A General Setting for Dedekind's Axiomatization of the Positive Integers

A Dedekind algebra is an ordered pair (B, h), where B is a non-empty set and h is a similarity transformation on B. Among the Dedekind algebras is the sequence of the positive integers. From a contemporary perspective, Dedekind established that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable. The purpose here is to show that this seemingly isolated result is a consequence of more general results in the model theory of second-order languages. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ?₀ isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on ω called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type that occurs in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. The second-order theory of any countably infinite Dedekind algebra is categorical, and there are countably infinite Dedekind algebras whose second-order theories are not finitely axiomatizable. It is shown that there is a condition on configuration signatures necessary and sufficient for the second-order theory of a Dedekind algebra to be finitely axiomatizable. It follows that the second-order theory of the sequence of the positive integers is categorical and finitely axiomatizable.     

GUILT AND THE SCIENCE OF EMOTION: HOW DOES PRAYER FIT?

This article engages sources regarding evolutionary development of guilt (Richard Joyce's The Evolution of Morality, Jesse Prinz's Gut Reactions, and others) and how they can be used to dialogue with material on the alleviation of guilt in the Christian tradition using examples in the work of Anselm of Canterbury and John Chrysostom. This raises a few key questions. If guilt is an evolutionary trait created to build reputation and relationship, how does this mesh with some theological approaches to solutions for guilt? To be more precise, guilt possibly evolved to create a motivation for beneficial communal actions, and necessitates belief in the authority of the rules that one breaks to induce it. That said, does religion play a role in awareness of one's guilt, while also providing a solution to that guilt? The possibilities are explored in this article as they relate to issues of repentance, atonement, and prayer.     

Socio-economic health inequalities: Their origins and implications

Abstract

Evidence attests to substantial variations in health contingent on socioeconomic position. It is argued that these effects cannot be dismissed as artefact nor can they be explained, in the main, by either social selection or an unequal distribution of accepted behavioural risk factors among different social groups. The most likely explanation would seem to be social causation. However, it is continuing social and material inequality that appears most implicated; accounts which locate the effects in childhood social and material causes are far less compelling. The persistence of socioeconomic health differentials into the materially better-off social strata and the possible determining role of relative as well as absolute living standards suggest that psychological, in addition to material, variables are likely to be involved. Isolating the key psychological variables and identifying the nature of their influences will not be easy tasks, although social relations, psychological stress, uplifts, and control have emerged as possible candidates. However, psychological mediators of this sort most probably constitute surface rather than basic causes. Socio-economic inequality, it is contended, remains the basic cause, and, as such, the proper target for intervention. Psychological interventions are unlikely to yield much in the way of dividends in this context and indeed could inadvertently contribute to victim blaming.     

Socio-ecological influences of attitudes toward disability among Kenyan undergraduate students

This study examined personal and contextual variables as predictors of attitudes toward disability at a Kenyan higher education setting. Participants were a convenience sample of 309 undergraduate students at a Kenyan university enrolled in Sociology, Social Work, Psychology, Political Science, and Public Administration majors. Data on attitudes were collected using the Attitudes Towards Disabled Persons scale (ATDP: Antonac & Livneh, 1988). A cross-sectional survey design was employed for data collection, and a multiple regression analysis was used for data analysis. Results revealed that the model was significant: F (9, 250)?=?2.784, p?=?0.004. However, only age (β?=?0.173, p?=?0.044) significantly predicted attitudes towards disability, indicating older students held more positive attitudes than their younger counterparts. Older students had a more favourable attitude towards people with disabilities than younger students. Seniority, by age, is highly valued in Africa than perhaps anywhere in the world. Kenyan older adults may be key to enhancing favourable attitudes toward individuals with disabilities in Kenya as well as interventions aimed at changing negative attitudes towards people with disabilities.     

Prolepsis and the Physics of Retrocausality

Ted Peters has emphasized the theological concept of prolepsis and a “retroactive ontology” in which God creates from the future. We consider here possible connections between prolepsis and scientific theories about transmission of signals backwards in time. After considering objections to time travel, we discuss putative means of achieving it—tachyons, “time machine” solutions of Einstein's equations, waves in dark energy, and advanced solutions of wave equations. We then reflect on ways those theoretical constructs, if realized, might be of theological interest. Applications to the resurrection of Jesus, predictive prophecy and the creation of the universe will be discussed.     

The Relationships Among Differing Loss Experiences,Adjustment, Beliefs,and Coping

Abstract

Losses are often equated for conceptual purposes, and it is often assumed that different types of losses result in similar grief reactions and exert similar effects on cognitive structures and coping patterns. This article examines the expectancies, beliefs, coping patterns, and psychological adjustment associated with loss due to death, parental. divorce, or illness and disability in a college student population. Loss groups did not differ from each other or from a no-loss group on cognitive variables, coping, or psychological adjustment. In instances in which associations between the cognitive measures and either coping or adjustment were indicated, the typical pattern was for loss groups to differ from the no-loss condition but not from each other.     

Test anxiety,emotional responding under guided imagery,and self-talk during an academic examination

Abstract

This investigation examined the assumption that phenomenological responses created by guidedimagery procedures pertinent to test anxiety are topographically similar to emotional responses experienced during an actual examination. Participants were divided on facilitating versus debilitating test anxiety and exposed to subclinical doses of stimulus-response propositions that involved test-taking, fear, and physical activity using the induction technique employed by Lang et al. (1980). Patterns of emotional responses obtained after each induction were compared to the pattern elicited immediately prior to students' final course examination as well as self-talk during the examination. Results indicated that exposure to test-related imagery elicited a pattern of emotional responding that was different than exposure to fear or action imagery but was nearly identical to emotional responses found before examinations. Negative emotional states before the examination also were associated with higher frequencies of negative self-statements during the examination. Treatment implications of these findings were explored.     

Kelly's Thought At Age 33: Suggestions For Conceptual And Methodological Refinements

Abstract

This paper argues that Neimeyer's (1985) crisis in methodology might not actually imply an overuse of grid techniques. Instead, the problem might consist of a serious underutilization of slightly different (but nonetheless constructivist) conceptual schemes and alternative methodologies derived from these conceptual schemes. In taking needed research risks we might hasten the next steps in the evolution of personal construct theory.     

Distance perception from motion parallax and ground contact

Meng and Sedgwick (2001, 2002) found that the perceived distance of an object in a stationary scene was determined by the position at which it contacted the ground in the image, or by nested contact relations among intermediate surfaces. Three experiments investigated whether motion parallax would allow observers to determine the distance of a floating object without intermediate contact relations. The displays consisted of one or more computer-generated textured cylinders inserted into a motion picture or still image of an actual 3-D scene. In the motion displays, both the cylinders and the scene translated horizontally. Judged distance for a single cylinder floating above the ground was determined primarily by the location at which the object contacted the ground in the projected image (“optical contact”), but was altered in the direction indicated by motion parallax. When more than one cylinder was present and observers were asked to judge the distance of the top cylinder, judged distance moved closer to that indicated by motion parallax, almost matching that value with three cylinders. These results indicate that judged distance in a dynamic scene is affected both by optical contact and motion parallax, with motion parallax more effective when multiple objects are present.