Identifying finite cardinal abstracts

Philosophical Studies - Objects appear to fall into different sorts, each with their own criteria for identity. This raises the question of whether sorts overlap. Abstractionists about...     

Discrimination of cardinal compass directions

The study tested the hypothesis that east-west is more difficult to discriminate than north-south because pre-experimentally the former is associated with right-left and the latter with up-down (or front-behind). Forty-eight undergraduates first learned north, south, east, and west in slides of unknown places. In one condition the compass directions were indicated by labels. Arrows presented in the plane of the slides were in other conditions used to create different associations between the compass directions and the egocentric directions right-left and front-behind. In a subsequent RT task subjects indicated if the directions were the same or different in two consecutively presented slides. No reliable effects were found for same responses but different responses supported the hypothesis in being slower for east-west than north-south when associated with right-left (or left-right) and faster when associated with front-behind (or behind-front).     

De Re Language,De Re Eliminability,and the Essential Limits of Both

De re modality is eliminable if there is an effective translation of all wffs into non-de re equivalents. We cannot have logical equivalence unless logic has odd theses, but we can have material equivalence by banning all essences, something the non-de re facts let us do, or by giving everything such humdrum essences as self-identity and banning the more interesting ones. Eliminability cannot be got from weaker assumptions, nor independent ones of even modest generality. The net philosophical import is that, quite apart from the merits of essentialism, de re language has scant utility.     

Methods for describing ordinal data with cardinal models

Several methods, both new and old, for describing ordinal data with a cardinal model are discussed in a newly developed and general context which broadens their applicability beyond their traditional use in multidimensional scaling. The relationships between the methods is investigated. It is shown that the two most commonly used methods (Guttman's rank-image principle and Kruskal's least-square monotonic transformation) are the boundary conditions of a newly proposed single parameter family of methods. An additional method is proposed which is shown to yield an equal-density model space. The commonly made distinction between “transformation” methods and “transformation-free” methods is shown to be a pseudodistinction. It is observed that all the methods can be stated as matrix operations on the model space with the conclusion that they try to optimize a linear combination of the model space.     

The ABC of cardinal and ordinal number representations

Numerical cognition encompasses the concepts of quantity ('how many?') and serial order ('which position?'). Yet, although numbers can convey different meanings, a recent imaging study by Fias and coworkers showed that ranking letters in the alphabet is subserved by a cortical network highly similar to that involved in judging magnitudes. In terms of neural processing, quantity and rank might just be two sides of the same coin.     

A new secretary problem with rank-based selection and cardinal payoffs

We present an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables X₁,X₂,…,X_n drawn i.i.d. from a uniform distribution on [0,1]. The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of x_t, the realization of X_t, for selecting the tth applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far. We prove that the optimal policy dictates skipping the first sqrt(n)-1 applicants, and then selecting the next encountered applicant whose value is a maximum.     

Inducing ordinal and cardinal representations of the first five natural numbers

The prediction that the ordinal property of natural number symbols (using these symbols to represent the terms in an ordered progression) is more easily learned than the cardinal property of natural number symbols (using these symbols to represent the manyness of collections) was examined in this experiment. Preschoolers who evidenced no proficiency with either the ordinal or cardinal properties of natural number symbols were trained to acquire these properties via simple feedback. Both properties proved to be trainable. The most important findings were that the ordinal property was much easier to train than the cardinal property, ordinal training effects were more durable across a 1-week interval than cardinal training effects, and ordinal training appeared to transfer better than cardinal training.     

Reference-frame misalignment and cardinal direction judgments: group differences and strategies

In 3 experiments, the authors examined how misalignment of egocentric and exocentric reference frames affects cardinal direction judgments. Experiments 1 and 2 demonstrated large differences in the accuracy and speed with which 104 less experienced and 7 experienced navigators made cardinal direction judgments. Reference-frame misalignment was associated with large performance decrements. The extent of these decrements diminished as ability and experience increased: however, even experienced navigators showed decrements when reference frames were misaligned. In Experiment 3, the authors used 55 college students to examine the individual subtasks of a common strategy for cardinal direction judgments and to isolate the effects of reference-frame misalignment to a particular subtask of this strategy. The tasks and strategies studied in this article can be applied in the development of navigational training and interfaces.     

About why there is a shift from cardinal to ordinal processing in the association with arithmetic between first and second grade

Digit comparison is strongly related to individual differences in children's arithmetic ability. Why this is the case, however, remains unclear to date. Therefore, we investigated the relative contribution of three possible cognitive mechanisms in first and second graders’ digit comparison performance: digit identification, digit–number word matching and digit ordering ability. Furthermore, we examined whether these components could account for the well‐established relation between digit comparison performance and arithmetic. As expected, all candidate predictors were related to digit comparison in both age groups. Moreover, in first graders, digit ordering and in second graders both digit identification and digit ordering explained unique variance in digit comparison performance. However, when entering these unique predictors of digit comparison into a mediation model with digit comparison as predictor and arithmetic as outcome, we observed that whereas in second graders digit ordering was a full mediator, in first graders this was not the case. For them, the reverse was true and digit comparison fully mediated the relation between digit ordering and arithmetic. These results suggest that between first and second grade, there is a shift in the predictive value for arithmetic from cardinal processing and procedural knowledge to ordinal processing and retrieving declarative knowledge from memory; a process which is possibly due to a change in arithmetic strategies at that age. A video abstract of this article can be viewed at: https://youtu.be/dDB0IGi2Hf8     

Children acquire the later‐greater principle after the cardinal principle

Many have proposed that the acquisition of the cardinal principle (CP) is a result of the discovery of the numerical significance of the order of the number words in the count list. However, this need not be the case. Indeed, the CP does not state anything about the numerical significance of the order of the number words. It only states that the last word of a correct count denotes the numerosity of the counted set. Here, we test whether the acquisition of the CP involves the discovery of the later‐greater principle – that is, that the order of the number words corresponds to the relative size of the numerosities they denote. Specifically, we tested knowledge of verbal numerical comparisons (e.g., Is ‘ten’ more than ‘six’?) in children who had recently learned the CP. We find that these children can compare number words between ‘six’ and ‘ten’ only if they have mapped them onto non‐verbal representations of numerosity. We suggest that this means that the acquisition of the CP does not involve the discovery of the correspondence between the order of the number words and the relative size of the numerosities they denote.     

Up north and down south: Implicit associations between topography and cardinal direction

Route planners show a reliable tendency to select south- relative to north-going routes between two horizontally (east/west) aligned landmarks, suggesting the application of a north-is-up heuristic (Brunyé, Mahoney, Gardony, & Taylor, 2010). The source of this north-is-up bias remains unknown, and there is no strong evidence to suggest that it is due to explicit strategy use. In four experiments, we attempt to further elucidate the source of this effect by testing whether it can be attributed to implicit associations between cardinal direction (north/south) and topography (mountainous/level terrain). Experiments 1 and 2 used an adapted Implicit Association Test and demonstrate automatically activated judgements that associate north with mountainous and south with relatively level terrain. Experiment 3 rules out the possibility that this effect is due to the local topography of New England by replicating in participants from the topographically dissimilar Midwestern United States. Finally, Experiment 4 tests the relative contribution of implicit versus explicit associations between cardinal direction and topography in predicting route-planning asymmetries; we show that implicit associations are a stronger predictor of southern route biases than explicit processes. Overall, results demonstrate that the conceptualization of space can be driven by physically unfounded implicit associations between cardinal directions and topographical features, and these associations are at least partially responsible for southern route preferences.     

Up north and down south: Implicit associations between topography and cardinal direction

Route planners show a reliable tendency to select south- relative to north-going routes between two horizontally (east/west) aligned landmarks, suggesting the application of a north-is-up heuristic (Brunyé, Mahoney, Gardony, & Taylor, 2010). The source of this north-is-up bias remains unknown, and there is no strong evidence to suggest that it is due to explicit strategy use. In four experiments, we attempt to further elucidate the source of this effect by testing whether it can be attributed to implicit associations between cardinal direction (north/south) and topography (mountainous/level terrain). Experiments 1 and 2 used an adapted Implicit Association Test and demonstrate automatically activated judgements that associate north with mountainous and south with relatively level terrain. Experiment 3 rules out the possibility that this effect is due to the local topography of New England by replicating in participants from the topographically dissimilar Midwestern United States. Finally, Experiment 4 tests the relative contribution of implicit versus explicit associations between cardinal direction and topography in predicting route-planning asymmetries; we show that implicit associations are a stronger predictor of southern route biases than explicit processes. Overall, results demonstrate that the conceptualization of space can be driven by physically unfounded implicit associations between cardinal directions and topographical features, and these associations are at least partially responsible for southern route preferences.     

Dissociating between cardinal and ordinal and between the value and size magnitudes of coins

In mathematics, the ordinal (relative) magnitude of a numerical object conveys a separate meaning from its cardinal (absolute) magnitude, whereas its physical size bears no inherent relationship to its magnitude. In numerical cognition, the ordinal-cardinal distinction has been scarcely addressed, whereas the size-magnitude distinction has been studied extensively, with the surprising demonstration of an interaction between semantic magnitude and physical size (Besner & Coltheart, 1979). The present work used coins to study the intricate relations between these meanings. In two experiments, Israeli observers (Experiment 1) and American observers (Experiment 2) performed numerical and physical comparative judgments of coins. Consensual markers of magnitude activation (e.g., the size congruity effect and the distance effect) were obtained. The results of the two experiments converged on the same conclusions. Comparisons of value were governed by ordinal magnitude. Magnitude interfered with comparisons of size, but size did not affect value. The results provided a set of clear dissociations between cardinal and ordinal magnitude and between value and size of coins. They highlight the important role played by ordinal information in magnitude processing.     

企业所有者与经营者双方合理确定合同基数的激励模型

1　引言　　在现代企业制度下 ,企业的所有权和经营权相分离 ,经营者对企业的经营成败负有主要责任 ,而经营者的报酬设计对他们的行为产生直接的影响。而且 ,两权分离的程度越高 ,激励性报酬在缩小所有者和经营者之间的利益差异 ,并在降低监督成本方面的作用就越高。因此 ,企业经营者的报酬制度是经营者激励机制良好运行的关键。经营者报酬主要包括经营者的基薪和剩余索取权两大部分。基薪一般不与经营者的业绩挂钩 ,对经营者没有什么激励作用 ;剩余索取权将经营者的收益与经营业绩直接挂钩 ,对经营者的激励作用较为明显。剩余索取权的实现…     

Grey parrot number acquisition: The inference of cardinal value from ordinal position on the numeral list

A Grey parrot (Psittacus erithacus) had previously been taught to use English count words ("one" through "sih" [six]) to label sets of one to six individual items (Pepperberg, 1994). He had also been taught to use the same count words to label the Arabic numerals 1 through 6. Without training, he inferred the relationship between the Arabic numerals and the sets of objects (Pepperberg, 2006b). In the present study, he was then trained to label vocally the Arabic numerals 7 and 8 ("sih-none", "eight", respectively) and to order these Arabic numerals with respect to the numeral 6. He subsequently inferred the ordinality of 7 and 8 with respect to the smaller numerals and he inferred use of the appropriate label for the cardinal values of seven and eight items. These data suggest that he constructed the cardinal meanings of "seven" ("sih-none") and "eight" from his knowledge of the cardinal meanings of one through six, together with the place of "seven" ("sih-none") and "eight" in the ordered count list.     

Living in the north is not necessarily favorable: Different metaphoric associations between cardinal direction and valence in Hong Kong and in the United States

The Conceptual Metaphor Theory (e.g., Lakoff & Johnson, 1980 ) suggests that people represent abstract concepts in terms of concrete concepts via metaphoric association. Participants in the United States (US) showed that cardinal direction (north/south) is metaphorically associated with valence (positive/negative), as reflected by their estimate for where a person with high or low socioeconomic status (SES) lives in a fictional city or their own living preference (Meier, Moller, Chen, & Riemer‐Peltz, 2011 ). The present study tested whether the cardinal direction–valence metaphoric association could be moderated by cultural differences. Although US participants believed that high‐SES and low‐SES individuals were more likely to live in the northern and southern part of the city, respectively, the reverse was so for Hong Kong (HK) participants (Study 1). When asked where they themselves would like to live, HK participants preferred to live in a southern area, whereas US participants showed no preference (Studies 2 and 3). These findings demonstrate cultural differences in metaphoric associations between cardinal direction and valence for HK and US participants. Copyright © 2014 John Wiley & Sons, Ltd.     

A Butterfly Dream in a Brain in a Vat

Zhuangzi’s Butterfly Dream story can be read as a skeptical response to the Cartesian Cogito, ergo sum solution, for it presents I exist as fundamentally unprovable, on the grounds that the notion about “I” that it is guaranteed to refer to something existing, which Descartes seems to assume, is unwarranted. The modern anti-skepticism of Hilary Putnam employs a different strategy, which seeks to derive the existence of the world not from some “indubitable” truth such as the existence of myself, but from the meaning of some particular assertion I make. In this paper, I argue, however, that Putnam’s argument fails to deliver on the promise of showing the self-refuting nature of the skeptical hypothesis, as it relies on a double use of “I”, a fallacy of equivocation, reflecting an unsolved tension between the argument’s general premise, which is rather Zhuangzian in spirit, and his unwitting adoption of that unwarranted notion about “I”. I try to show further that the skepticism in Zhuangzi’s Butterfly Dream not only can be used to refute the proofs of the existence of the empirical I, but also is effective against accounts concerning the existence of the transcendental I.     

Finding a face in a face-like object

Humans have the tendency to perceive a face even in a non-living object. Previous studies report that people perceive facial features and even interpret a personality in a car front. Following these findings, we investigated whether the perception of a face in a face-like object is mediated by human face processing, which involves both featural and configural processing. In our experiment, participants were presented with 30 face-like objects and were asked about the existence of facial features, the intensity of typicality/distinctiveness, and the intensity of facial expression. Using multiple regression analysis, which predicts the perception of a face in a face-like object, we found that the existence of eyes was a significant predictor of variance in perceiving a face in a face-like object.