison (“more dogs or more cats?”) and a standard question (“more dogs or more animals?”), which resulted in a higher performance than that of a control group. A likely explanation is that the possibility for the hypernym to refer to the minor subclass of cats is blocked by the use of the minority hyponym (cats) to refer to it. Ahr and Youniss (1970) used all three nouns in the question (“more animals, or more dogs, or more cats”) and observed a significant improvement, explainable by the same mechanism. Unhappily, their participants had already received a class inclusion question, and the novel questions were formulated with “less” or with “more”. But in the latter case the exclusive and inclusive comparisons are indistinguishable because both lead to a correct answer, so that the source of the overall improvement is not clearly identifiable.

There is, however, evidence that the mention of all three nouns enhances performance. This comes indirectly from the investigation of the so-called “verbal facilitation” described by Wohlwill (1968). He observed higher performance when the class inclusion question was presented only verbally without pictures or objects, which was replicated by Winer and Kronberg (1974) at all ages from 6 to 11, and by Padilla and Romero (1976) with 9- and 11-year-olds (but Cameron and Goard (1982) failed to replicate this effect). As noted by Winer (1974) the strict verbal presentation is accompanied with additional verbal cues, namely the mention of the minority hyponym. In fact the question posed was always of the type “if I had four apples and three pears, would I have more apples or more things to eat?” That the facilitation stems from this confounding factor rather than from the absence of material is supported by the absence of difference in performance between a group that received the modified question without material and another one with material. Another confirmation comes from a study by Brainerd and Kaszor (1974) who failed to replicate the effect when using a formulation in which the minority hyponym did not appear (“Are there more red circles than there are circles?”) and the picture was turned face down.

In brief, it seems that the mention of the three class nouns does improve performance and the reason is clear. The hypernym is less likely to refer to B’ (and consequently more likely to refer to A) when the minority hyponym which refers to B’ is used in the sentence: In other words, this helps disambiguate the sentence.

The role of the minority hyponym was subsequently discussed by Agnoli (1991) within the conceptual framework of representativeness. She presented 9-, 11-, and 13-year-old children with class inclusion questions without material. There were two question types that differed by the representativeness of the major subclass, such as: “In summer on the beach, are there more ladies or more tanned ladies?” versus “…or more pale ladies?” The rate of errors was 62 % and 28 %, respectively, which coincides with choosing the representative class (tanned ladies) in the first case and avoiding the non representative class (pale ladies) in the second case. However, these results, which reproduce and generalise those obtained by Carson and Abrahamson (1976) and Lane and Hodkin (1985), are explanable linguistically as the author noted. If ladies tends to refer to the complementary subclass B’, an incorrect response is more probable when the hyponym mentioned is tanned ladies (the complementary subclass pale ladies is less numerous) than when it is pale ladies (the complementary subclass tanned ladies is more numerous). The author tried to test this hypothesis by adding a question with all three nouns. The results indicate a persistent preference for the representative answer but the within-participant design of the experiment makes the result hard to interpret. The effectiveness of this kind of modified question will be demonstrated in “The factors that affect performance” section.

Learning inclusion

A variety of learning procedures have been shown to improve performance. Simple repetition with feed-back is one of these (Ahr and Youniss 1970; Brainerd 1974; Siegel et al. 1978; Youniss 1971). This is not surprising as following negative feed-back the child will tend to change interpretation by changing the reference of the hyponym.

Judd and Mervis (1979) asked 5-year-olds to count the objects in the superclass and the subclasses (three toys, two balls, one bear), after which the class inclusion question was posed and the counting repeated if the answer was incorrect, and again until success. After this training a new class inclusion question was asked as a posttest where the rate of success exceeded 80 % against just a few percent in a pretest. This increase was attributed by the authors to the contradiction between the result of the correct counting (three toys, two balls) and the incorrect answer (more balls than toys) which finally the children must become aware of. However, no precise description of the process that leads to the answer is proposed. A likely explanation is that the child is offered an occasion to disambiguate the reference of “toy”: The hypernym initially refers to the bear in the question, but to the superclass when counting so that in the end it is given the intended reference. In other words, the counting and training procedure enable the child to learn the experimenter’s use of the names.

Kohnstamm (1963) was even more directive in explaining that “there are more A because B are also A. B and B’ are all A and so there are always more A”, or “they are all A and only two are B”, etc. following which most children aged 5–7 were successful.

In sum, a learning method for the inclusion task is effective if it enables the child to realise that the intended comparison is that of the major subclass to the superclass. All these methods have in common that in the end the child has learned the experimenter’s use of the words, that is, the hypernym refers to the superclass and not to the minor subclass.

Young children’s referential attribution of the hypernym

The first claim, which is implicit, is that the younger children do understand the referential properties of class names, that is, know that the hypernym can also be used to refer to a subclass. This was demonstrated by Smith and Rizzo (1982). In a first experiment, 4- and 5-year-olds were presented with materials such as three daisies and three roses and requested to tell whether a puppet named objects correctly or not (e.g., flowers for the roses, flowers for all the flowers, roses for the roses). About two thirds of the children accepted the reference of the hypernym to both the superclass and the subclass indicating knowledge of the referential properties of the hypernym.

The results of two other experiments support the notion that the hypernym is ambiguous. In a second experiment 5-year-olds were requested to get a set of objects, put it back and then get another set; this was done in the case of two subclasses (e.g., daisies then roses) and in the case of a superclass and a subclass (e.g., flowers then roses) by instructing the child to “get the—and then get the—”. Performance was virtually perfect in the first case but did not exceed 14 % in the second case, suggesting difficulty in attributing reference to the complementary subclass—however children may also fail because, as the authors acknowledge, the question requiring to take back some objects already taken is particularly tricky. In a third experiment one group of 5-year-olds was given the same task as in the second experiment while another group received this task with feedback. In addition, both groups received a class inclusion question as a pretest and as a posttest. The no-feedback group committed three times as many errors as the other, suggesting that the source of the errors is a lack of clarity in the reference of the hypernym, which was remedied by the feedback as the intended reference got progressively fixed across trials. Also the no-feedback group did not improve from the pretest to the posttest whereas the other group jumped from 20 to 75 % correct. This suggests that the training was effective in disambiguatng the hypernym. This work is important in showing that 5-year-old children know that a hypernym can refer to the subclass and to the superclass, and also in indicating—although indirectly—that the hypernym is ambiguous and that this can be overcome by a training procedure which helps disambiguate the hypernym.

The subclass-to-subclass comparison

The other claim of the present approach, which is explicit, is that the younger children who fail the question make subclass to subclass comparisons. Starting from Piaget himself, there is unanimity in favour of this claim, with the only exception of Brainerd and Kaszor (1974). They based their denial on the results of one of their experiments in which they asked children to recall the question. They hypothesised that if children referred to the subclass by the hypernym, one should observe substitutions during recall (the child reformulating the question as “more B or more B’ ”) and such errors should be more frequent after an incorrect response. Because they found few cases of substitution and no differences in frequency in a condition with immediate recall, they rejected the hypothesis. This clearly is too hasty, for the hypothesis is based on the assumption that children should reformulate the question in the same terms that coincide with their interpretation. This is very doubtful as it is the experimenter’s role to define the task, give the instructions and fix the use of the vocabulary. If a child hears the name A and interprets it as referring to B’, he is likely to continue to use the experimenter’s word A to refer to B’, especially for an immediate recall.

This is borne out by results obtained by McCabe et al. (1982) who asked five class inclusion questions with various concepts and only then asked a recall of the questions: Among the 5-year-olds who answered incorrectly, the majority recalled the question in terms of the hyponyms. Further evidence of exclusive comparisons can be found in a study by Ahr and Youniss (1970) who varied the ratios of the number of items in the subclasses (dogs and cats). With eight dogs and no cat most 6- to 8-year-olds answered “more dogs” suggesting an unsuccessful search for cats. This interpretation is born out by the answer to the question formulated by “fewer”, which was “fewer animals” most of the time. Even more significantly, with four dogs and four cats the tendency was to answer “same” (half of the children to the “more” question and the great majority to the “fewer” question). Trabasso et al. (1978) offer further evidence in an investigation in which the standard question (“more A or more B”) was compared with a question of the type “more A or more B’ ”). Whereas the rate of success ranged from one third to two thirds, depending on age, it was always above 90 % with the second question. This is easily explained if the children make exclusive comparisons. B is always chosen because there are more B than B’; so, with the standard question B is denoted by the hyponym B and the children answer “B” whereas with the other question B is denoted by the hypernym A so that they answer “A”, which surreptitiously increases the rate of apparently correct responses. Naturally, the use of B in the formulation of the standard question is motivated to avoid this possibility. Interestingly, McCabe (1987) has shown that even adults may commit errors under time constraint. When requested to identify the question asked, subclass comparisons were falsely recognised 30 % of the time.

In brief, there is overwhelming evidence in support of the claim that participants actually perform an exclusive comparison between subclasses following the class inclusion question.

Demonstration of the referential ambiguity in the standard question: experiment 1

The claim that the hypernym can be used to refer to the subclass as well as to the superclass will now be substantiated by demonstrating that the spontaneous reference attributed by children to a hypernym depends on whether or not it follows the mention of one of its hyponyms. No class inclusion question was asked in this experiment; there were only requests for designation.

Elaborating a modified question: experiments 2 and 3

A modification to the standard class inclusion question suggests itself, namely mentioning the superclass and the two subclasses in the question. As reported ealier, this was already done by Ahr and Youniss (1970) and by Agnoli (1991), but with inconclusive results. Experiment 2 was designed to test the effect of this manipulation.

Experiment 3

The developmental trend: experiment 4

The results of experiment 2 suggest that children as young as 5 or 6 years old could pass the question if it was properly interpreted. Consequently in experiment 4 the age range started as early as 4;6 (finishing at 8;9).

More on the psycholinguistic analysis of the question: experiment 5

In the formulation of the modified question the hypernym A was placed at the end on purpose. Indeed, the order of the names is not indifferent from the viewpoint of the linguistic theory. When both hyponyms B and B’ have already appeared in the sentence, the hypernym A is unlikely to be given the same reference as B or B’ because the extension of the subclasses has already been denoted; this optimises the exploitation of the use of B’ to disambiguate A. But if A appears before both B and B’, there are a number of possibilities such as deferring reference until after B and B’ have been mentioned, or give A a revocable reference that may or may not be revoked at the end: The final assignment of A to B’ is not so straightforward and less warranted. Experiment 5 was designed to test the hypothesis that performance is affected by the position of A in the question.

Conclusion of experiments 1–4

The experiments reported offer direct evidence that in the standard class inclusion question the hypernym (A) has referential ambiguity (of the privative variety). Experiment 1 has shown that it can refer with an inclusive denotation to the superclass, but also with an exclusive denotation to the subclass that is not mentioned in the question, that is, the minor subclass B’. The main claim of this paper is that the interpretation of the hypernym is pragmatically determined as a function of the child’s perception of the aim of the standard task, which evolves with age. Depending on their level of development, children may or may not adopt spontaneously the interpretation that enables the experimenter to test their acquisition of the simple inclusion judgement. One interpretation (the exclusive one) does not offer this possibility. Consequently, experimenters who wish to know whether the younger children are capable of the simple inclusion judgement should attempt to disambiguate the hypernym and help interpret the question in such a way that the hypernym refers to the superclass, which is its intended meaning in the standard question; only then can it be considered that the children are put to a valid test. The results of experiments 2, 3, and 4 have shown that when one, or even better, two disambiguation procedures are applied, the children reach the critical behavioural criterion of inclusion three to four years earlier than is usually claimed in the literature, that is, as early as five years of age. This is by no means a lower bound, rather it may be the limit that the present means of investigation is able to reach.⁴

Experimental investigation of the role of collections

We have mentioned earlier (“Classes versus collections” section) that facilitation was observed when the name of a superclass is replaced by the name of a collection and we have offered a linguistic account of it. Here we take a closer look at this phenomenon and we test the linguistic explanation against an explanation based on the internal organisation of collections and their psychological coherence.

The fuzzy trace theory

The fuzzy trace theory of class-inclusion (Brainerd and Reyna 1990; Reyna 1991) may be the most sophisticated approach to this task. It has the advantage of being part of a wider theoretical background that applies to various reasoning and judgment tasks.⁶ The main claim of the theory is that mature inclusion reasoning is not quantitative but qualitative; it is pattern based and therefore nonnumerical. The patterns are the result of the extraction and storage of a type of gist, namely the familiar relationship of inclusion hierarchy; then they are processed by the application of a qualitative ordering rule, namely the cardinality principle which states that the more inclusive of two sets is necessarily the more numerous. For a mature individual, there is an algorithmic procedure to answer the class inclusion question: Encode and store the gist (“there is an inclusion relation”), retrieve the cardinality principle in memory, and apply it, which is little demanding. When solving the task, the child encodes both the inclusion gist (e.g., cows are animals, horses are animals) but also the “relational” gist (that is, the exclusion relation: There are more cows than horses). Encoding or storage are not a source of difficulty. The source of erroneous responding is that the relational gist is more salient, hence a tendency to judge relative numerosity instead of applying the cardinality principle. In the inclusion task there is a difficulty specific to the comparison of the numbers of A and B because this requires keeping the whole in memory while one of its parts has been separated. (So the theory applies to numerosity at a processing level the analysis that Piaget applied to sets at a logical level). The inclusion relation, even though it is understood, is implicit whereas the “relational” relation is visible and explicit. The two relations compete and failure occurs when the latter dominates the former. This immature reasoning may take place even if the child possesses the cardinality principle. In brief, failure reflects a defective performance, not a lack of competence. For the younger children there may be a retrieval failure, and for the older ones a processing failure. In this latter case, there is difficulty fitting the cardinality principle to memory for the inclusion gist. This is why it is expected that cuing members of the superclass with a distinctive tag makes the hierarchical levels more separable. The processing of the principle will be more accurate and a higher performance is expected.

Brainerd and Reyna (1991) tested the latter prediction in several experiments (inspired by Wilkinson 1976, and by Dean et al. 1981) in which the salience of the members of the superclass was manipulated. These will not be described here for lack of space. We note that all the results can be accounted for within the pragmatic framework. For instance, the manipulations that increase the salience of the members of A (e.g., red) together with a qualification of the hypernym (the red A) are equivalent to those discussed earlier (see section on qualifying): They are genuine procedures of disambiguation which increase the likelihood that the hypernym refers to all the A.

One may wonder whether, reciprocally, the effect of all the sucessful manipulations described in “The factors that affect performance” section and the novel ones described in “Testing the pragmatic approach” section can be explained by the fuzzy trace theory. The answer seems negative. Take for instance the effect of the typicality of the minor subclass on performance. Introducing an atypical subclass keeps the irrelevant gist (more in the major subclass) unaltered as well as the relevant gist (the major subclass is part of the superclass), so that the effect is unexplained. Or take the question using three terms (the modified question, “Testing the pragmatic approach” section). Mentioning the minor subclass B’ does not increase the salience of the relation of B in A or decrease the salience of the numerosity of the relation between B and B’.

Finally, the proponents of the fuzzy trace theory seem to misunderstand the linguistic characteristics of the inclusion question. Reyna (1991) examined the linguistic account of the performance and acknowledged the fact that children’s erroneous answers reflect subclass comparison. However she claimed that the interpretation of the question that leads to error is not due to linguistic principles, but rather to a cognitive illusion due to the way the information is presented, which results in the child’s choice of one of the possible interpretations of the question. The question is recognised as ambiguous but this does not create the illusion. This stems from the quantitative information, which is unnecessary to solve the task, and renders the subclass relation salient. In brief, it is because the children attempt to make numerical comparisons that they make subclass comparisons. Reyna put forward three arguments in support of this claim.

First, she claimed that the direction of the developmental data is contrary to the predictions of the psycholinguistic account. This is based on Shipley’s (1979) analysis which considers the exclusive comparisons as ungrammatical and only the inclusive comparisons grammatical; consequently, as the children grow older, they would shift from a grammatical to an ungrammatical interpretation, which is implausible. However, this critique is pointless because it is directed at a hypothesis that is not part of the linguistic pragmatic theory (and is clearly erroneous).

Second, Reyna claimed that the experimental data rule out a causal role for the linguistic factor. This claim is based on two observations. One, mentioned earlier, is that children requested to repeat the question do not substitute the minority hyponym to the hypernym (Brainerd and Kaszor 1974). We have shown (“The subclass-to-subclass comparison” section) that the premises of this argument are unfounded. Two, Brainerd and Kingma (1985) found that numerical probes given after the class inclusion question of the type “How many A were there in the picture, a or b’ ?” (where a and b’ are the numbers of elements in A and B, respectively) were answered correctly, that is, the children did not substitute b’ for a. This is as inconclusive as the previous manipulation because the linguistic theory does not predict that the hypernym in isolation should refer to the minor subclass.

Third, Reyna attributes to the linguistic approach the claim that the inclusive interpretation of the hypernym is the basic one. It follows that older children (and adults) who are more likely to suppose that the experimenter does not ask a question to which she already knows the answer (because the hypernym refers to A, which is the preferred interpretation) would be enclined to choose the alternative, exclusive, interpretation. Consequently one should observe an increase in erroneous responses with age. This argument is flawed for two reasons. One, the claim is wrongly attributed. The correct linguistic approach claims that there is ambiguity and that disambiguation depends on attribution processes, which themselves vary developmentally, so that there is no such a thing as a basic interpretation. Two, the process of attribution is very superficially sketched. It is correct that the older children know that the experimenter knows how to answer whether there are more A than B’, but it should not be forgotten that they also know whether there are more B than B’. The meta-knowledge is necessary but insufficient to suggest an interpretation. The essential point that is missing in this account is what guides the child in his interpretation, namely considerations of relevance. It is because showing mastery of the inclusion relation has become more relevant for the older children than showing mastery of the exclusion relation that they opt for the former. The mature child prefers to show that he knows that there is more in the whole than in the part than to show that, e.g., five is greater than three. To conclude, Reyna (1991) misrepresented the linguistic account and consequently her arguments to refute it are flawed.

In sum, the claim, repeated in Reyna and Brainerd (1995), that wording allows the class-inclusion error but does not create it is clearly incorrect. On the contrary, throughout the present paper it has been shown that the ambiguous formulation of the question is crucial: Whenever a manipulation succeeds in facilitating a correct response it does so by suppressing the ambiguity of the question.