龟卜筮占的递兴与《易》卦符号的性质

先民信奉的术数有天启与人为之別。天启是消极被动地等待"天垂象,示吉凶",人为则是以卜筮"决嫌疑,定犹豫"。龟卜繁难,筮占简易。殷人尚卜与周人用筮,实为不同民族的稽疑习惯。周人受封于商,殷周始有文化往来,而周人迁岐之后,殷人之龟卜乃行于周邦,但周人仍以筮占为主。周朝开国立基,依其传统的稽疑之法编纂筮书,称之为《易》,其命名之朔,正是着眼于龟卜的繁难与筮占的简易。而《周易》卦爻辞乃旧有之象占、星占及筮占甚至龟卜之辞的鸠合与改编,具有相当程度的加工与润色。六十四卦卦画符号的原初功能就是"纪数"与"检索"。内"贞"外"悔"的爻辞顺序,也是针对六十四卦卦画绝大多数皆可"表里视之,遂成两卦"所作的规定。因此,《易》之所以名"易",一是相对龟卜而言,筮占简单容易;二是筮书编成之后,卦画符号具有方便的检索功能。而各种不同的筮法,皆可视为筮书的不同检索方式。     

《河图》五行数与《周易》四象数之间的关系

<河图>的五行成数不能与<周易>四象数混同."六、七、八、九"四数在<周易>与<河图>中的含义并不一致;五行成数实际存在两种说法,先秦文献中使用的土的成数是"五",而不是"十",因而五行数到"九"为止;土有成数"十"最初见于汉代,实际是五行学说在<易>理指导下发展的产物.     

略论《周易》对中国古代历法的影响--兼与李申先生商榷

在古代历法的发展过程中,<周易>起了积极的作用,而且这种作用在不同时期有着不同的特征.早期主要表现为用易数解释历数,这种作用在唐以后逐渐消失;"卦气说"曾在一段时期内被作为历法的内容;而<周易>的"治历明时"思想对于历法研究一直起着积极的作用,成为重要的治历原则之一.无论如何,<周易>对于古代历法发展的作用是不可低估的.     

数字表征的表象赋义效应:来自数字线估计任务的证据

已有研究中数字线估计任务几乎都使用纯数字。本研究以二到六年级儿童为被试,采用纯数字任务和赋义数字任务来探索赋义表象对数字表征形式的影响。结果表明,对0~1000的数字赋义后,对数模型的解释力上升,而线性模型的解释力下降;表象大小对于赋义数字的估计影响显著,大表象赋义提高了对数模型解释力而降低了数字估计的准确性,小表象的影响比较微弱。     

大学生SCL－90测试结果的研究

采用ＳＣＬ－９０临床症状自评量表,对随机抽取的安徽大学１－４年级２００名学生进行测试,结果表明：大学生心理健康总体水平低于全国成人常模;生源于城市和农村的大学生相比,总体差异不显著;生源于应届高中毕业生和历届高中毕业的大学生相比,在恐怖和精神病性两因子上,前者的均分显著高于后者;男女大学生相比,女大学生在抑郁和恐怖两个因子上的均分显著高于男大学生。     

Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege" s="" grundgesetze="" in="" object="" theory"="

In this paper, the author derives the Dedekind–Peano axioms for number theory from a consistent and general metaphysical theory of abstract objects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege"s Grundgesetze. The proofs of the theorems reconstruct Frege"s derivations, with the exception of the claim that every number has a successor, which is derived from a modal axiom that (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege"s conception of numbers and logical objects.     

Negative numbers in simple arithmetic

Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N?=?66) solved standard addition and subtraction problems such as 3?+?4 and 7 – 4 and recasted versions that included explicit negative signs—that is, 3 – (–4), 7?+?(–4), and (–4)?+?7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.     

The representation of negative numbers: Exploring the effects of mode of processing and notation

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.     

Dissociation between magnitude comparison and relation identification across different formats for rational numbers

ABSTRACT

The present study examined whether a dissociation among formats for rational numbers (fractions, decimals, and percentages) can be obtained in tasks that require comparing a number to a non-symbolic quantity (discrete or else continuous). In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was performed more quickly using decimals (for both quantity types), whereas the relation task was performed more accurately with fractions (but only when the image showed discrete entities). The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display.     

The revelation of the negative side of a mental number line depends on list context: Evidence from a sign priming paradigm

Two parity judgement experiments examined how the activation of spatial-numerical associations of a single, centrally presented digit, reflected by the Spatial-Numerical Association Response Codes (SNARC) effect, is modulated by a preceding + (plus) or ? (minus) prime. The centrally presented prime prior to a digit presentation presumably triggers its positive or negative attributes. When the plus- and minus-primed trials were blocked, the left-small/right-large SNARC effects occurred regardless of prime type. When the plus- and minus-primed trials were randomly intermixed, this left-small/right-large SNARC effect occurred for plus-primed digits, but was reversed for minus-primed digits. The implications of this finding for context-dependent SNARC effects are discussed.     

The SNARC effect in the processing of second-language number words: Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college‐educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.     

Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method

A procedure for generating multivariate nonnormal distributions is proposed. Our procedure generates average values of intercorrelations much closer to population parameters than competing procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random deviates, and it is simpler to code in a programming language (e.g., FORTRAN). Numerical examples demonstrating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, and kurtosis.     

邵雍易数哲学探微

本文将分五个部分以论邵雍之易数思想：首先,以天地之数和圆方之数作为天地源起之象征,并以此二数分为十六大位,以穷究天地体用之变化。其次,以阴阳奇偶之数作为天圆地方之数的基础,并以阴阳刚柔之四象、八卦配合干支之数,参以天地变化之数和体四月三之原则,以导出象征生灵万有之动植通数。再次,结合前两部分所探讨之天圆地方变化十六位数和阴阳刚柔奇偶动植通数,以呈现出一体用生物运行具象之数,以此代表天地万物的流行生化之象《天主运行,地主生化》。再次,将天行刚健之数进一步具体细分为元会运世之数．以成就邵雍独创之历法纪年。同时,将地生柔顺之数进一步体现于律吕声音之多元性和差异性来表现动植生物之不齐与参差。最后,以此五类大数施行、旁通而统贯于自然界与人文界之一切万有,以作为邵雍易学中穷理之学的终结。     

Holistic representation of negative numbers is formed when needed for the task

Past research suggested that negative numbers are represented in terms of their components—the polarity marker and the number (e.g., Fischer & Rottmann, 2005 Fischer, M. and Rottmann, J. 2005. Do negative numbers have a place on the mental number line?. Psychology Science, 47(1): 22–32.  [Google Scholar]; Ganor-Stern & Tzelgov, 2008 Ganor-Stern, D. and Tzelgov, J. 2008. Negative numbers are generated in the mind. Experimental Psychology, 55(3): 157–163.  [Google Scholar]). The present study shows that a holistic representation is formed when needed for the task requirement. Specifically, performing the numerical comparison task on positive and negative numbers presented sequentially required participants to hold both the polarity and the number magnitude in memory. Such a condition resulted in a holistic representation of negative numbers, as indicated by the distance and semantic congruity effects. This holistic representation was added to the initial components representation, thus producing a hybrid holistic-components representation.     

Response patterns of young children from two contrasting SES contexts to different numerical tasks with numbers 1–5

This study contributes to a multifaceted picture of young children’s emergent number knowledge by focusing on the variety of ways in which children express and use quantitative information. The authors’ aims are to (a) explore the extent to which quantifying collections 1–5 and using that information pose different levels of difficulty to children from 33 to 47?months old, (b) identify intra- and intertask response patterns, and (c) analyze the influence of socioeconomic status and age on these response patterns. Sixty-six children from two contrasting socioeconomic status groups (very low and middle) were asked to solve tasks with 1–5 elements in the context of a game. Using quantitative information turned out to be more complex than quantification. Intra- and intertask response patterns showed that children gradually come to understand the first five numerical values according to the numerical sequence in a much less strict way than that proposed by the cardinal-knowers model that posits that children progress in an orderly way in their number knowledge. Children in different ages and socioeconomic status groups were found to be more similar to each other when the whole arc of responses provided was considered than when solely correct performance was measured.     

A Note on Finiteness in the Predicative Foundations of Arithmetic

Recently, Feferman and Hellman (and Aczel) showed how to establish the existence and categoricity of a natural number system by predicative means given the primitive notion of a finite set of individuals and given also a suitable pairing function operating on individuals. This short paper shows that this existence and categoricity result does not rely (even indirectly) on finite-set induction, thereby sustaining Feferman and Hellman's point in favor of the view that natural number induction can be derived from a very weak fragment of finite-set theory, so weak that finite-set induction is not assumed. Many basic features of finiteness fail to hold in these weak fragments, conspicuously the principle that finite sets are in one-one correspondence with a proper initial segments of a (any) natural number structure. In the last part of the paper, we propose two prima facie evident principles for finite sets that, when added to these fragments, entail this principle.