Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella)

Recent assessments have shown that capuchin monkeys, like chimpanzees and other Old World primate species, are sensitive to quantitative differences between sets of visible stimuli. In the present study, we examined capuchins’ performance in a more sophisticated quantity judgment task that required the ability to form representations of food quantities while viewing the quantities only one piece at a time. In three experiments, we presented monkeys with the choice between two sets of discrete homogeneous food items and allowed the monkeys to consume the set of their choice. In Experiments 1 and 2, monkeys compared an entirely visible food set to a second set, presented item-by-item into an opaque container. All monkeys exhibited high accuracy in choosing the larger set, even when the entirely visible set was presented last, preventing the use of one-to-one item correspondence to compare quantities. In Experiment 3, monkeys compared two sets that were each presented item-by-item into opaque containers, but at different rates to control for temporal cues. Some monkeys performed well in this experiment, though others exhibited near-chance performance, suggesting that this species’ ability to form representations of food quantities may be limited compared to previously tested species such as chimpanzees. Overall, these findings support the analog magnitude model of quantity representation as an explanation for capuchin monkeys’ quantification of sequentially presented food items.

序数表征及其脑机制

人类天生就具有一些初级的数概念。研究表明,顶内沟是基数表征的脑基础,这一区域受损或发展受阻将导致计算失能等与数有关的认知障碍。尽管序数与基数存在相似的行为效应,但与序数相联系的皮层通路不同于基数,序数表征主要激活前额皮层与颞叶皮层区域。序数是否也存在符号效应以及跨文化差异等问题有待进一步研究     

Processing of Syllables in Production and Recognition Tasks

Empirical evidence for a functional role of syllables in visual word processing is abundant, however it remains rather heterogeneous. The present study aims to further specify the role of syllables and the cognitive accessibility of syllabic information in word processing. The first experiment compared performance across naming and lexical decision tasks by manipulating the number of syllables in words and non-words. Results showed a syllable number effect in both the naming task and the lexical decision task. The second experiment introduced a stimulus set consisting of isolated syllabic and non-syllabic trigrams. Syllable frequency was manipulated in a naming and in a decision task requiring participants to decide on the syllabic status of letter strings. Results showed faster responses for syllables than for non-syllables in both tasks. Syllable frequency effects were observed in the decision task. In summary, the results from these manipulations of different types of syllable information confirm an important role of syllabic units in both recognition and production.     

A Dissociation between Symbolic Number Knowledge and Analogue Magnitude Information

Semantic understanding of numbers and related concepts can be dissociated from rote knowledge of arithmetic facts. However, distinctions among different kinds of semantic representations related to numbers have not been fully explored. Working with numbers and arithmetic requires representing semantic information that is both analogue (e.g., the approximate magnitude of a number) and symbolic (e.g., what / means). In this article, the authors describe a patient (MC) who exhibits a dissociation between tasks that require symbolic number knowledge (e.g., knowledge of arithmetic symbols including numbers, knowledge of concepts related to numbers such as rounding) and tasks that require an analogue magnitude representation (e.g., comparing size or frequency). MC is impaired on a variety of tasks that require symbolic number knowledge, but her ability to represent and process analogue magnitude information is intact. Her deficit in symbolic number knowledge extends to a variety of concepts related to numbers (e.g., decimal points, Roman numerals, what a quartet is) but not to any other semantic categories that we have tested. These findings suggest that symbolic number knowledge is a functionally independent component of the number processing system, that it is category specific, and that it is anatomically and functionally distinct from magnitude representations.     

Erkenntnistheorie der Zahldefinition und philosophische Grundlegung der Arithmetik unter Bezugnahme auf einen Vergleich von Gottlob Freges Logizismus und platonischer Philosophie (Syrian, Theon von Smyrna u.a.)

The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition is found in the arithmetic in Euclid's Elements. To draw this conclusion a profound reflection on the role of epistemology for the foundation of mathematics, especially for the method of definition of number, is indispensable; a reflection not to be found in the contemporary debate (the predominate ‘pragmaticformalism’ in current mathematics just shirks from trying to solve the epistemological problems raised by the debate between logicism, intuitionism, and formalism). Frege's definition of number, ‘The number of the concept F is the extension of the concept ‘numerically equal to the concept F”, which is still substantial for contemporary mathematics, does not fulfil the requirements of logical and methodological correctness because the definiens in a double way (in the concepts ‘extension of a concept’ and ‘numerically equal’) implicitly presupposes the definiendum, i.e. number itself. Number itself, on the contrary, is defined adequately by Euclid as ‘multitude composed of units’, a definition which is even, though never mentioned, an implicit presupposition of the modern concept ofset. But Frege rejects this definition and construes his own - for epistemological reasons: Frege's definition exactly fits the needs of modern epistemology, namely that for to know something like the number of a concept one must become conscious of a multitude of acts of producing units of ‘given’ representations under the condition of a 1:1 relationship to obtain between the acts of counting and the counted ‘objects’. According to this view, which has existed at least since the Renaissance stoicism and is maintained not only by Frege but also by Descartes, Kant, Husserl, Dummett, and others, there is no such thing as a number of pure units itself because the intellect or pure reason, by itself empty, must become conscious of different units of representation in order to know a multitude, a condition not fulfilled by Euclid's conception. As this is Frege's main reason to reject Euclid's definition of number (others are discussed in detail), the paper shows that the epistemological reflection in Neoplatonic mathematical philosophy, which agrees with Euclid's definition of number, provides a consistent basement for it. Therefore it is not progress in the history of science which hasled to the a poretic contemporary state of affairs but an arbitrary change of epistemology in early modern times, which is of great influence even today. This revised version was published online in August 2006 with corrections to the Cover Date.     

幼儿对数的认知及其策略

该研究探查幼儿对基数、数序、运算和解应用题的认知发展过程及其认知策略。着重探查：(1)不同认知任务对幼儿数认知发展的影响;(2)幼儿对基数和数序两者认知发展的顺序;(3)从幼儿主动解决问题的策略探究其认知发展水平。该研究采用定性和定量相结合的研究方法。被试为4、5、6岁城市幼儿园儿童,共92人,男女约各半。全部实验以个别方式进行。主要研究结果表明：(1)幼儿对基数、数序、运算和解应用题的认知成绩均有随年龄发展的趋势,但快速发展的年龄阶段因任务的难度而异;(2)幼儿对基数和数序的认知在4—5岁显示出不同步的发展,对基数的认知成绩优于对数序的认知,而到6岁两者具有同步发展的趋势;(3)幼儿解决问题的策略水平随年龄发展,显示了由外化水平的智力活动向完全内化的智力操作的发展过程,并具有明显的层次性。该研究结果为幼儿数能力的培养和促进提供参考依据。     

不同注意提示线索条件下汉字数字加工的SNARC效应

采用Ponser的实验范式.以判断"壹"到"玖"的汉字数字奇偶为任务,探讨不同提示线索时在注意条件与非注意条件下的空间数字反应编码联合效应(SNARC效应).实验结果发现: (1)当有效提示线索为80%时,注意条件下汉字数字出现了SNARC效应,而非注意条件下对汉字数字的加工没有出现SNARC效应; (2)当有效提示线索为50%时,在注意和非注意条件下汉字数字都出现了明显的SNARC效应.结果表明注意水平对SNARC效应产生了影响.     

The associations between space and order in numerical and non-numerical sequences

Spatial-numerical associations have been found across different studies, yet the basis for these associations remains debated. The current study employed an order judgment task to adjudicate between two competing accounts of such associations, namely the Mental Number Line (MNL) and Working Memory (WM) models. On this task, participants judged whether number pairs were in ascending or descending order. Whereas the MNL model predicts that ascending and descending orders should map onto opposite sides of space, the WM model predicts no such mapping. Moreover, we compared the spatial-order mapping for numerical and non-numerical sequences because the WM model predicts no difference in mapping. Across two experiments, we found consistent spatial mappings for numerical order along both horizontal and vertical axes, consistent with a MNL model. In contrast, we found no consistent mappings for letter sequences. These findings are discussed in the context of conflicting extant data related to these two models.