MODELING RELATIONS

In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. The question is what is the internal structure of relations? Is the use of positions still justified, and if so, what is their ontological status? In this paper mathematical models for relations are developed that provide more insight into the structure of relations “out there” in the real world.     

Apprentissage de concepts perceptuels, associationnels et relationnels chez le pigeon

The study of concepts in cognitive psychology has generally been anthropocentric with respect to both content and theory. A broader comparative perspective on the various forms of concept learning would provide a more inclusive view of conceptual behavior. It would also provide a more objective perspective from which to identify underlying processes. Several of the major varieties of conceptual classes claimed for humans alone also appear to be represented in nonhuman animals and young children: perceptual classes involving classification according to the shared attributes of objects, associative classes or functional equivalences in which stimuli form a class based on common associations and relational classes, in which the conceptual relationship between stimuli defines the class.     

The Space–Time Congruency Effect: A Meta‐Analysis

Several reaction time (RT) studies report faster responses when responses to temporal information are arranged in a spatially congruent manner than when this arrangement is incongruent. The resulting space–time congruency effect is commonly attributed to a culturally salient localization of temporal information along a mental timeline (e.g., a mental timeline that runs from left to right). The present study aims to provide a compilation of the published RT studies on this time–space association in order to estimate the size of its effect and the extent of potential publication bias in this field of research. In this meta‐analysis, three types of task are distinguished due to hitherto existing empirical findings. These findings suggest that the extent to which time is made relevant to the experimental task has a systematic impact on whether or not the mental timeline is activated. The results of this meta‐analysis corroborate these considerations: First, experiments that make time a task‐relevant dimension have a mean effect size of d = 0.46. Second, in experiments in which time is task irrelevant, the effect size does not significantly deviate from zero. Third, temporal priming studies have a surprisingly high mean effect size of d = 0.47, which, however, should be adjusted to d = 0.36 due to publication bias.     

The mathematics of geographic profiling

We begin by describing some of the mathematical foundations of the geographic profiling problem. We then present a new mathematical framework for the geographic profiling problem based on Bayesian statistical methods that makes explicit connections between assumptions on offender behaviour and the components of the mathematical model. It also can take into account local geographic features that either influence the selection of a crime site or influence the selection of an offender's anchor point. Copyright © 2009 John Wiley & Sons, Ltd.     

Choosing normative properties: a reply to Eklund’s Choosing Normative Concepts

ABSTRACT

The literature surrounding Horgan and Timmons’s Moral Twin Earth scenarios has focused on whether such scenarios present a metasemantic problem for naturalist realists. But in Choosing Normative Concepts, Eklund uses a similar scenario to illuminate a novel, distinctly metaphysical problem for normative realists of both naturalist and non-naturalist stripes. The problem is that it is not clear what (if anything) would suffice for the sort of ardent realist view that normative realists have in mind – the view that reality itself favors certain ways of acting and valuing. Eklund then offers a metasemantic view that he thinks can provide the best solution to this problem. In this reply to Eklund, I argue that Eklund’s treatment of the problem and his solution re-entangle metaphysical and metasemantic issues that ought to be kept separate. I also argue that there is a purely metaphysical solution to the problem at hand, which Eklund’s own solution seems to implicitly rely upon. While these criticisms do not suggest that Eklund’s positive view is false, they do undermine some of the broader lessons that Eklund hopes to draw from the view.     

The roles of different executive functioning skills in young children’s mental computation and applied mathematical problem-solving

This study investigated the relationships of four executive functioning skills (including verbal working memory, spatial working memory, inhibitory control, and cognitive flexibility) with young children’s mental computation and applied mathematical problem-solving. Two hundred and twenty-five Chinese kindergarteners were tested with a battery of general cognitive, executive functioning and mathematics skills. Results showed that when children’s age, gender, non-verbal intelligence, and listening comprehension skills were controlled, verbal working memory and cognitive flexibility were significant correlates of mental computation, whereas verbal working memory, spatial working memory, and cognitive flexibility were significant correlates of applied mathematical problem-solving. Inhibitory control was not significantly associated with the two domains of mathematics under investigation. The findings highlight the differential roles of different executive functioning skills in early mathematical skills and offer practical implication for helping young children in learning complex mathematical skills.     

Conceptual engineering for mathematical concepts

In this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory.     

Not quite neo-sentimentalism

The view that some evaluative concepts are identical to some affective concepts naturally falls out of neo-sentimentalism, but it is unstable. This paper argues for a view of evaluative concepts that is neo-sentimentalist in spirit but which eschews the identity claim. If we adopt a Peacockean view of concepts, then we should think of some evaluative concepts as having possession conditions that are affective in some way. I argue that the best version of this thought claims that possessing those concepts requires being rationally compelled to form evaluative beliefs in response to certain emotions.     

个体近似数量系统与其数学能力之间的关系：发展研究的证据

近似数量系统在个体数学能力的发展中起着重要的作用, 二者之间的关系受到年龄因素的影响。主要表现为, 随着年龄的增长, 相关程度逐渐减弱, 二者之间关系的作用机制可能由基数知识中介转变为多种中介变量的共同作用。未来可采用更严格的实验设计和多种研究方法考察各年龄段儿童近似数量系统与不同数学能力之间关系的发展趋势、因果方向、关键转折点和潜在机制, 以更好地理解近似数量系统在个体数学能力发展中所起的作用。     

Attributes of God: Conceptual Foundations of a Foundational Belief

Anthropomorphism, or the attribution of human properties to nonhuman entities, is often posited as an explanation for the origin and nature of God concepts, but it remains unclear which human properties we tend to attribute to God and under what conditions. In three studies, participants decided whether two types of human properties—psychological (mind‐dependent) properties and physiological (body‐dependent) properties—could or could not be attributed to God. In Study 1 (n = 1,525), participants made significantly more psychological attributions than physiological attributions, and the frequency of those attributions was correlated both with participants’ religiosity and with their attribution of abstract, theological properties. In Study 2 (n = 99) and Study 3 (n = 138), participants not only showed the same preference for psychological properties but were also significantly faster, more consistent, and more confident when attributing psychological properties to God than when attributing physiological properties. And when denying properties to God, they showed the reverse pattern—that is, they were slower, less consistent, and less confident when denying psychological properties than when denying physiological properties. These patterns were observed both in a predominantly Christian population (Study 2) and a predominantly Hindu population (Study 3). Overall, we argue that God is conceptualized not as a person in general but as an agent in particular, attributed a mind by default but attributed a body only upon further consideration.