A constraint on comparisons: Equally detailed alternatives

Children's errors in collective comparison tasks are atributed to the comparison of the wrong classes. It is specifically hypothesized that alternative classes are erroneously formed subject to the constrain that the same kinds of properties are criterial for each alternative. This hypothesis, called the equally detailed alternatives hypothesis, is tested in three experiments with hierarchically organized stimuli and requests to compare a superordinate class and a nonincluded subclass, for example, dogs and yellow cats. In all three experiments 4-year-old children's comparisons were found to be in accord with the hypothesis. In the first experiment both perceptual and linguistic factors determine which classes are compared. In the second experiment, as predicted, erroneous subclass comparisons were more common when all subclasses were distinguished by the same kinds of properties. In the third experiment, the children were asked to partition the stimulus objects into the classes to be compared. The vast majority of partitions were erroneous and in accord with the hypothesis. Potential benefits of the constrain are considered.     

Classes and collections: Internal organization and resulting holistic properties

This work presents an analysis of a type of concept, the collection, not readily characterized by class inclusion models. Collections, the referents of collective nouns (e.g., pile, family, bunch), are argued to differ from classes in (a) how membership can be determined, (b) part-whole relationships, (c) internal structure, and (d) the nature of the higher order units they form. From this analysis, it is hypothesized that the psychological integrity of collections is greater than that of classes. Collections and objects, in contrast to classes, both require specified relationships among the parts and both result in a coherent psychological unit. It was suggested that objects form a relatively more stable unit than collections. Corresponding to this analysis the degree of psychological integrity is hypothesized to lead to different degrees of difficulty in making part-whole comparisons for objects, collections, and classes in modified Piagetian class-inclusion paradigms. The hypothesized difference in performance was found for collections and classes and an alternative linguistic explanation for the greater success with collections was eliminated. However, children performed equally well on tasks involving collections and objects, raising the possibility that when elements are organized into collections, they form psychological units which are as coherent as objects.     

Inhibitory control in number-conservation and class-inclusion tasks: A neo-Piagetian inter-task priming study

We investigated whether success in number-conservation and class-inclusion tasks relies on a general ability to inhibit misleading strategies. Two groups of 10-year-olds performed inter-task priming between computerized versions of class-inclusion and number-conservation tasks (Experiment 1). In one group, the class-inclusion task served as a prime and the number-conservation task as an assessment probe and vice versa in the other group. Response times were shorter in the number-conservation task when performed after the class-inclusion task (and vice versa in the other group) than in control prime-probe sequences in which the primes did not require the inhibition of a misleading strategy. Experiment 2 showed that these inter-task priming effects did not simply reflect that class inclusion and number conservation rely on the reversibility of concrete operations as Piaget would have hypothesized. Taken together the results are consistent with the neo-Piagetian assumption that cognitive development is rooted in both the acquisition of knowledge of incremental complexity and the ability to resist (inhibit) previous knowledge. Critically, the present finding suggests that the inhibitory ability is not domain- or strategy-specific.     

Failure in Class-Inclusion Reasoning in a University Sample

Two studies were undertaken with the purpose of examining adult performance on tasks of class-inclusion reasoning. Both duration of visual presentation and instructions regarding speed of response were varied. In both studies overall performance was low (approximately 60% of items were answered correctly) but neither duration of visual presentation nor speed of responding were shown to be systematically related to errors. Even when participants were permitted unlimited time to view the visual display and put under no pressure to respond quickly performance only reached 80% correct. Significant improvement over trials was observed, which suggests that participants may not have initially understood the task. Results are discussed in terms of the adequacy of class-inclusion tasks as measures of competence in logical reasoning about classes.     

Testing for developmental continuity or discontinuity: Class inclusion and reversal shifts

Often the data in cognitive development consist of continuous cross-sectional increases in the proportion of children who respond in one of two ways to a diagnostic task. Such developmental trends are, however, ambiguous with reference to the course of individual, longitudinal development because they could be the result of either saltatory or gradual ontogenetic change. The present research tested a nonlongitudinal procedure for discriminating between these two alternatives. This procedure involves the administration of several equivalent versions of the diagnostic task at weekly intervals to children within a given age level in order to obtain a frequency distribution of the number of “successes” produced by each child. A bimodal distribution is interpreted as indicating saltatory ontogenetic change, while a unimodal distribution is taken to indicate gradual change. This method was applied to Piaget's class-inclusion problem and to the optional-shift task by administering four versions of each task to a range of different age-level samples. The optional-shift task produced clearly unimodal, bell-shaped distributions at all tested age levels, results which were interpreted to indicate a gradual ontogenetic increase in the probability of making reversal shifts. On the other hand, the frequency distributions for the class-inclusion task, at the appropriate age levels, were distinctly bimodal, and therefore consistent with a discontinuous ontogenetic transition. The capacity of the repeated-measures method to produce reliable within-task results and to differentiate between tasks was thus demonstrated.     

Leading questions and the eyewitness report

A total of 490 subjects, in four experiments, saw films of complex, fast-moving events, such as automobile accidents or classroom disruptions. The purpose of these experiments was to investigate how the wording of questions asked immediately after an event may influence responses to questions asked considerably later. It is shown that when the initial question contains either true presuppositions (e.g., it postulates the existence of an object that did exist in the scene) or false presuppositions (e.g., postulates the existence of an object that did not exist), the likelihood is increased that subjects will later report having seen the presupposed object. The results suggest that questions asked immediately after an event can introduce new—not necessarily correct—information, which is then added to the memorial representation of the event, thereby causing its reconstruction or alteration.     

Gist another panacea? Or just the illusion of inclusion

In this article, we call for a formal approach to modeling the development of reasoning. We discuss the need to operationalize the nature of encoding and processing. These problems are reviewed in the context of fuzzy-trace theory with particular emphasis on class-inclusion reasoning experiments. We argue that salience manipulations (perceptual or linguistic) give the illusion of inclusion by promoting subclass-subclass comparisons. We present an alternate, mathematical model of class-inclusion reasoning in which memory and reasoning parameters are estimated and integrated in a skills analysis of performance. We conclude that without similar formal modeling efforts, the nature of children's reasoning will remain elusive.     

Language and Operations in Children's Class Inclusion Reasoning: The Operational Semantic Theory of Reasoning

In this article we critique two prominent theories of reasoning—mental logic and mental models—and argue that reasoning does not consist of either applying logical rules or constructing mental models. Instead, we propose anoperational semantictheory of reasoning, according to which reasoning is based on children's operational understanding of key terms in a given problem. We then go on to consider an important recent developmental theory of reasoning, fuzzy-trace theory. In order to illustrate the view of reasoning proposed here we report a study of class inclusion. Dramatic differences in class inclusion performance were found as the result of linguistic context; performance was significantly higher when an explicit request for a subclass comparison preceded the class inclusion question as compared to a standard condition when the class inclusion question alone was asked. This was the case, however, only when the prior subclass comparison question referred to the same dimensions as the class inclusion question and not when irrelevant subclasses were referred to. Children's performance was also better when they sorted the materials into the supraordinate class as compared to the subclasses, but not when the experimenter sorted them for the child. These effects due to the operational and linguistic manipulations are discussed in terms of a generaloperational semantictheory of reasoning.     

Generalization of cross-modal stimulus equivalence classes: operant processes as components in human category formation.

This study employed a stimulus-class rating procedure to explore whether stimulus equivalence and stimulus generalization can combine to promote the formation of open-ended categories incorporating cross-modal stimuli. A pretest of simple auditory discrimination indicated that subjects (college students) could discriminate among a range of tones used in the main study. Before beginning the main study, 10 subjects learned to use a rating procedure for categorizing sets of stimuli as class consistent or class inconsistent. After completing conditional discrimination training with new stimuli (shapes and tones), the subjects demonstrated the formation of cross-modal equivalence classes. Subsequently, the class-inclusion rating procedure was reinstituted, this time with cross-modal sets of stimuli drawn from the equivalence classes. On some occasions, the tones of the equivalence classes were replaced by novel tones. The probability that these novel sets would be rated as class consistent was generally a function of the auditory distance between the novel tone and the tone that was explicitly included in the equivalence class. These data extend prior work on generalization of equivalence classes, and support the role of operant processes in human category formation.     

On the Logic of Classes as Many

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.     

Parents' gender-based attitudes toward marital roles and child rearing: Development and validation of new measures

Factor analysis of 18 Likert-type items dealing with gender stereotypes about family roles was conducted and yielded two measures: one focused on marital roles and one focussed on child rearing. Respondents were parents of children in the third and fourth grades of a large industrialized city in the Midwest. The sample included 364 families equally divided between middle and lower class with 23% African American and 77% European American. For both scales, more stereotyped scores were obtained by parents who were lower in social status, less educated, full-time homemakers, African Americans, and fathers. Parents' scores related to a separate measure of children's stereotypes and the marital-role attitudes related to actual roles reported by family members. Daughters whose parents obtained less stereotyped scores had a more internal locus of control, showed a trend toward more independent coping skills, and—in the middle class—obtained higher scores on achievement tests.This research was supported by Grant No. 91-1437-91 from the William T. Grant Foundation.     

Variations in gender-role equality among classes: A research note

A widely accepted view describes gender-role inequality as less prevalent among the middle class than the working class. Gender-role inequality within the intact nuclear family is asserted to be a syndrome characterized by unequal husband—wife authority, rigid division of household labor, and greater freedom in leisure pursuits for the husband. This view is generally unsupported by the findings of the present study, a secondary analysis of a sample survey conducted in Houston in 1969–1970. Two classes (working and middle) were compared, with ethnicity (Anglo, Black, Mexican-American) and sex controlled. Questionnaire items concerned leisure-time freedom for wives, gender differences in children's socialization, and sexual division of labor in the household. Differences between groups were generally small and inconsistent. In some cases, sexual and ethnic differences were greater than those of class. An intercorrelation matrix revealed few significant correlations between egalitarian responses to the various items, suggesting that egalitarianism or its opposite is not a syndrome.This paper utilized data collected on a project partially supported by NIMH Grant No. MH 15708. Computer services were provided by the Institute of Computer Sciences, Baylor College of Medicine, Houston, Texas, supported by NIH Grant No. RR 00259, and the Institute for Computer Services and Applications, Rice University, Houston, Texas. Secondary analysis of data was carried out in the Winter of 1975–1976. We wish to thank Dr. George Antunes of the University of Houston, Dr. Richard Hamilton of McGill University, and Judith Scott of Texas Research Institute of Mental Sciences for their critical reading of an earlier draft of this paper.     

What do children know about the universal quantifiers all and each?

Children's comprehension of the universal quantifiers all and each was explored in a series of experiments using a picture selection task. The first experiment examined children's ability to restrict a quantifier to the noun phrase it modifies. The second and third experiments examined children's ability to associate collective, distributive, and exhaustive representations with sentences containing universal quantifiers. The collective representation corresponds to the “group” meaning (for All the flowers are in a vase all of the flowers are in the same vase). The distributive representation implies a pairing (e.g., each flower paired with a vase for Each flower is in a vase). The exhaustive representation exhausts both sets (e.g., for The flowers are in the vases all the flowers are in vases and all the vases have flowers in them). Four- to 10-year-old children had little difficulty restricting the quantifier all to the noun it modified in a task which required them to attend to the group feature of all. In contrast, only 9- and 10-year-olds were able to solve the task when the quantifier was each and the pictures showed entities in partial one-to-one correspondence. Children showed a preference for associating collective pictures with sentences containing all and distributive pictures with sentences containing each. The results suggest that between the ages of 5 and 10 years, children's semantic representations undergo less radical changes than others have proposed. Instead, developmental change may occur gradually as children acquire linguistic cues which map onto existing semantic representations.     

A further comparison of oblique factor transformation methods

Four prominent oblique transformation techniques—promax, the Harris-Kaiser procedure, biquartimin, and direct oblimin—are examined and compared. Additionally, two newly-developed procedures, falling into the category designated as Case III by Harris and Kaiser [1964], are presented and included in the comparisons. The techniques are compared in light of their freedom from bias in the interfactor correlations, and their ability to yield clear simple structures, over many data sets—some constructed and some real—varying widely in terms of number of variables and factors, factorial complexity, and clarity of the hyperplanes. Results are discussed, and implications for practice are noted.     

The Influence of Family and Experimental Context on Cognition in Anxious Children

Examined the influence of family on anxious children's cognition. Research by Barrett, Rapee, Dadds, and Ryan (1996) found anxious children reported increased avoidance after interacting with their parents. They labelled this finding the FEAR effect—Family Enhancement of Avoidant Responses. Whilst some subsequent studies have found similar results, others have not. These contradictory findings question whether the direction of parental influence on anxious children is determined by the perceived demands of the experimental context. Anxious children (N = 101) and their parents were asked to interpret seven ambiguous situations and to discuss what their child would do if the scenario actually occurred. Study 1 found that children in the anxious group and an externalizing control group were more likely to interpret ambiguous situations as threatening than nonclinic children were. Study 2 sought to examine changes in the children's responses from pre- to postfamily discussion, and to identify variables associated with the FEAR effect in anxious families. Interestingly, anxious children whose families completed the discussion task after they (children) had been offered treatment were more likely to show a FEAR effect than anxious families who completed the task as part of assessment. Study 3 examined predictors of enhanced avoidance in anxious families. Treatment context and maternal distress were correlated with the child's increased avoidance following family discussion. Limitations of these studies and directions for future research are discussed.     

Logical matrices and the amalgamation property

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.     

Modern Maladies of the Self: Borrowed Selves and Collective Faith

Cultures give rise to and support different kinds of self-constructions and types of faith. In this article I argue that particular Western beliefs and values can give rise to modern maladies of self and faith—borrowed selves and collective faith. Borrowed selves reveal a fundamental insecurity or anxiety that comes from a felt lack of possessing or owning the attributions of one's identity, which in turn shapes the very relationships and faith upon which identity is linked. More specifically, I identify two distinct, though related, manifestations of borrowed selves—normotic selves and nomadic selves—and their concomitant types of collective faith—merged faith and eclectic-autonomous faith. Both self-constructions and types of faith manifest persons' specific stance with regard to community and its traditions, and both are fueled by an unconscious anxiety and a belief in what I call relativistic individualism.     

Sex differences in self- and teachers' reports of self-esteem in preadolescents

The short form of the Coopersmith Self-Esteem Inventory was administered to 952 fourth- and fifth-grade children (482 males, 470 females) from 41 classes. The children's teachers completed Coopersmith's Behavior Rating Form, a measure of self-esteem-related behavior. In the self-ratings, girls were significantly lower than boys; in the teachers' ratings, girls were significantly higher. In 32 of the 41 classes, boys ranked higher in their self-ratings than in the teacher ratings; the reverse was true for girls — a highly significant difference. This pattern of findings did not occur in the 8 classes which had male teachers. Issues concerning the measurement and conceptualization of self-esteem are discussed.This research was supported by Lehigh University, using Institutional Grant funds from the National Science Foundation. The authors wish to express their appreciation to Patricia Horton for her assistance in the collection of the data.     

An axiom system for orthomodular quantum logic

Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to be an orthomodular lattice whose unit element is the equivalence class of theses ofOMC.This research was supported by National Science Foundation Grant Number SOC76-82527.     

Individual differences in working memory and reasoning-remembering relationships in solving class-inclusion problems

In the present experiment, we evaluated the effects of individual differences in reading span and variation in memory demands on class-inclusion performance. One hundred twenty college students whose reading spans ranged from low to medium to high (as indexed by a computerized version of the Daneman and Carpenter [1980] reading-span task) solved 48 class-inclusion problems. Half of the subjects had the solution information available when the problems were presented; the other half performed a detection task between solution information and problem presentation. The results from both standard statistical analyses and from a mathematical model indicated that differences in reading span and memory load had predictable, similar effects. Specifically, the sophistication of reasoning strategies declined when memory demands increased or when reading spans decreased. Surprisingly, these effects were primarily additive. The results were interpreted in terms of global resource models and findings from the developmental literature.