Predictions about bisymmetry and cross-modal matches from global theories of subjective intensities

The article first summarizes the assumptions of Luce (2004, 2008) for inherently binary (2-D) stimuli (e.g., the ears and eyes) that lead to a "p-additive," order-preserving psychophysical representation. Next, a somewhat parallel theory for unary (1-D) signals is developed for intensity attributes such as linear extent, vibration to finger, and money. The 3rd section studies the property of bisymmetry in these 2 cases. For the 2-D case and the nontrivial p-additive forms, Proposition 3 shows that bisymmetry implies commutativity of the presentations. Bisymmetry has been empirically well sustained, whereas commutativity has been rejected for loudness, brightness, and perceived contrast, thus implying that pure additivity must obtain in the 2-D context. By contrast, bisymmetry and commutativity are automatically satisfied by the p-additive 1-D theory. The 4th section explores the resulting complex of cross-modal predictions. For the additive 1-D case and the 2-D case, the predictions are power functions. For the nonadditive 1-D cases, other relations are predicted (see Table 2). Some parameter estimation issues are taken up in Appendices B and C.     

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Background: Understanding arithmetical principles is a key part of a conceptual understanding of mathematics. However, very little attention has been paid to children's understanding of multiplicative, as compared to additive, principles. Aims: This study investigated(a) children's ability to use commutative and distributive cues to solve multiplication problems, (b) whether their ability to use these cues depends on the problem context, and(c) whether separate mechanisms might underlie children's understanding of commutativity and distributivity. Sample: Twenty‐seven 9‐year‐olds (Year 5) and thirty‐two 10‐year‐olds (Year 6). Methods: Forty‐eight multiplication problems (with a multiple‐choice response format) were presented to children. There were four types of problem: Commutative, Distributive, Combined commutative‐distributive(all preceded by a cue) and No cue problems. Each type of problem was presented in three different contexts: Isomorphism of measures, Area, and Cartesian product. Results: Children demonstrated a good understanding of commutativity but a very poor understanding of distributivity. A common mistake in the distributive problems was to select the number that was one more, or one less, than the answer in the cue. Children's understanding of distributivity (butnot commutativity) seemed to depend on the problem context. Factor analysis suggested that separate factors underlie the ability to solve commutative and distributive problems. Conclusions: Nine‐ and 10‐year‐olds understand commutativity, but are unable to use the distributive principle in multiplication. Their errors suggest that they may confuse some of the principles of multiplication with those of addition. When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems. The implications for mathematical education are discussed.     

Torgerson’s conjecture and Luce’s magnitude production representation imply an empirically false property

The prediction presented is based upon the empirically well sustained magnitude production representation that arose in both of Luce’s global psychophysical theories for subjective intensity of binary and unary continua coupled with Torgerson’s (1961) conjecture that respondents fail to distinguish subjective differences from subjective ratios. When applied to eqisections and fractionation the conjecture implies that the cognitive distortion function of the magnitude production representation is the identity function, which is firmly rejected by existing data.     

The Development of the Commutativity Principle and Economical Addition Strategies

What is the relationship between the principle of commutativity and the development of addition strategies that disregard addend order? It has been proposed that the assumption (Conjecture 1) or discovery (Conjecture 2) of commutativity is a necessary condition for the invention of such advanced addition strategies. A third hypothesis suggests that children may invent labor-saving addition strategies without necessarily appreciating the commutativity principle. This study tested the three conjectures by evaluating 36 kindergartners on two types of commutativity tasks. Both tasks involved predicting whether commuted and noncommuted pairs of problems would produce the same or different answers. Commutativity was not naturally assumed by children (as proposed by Conjecture 1), but appeared to be discovered. However, contrary to Conjecture 2 and consistent with Conjecture 3, an understanding of commutativity was not evident in all those who invented labor-saving addition strategies. This study also confirmed that counting-all starting with the larger addend-a mental strategy recently discovered in a case study-was not an uncommon labor-saving device among young children.     

The development of mental models for auditory events: Relational complexity and discrimination of pitch and duration

This experiment investigated relational complexity and relational shift in judgments of auditory patterns. Pitch and duration values were used to construct two‐note perceptually similar sequences (unary relations) and four‐note relationally similar sequences (binary relations). It was hypothesized that 5‐, 8‐ and 11‐year‐old children would perform unary level pitch and duration discrimination tasks accurately. Relational shift predicted a poorer performance of the younger age groups on binary relation tasks; relational primacy predicted no effect of age. Accuracy was operationalized as a discrimination index (DI: hit rate minus false alarm rate). Results supported relational shift: DI for all age groups exceeded chance on unary and binary relation tasks, with significantly poorer performance by all age groups on binary relation tasks. The 5‐years age group showed evidence of perceptual similarity. Relational complexity of auditory dimensions and tasks, and manipulation of domain specific musical knowledge in evaluating theories of relational processing, are discussed.     

Annotation Theories over Finite Graphs

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21].     

Theory and tests of the conjoint commutativity axiom for additive conjoint measurement

The empirical study of the axioms underlying additive conjoint measurement initially focused mostly on the double cancellation axiom. That axiom was shown to exhibit redundant features that made its statistical evaluation a major challenge. The special case of double cancellation where inequalities are replaced by indifferences–the Thomsen condition–turned out in the full axiomatic context to be equivalent to the double cancellation property but without exhibiting the redundancies of double cancellation. However, it too has some undesirable features when it comes to its empirical evaluation, the chief among them being a certain statistical asymmetry in estimates used to evaluate it, namely two interlocked hypotheses and a single conclusion. Nevertheless, thinking we had no choice, we evaluated the Thomsen condition for both loudness and brightness and, in agreement with other lines of research, we found more support for conjoint additivity than not. However, we commented on the difficulties we had encountered in evaluating it. Thus we sought a more symmetric replacement, which as Gigerenzer and Strube (1983) first noted, is found in the conjoint commutativity axiom proposed by Falmagne (1976, who called it the “commutative rule”). It turns out that, in the presence of the usual structural and other necessary assumptions of additive conjoint measurement, we can show that conjoint commutativity is equivalent to the Thomsen condition, a result that seems to have been overlooked in the literature. We subjected this property to empirical evaluation for both loudness and brightness. In contrast to Gigerenzer and Strube (1983), our data show support for the conjoint commutativity in both domains and thus for conjoint additivity.     

中小学教师知识观与教学观研究

本文就中小学教师对于知识和教学的基本观点以及它们之间的相互关系进行了初步探讨,结果表明：教师们普遍认识到知识是相对的、辩证的和有联系的,认为教学不是知识的简单地灌输而是帮助学生完成意义的建构。教师在知识观的“机械-辩证”和教学观的“接收-建构”两个维度之间存在显著的正相关．     

Meaning and Truth in Habermas's Pragmatics

The article examines Habermas's formal-pragmatic theory of meaning from the point of view of his attempt to defend a postmetaphysical yet context-transcendent conception of validity. It considers his attempt to develop a pragmatic account of understanding utterances that emphasises the mediation of knowledge through socio-cultural practices while simultaneously stressing that understanding has a cognitive dimension that is inherently context-transcendent. It focuses on his recent "Janus-faced" conception of truth, looking more briefly at his purely epistemic conception of moral validity. It raises three objections: the first to his attempt to maintain a notion of "unconditionality" that has no otherworldly origins but is purely immanent to this world, the second to the alleged non-arbitrary status of his conception of truth, and the third to his rejection of metaphysical thinking. It concludes that the objections, if valid, have profound implications for Habermas's postmetaphysical enterprise and for his programme of formal pragmatics.     

分心抑制和关系整合对学前儿童类比推理的影响

为探究分心抑制和关系整合对学前儿童类比推理的影响,实验一先初步探究分心抑制和关系整合对25名3~4岁和26名5~6岁儿童完成含有知觉分心的类比情景任务的影响。其次,揭示知觉分心与关系整合在类比推理中的具体作用模式。实验二先初步探究分心抑制和关系整合对30名3~4岁和28名5~6岁儿童完成含有语义分心的类比情景任务的影响。其次,揭示语义分心与关系整合在类比推理中的具体作用模式。结果表明,抑制控制能显著预测儿童完成各种类型类比推理成绩,工作记忆能显著预测儿童完成含有语义分心的类比推理成绩而不能显著预测含有知觉分心的类比推理成绩。儿童完成类比情景中的分心抑制是在关系整合中完成的,当类比情景中的关系整合没有超过儿童的工作记忆容量时,知觉或语义分心才能造成对儿童类比推理的影响。     

Brightness of different hues is a single psychophysical ratio scale of intensity

Recent studies based on testable behavioral axioms have concluded that psychological scales of subjective intensive attributes involving the ears and eyes form ratio scales. These studies have shown that a certain commutativity of proportion property must hold under either successive increases or successive decreases, with all other independent dimensions fixed. However, until recently limited attention has been paid to whether such subjective intensity scales differ when a dimension independent of intensity, such as frequency or wavelength (e.g., pitch in audition, hue in vision) is varied. Using a simple and favorably tested theoretical model for global psychophysics, Luce, Steingrimsson, and Narens (2010) arrived at a necessary and sufficient cross-frequency, commutativity condition for there to exist a common intensity ratio scale. Here we show that brightness--already established to be a ratio-scalable dimension--and hue satisfy the same conditions.     

Young children's performance on the balance scale: the influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains--transitivity and class inclusion--accounted for 93% of the age-related variance in balance scale scores.     

儒家思想对于现代心理咨询的启示

儒家思想曾居中国传统文化主导地位。鉴于文化的传承性和对心理健康作用的必然性,儒家思想的心理咨询价值应当充分关注。文章强调,不宜刻板化否定儒家思想的心理咨询价值。基于心理咨询的常见问题,文章初步讨论了儒家思想对心理咨询可能有贡献的9个领域：人生意义、应对、生死教育、哀伤辅导、心理调节、人际认知、社会生活技能、人格发展、心理咨询技术等。进而,讨论了以儒家思想为资源,以心理学为目的,通过整理和发现、发展、操作化和验证等环节,构建儒家心理咨询学说的方法论问题     

Development of the understanding of the polysemous meanings of the mental-state verb know

This study investigated children's understanding (3-, 6-, 9-, and 12-year-olds) of the different levels of meaning of the cognitive verb know as defined by the Hall, Scholnick, and Hughes (1987) abstractness and conceptual difficulty hierarchy. We found that cognitive verb knowledge increased with development and that certain low levels of meaning were mastered before certain high levels of meaning irrespective of the medium of presentation: video-taped “skits” and audio-taped “stories.” However, children developed an understanding of low levels of meaning at a more rapid rate than high levels of meaning. This resulted in a more differentiated and hierarchical cognitiveverb knowledge in older children. Finally, we found that the audio-taped stories were more difficult than the video-taped skits, and that both tasks were significantly correlated with a standardized vocabulary measure for all ages except the 3-year-olds. The implications of this study and others for a model of the cognitive-verb lexicon are discussed.     

Meaning Relations,Syntax, and Understanding

Axiomathes - This paper revisits the conception of intelligence and understanding as embodied in the Turing Test. It argues that a simple system of meaning relations drawn from words/lexical items...     

The development of the concept of multiplication

Two alternative hypotheses have been offered to explain the origin of the concept of multiplication in children's reasoning. The first suggests that the concept of multiplication is grounded on the understanding of repeated addition, and the second proposes that repeated addition is only a calculation procedure and that the understanding of multiplication has its roots in the schema of correspondence. This study assessed the two hypotheses through an intervention method. It was hypothesised that an intervention based on the origin of the concept of multiplication would be more effective than the one that did not offer the learners a conceptual basis for learning. Pupils (mean age 6 years 7 months) from two primary schools in England, who had not been taught about multiplication in school, were pretested in additive and multiplicative reasoning problems. They were then randomly assigned to one of two treatment conditions: teaching of multiplication through repeated addition or teaching through correspondence. Both groups made significant progress from pre- to posttest. The group taught by correspondence made significantly more progress in multiplicative reasoning than in additive reasoning problems. The group taught by repeated addition made similar progress in both types of problems. At posttest, the correspondence group performed significantly better than the repeated addition group in multiplicative reasoning problems even after controlling for level of performance at pretest. Thus, this study supports the hypothesis that the origin of the concept of multiplication is in the schema of correspondence rather than in the idea of repeated addition.     

The Influence of Bloomfield's Linguistics on Skinner

Bloomfield''s “Linguistics as a Science” (1930/1970), Language (1933/1961), and “Language or Ideas?” (1936a/1970), and Skinner''s Verbal Behavior (1957) and Science and Human Behavior (1953) were analyzed in regard to their respective perspectives on science and scientific method, the verbal episode, meaning, and subject matter. Similarities between the two authors were found. In particular both asserted that (a) the study of language must be carried out through the methods of science; (b) the main function of language is to produce practical effects on the world through the mediation of a listener; and (c) a physicalist conception of meaning. Their differences concern the subject matter of their disciplines and their use of different models for the analysis of behavior. Bloomfield''s linguistics and Skinner''s functional analysis of verbal behavior are complementary approaches to language.