Mathematical concepts for analyzing ambiguous situations

Abstract

We examine some mathematical tools for dealing with ambiguous situations. The main tool is the use of non-standard logic with truth-values in what is called a locale. This approach is related to fuzzy set theory, which we briefly discuss. We also consider probabilistic concepts. We include specific examples and describe the way a researcher can set up a suitable locale to analyse a concrete situation.     

Sacrifice and At-one-ment: Joseph de Maistre and Cudworth's Types and Shadows Admired

This article pursues the perhaps surprising interest of the Savoyard polemicist and counter-revolutionary philosopher Joseph de Maistre for the early work of the Cambridge Platonist Ralph Cudworth. I argue that their shared Platonism and fascination for the imagery of the Temple of the Hebrews helps explain this unlikely alliance. I refer to the innovative work of Margaret Barker on Temple imagery in Christian theology to elucidate the biblical dimension of the theory of correspondences employed by both men.     

Psychological Type: A 32-Year Follow-Up

This study is a follow-up to three previous studies of psychological type published in this Journal in 1964, 1976 and 1978 by Bradway, Bradway and Detloff, and Bradway and Joseph Wheelwright. Participants in all of our studies were limited to Jungian analysts and candidates. Participants of the first two studies and of the current study were from California; participants of the 1978 study included the participants from the previous study plus persons attending the 1974 International Congress in London. In 1993 we sent letters to the 232 current analysts and candidates in the San Francisco and Los Angeles C.G. Jung Institutes, as well as to the nine participants in our 1974 study who were no longer members of the Institutes but could be located, asking them to fill out a questionnaire that included self-typing, and to self-administer the Gray-Wheelwrights Jungian Type Survey (GW). The response rate was high: 196 or 81% of the 241 persons to whom we sent letters returned filled-in questionnaires and GWs; all 67 or 100% of the participants in the 1974 study who could be located returned the filled-in material. Eight of those 67 had also been in the 1961 study. The current study provides data on the changes in psychological type over time, in some instances over a period of 32 years. It added for the first time a consideration of analysts' rating of themselves as primarily clinically or symbolically orientated, and a survey of analyst opinions as to the determinants of psychological type. Summarizing the results: A smaller percentage of analysts typed themselves as intuitive thinking than in 1961; the percentages of congruence between self-typing and the Gray-Wheelwrights scores in the three dimensions (introvert/extravert, sensation/intuition, and thinking/feeling) in 1961, 1974 and 1993 are between 76% and 96%; changes in typology from 1961 to 1993 occur more frequently in the younger age group than in the older age group; 65% of the participants considered the distinction between clinical and symbolic important, but only 41% rated themselves as either primarily clinically oriented or symbolically oriented with essentially no relationship between that orientation and typology; a sub-study of typology of partners within this study does not support the concept that opposites marry; according to the opinion of this group of analysts and candidates as to the determinants of adult typology, genetics (chromosomes) is distinctly the strongest contributor with family dynamics a not-very-close next contributor.     

Empirical derivation of SVIB-Holland scales and conversion tables

Significant relationships between the Holland Vocational Preference Inventory (VPI) and the Strong Vocational Interest Blank (SVIB) were again empirically demonstrated in this study, and conversion equations were developed to use standard scores of SVIB scales, rather than items, to produce estimates of VPI scores. Cross validation on a limited population yielded supportive evidence that these conversion equations can provide meaningful VPI estimates from SVIB scale scores. The need for validation across a variety of populations was underscored in order to assess further generalizability of these findings.     

Prototypes of Faith: Findings with the Faith Q‐Sort

Defining religion and finding ways to assess it in individual lives has long challenged psychologists of religion. At first, open‐ended questionnaires were used, but with the advent of modern statistical methods, a succession of religiosity scales was developed. But these usually brief scales were typically based on the preconceptions of their authors, who were overwhelmingly Protestant Christian and often conservative, much as were those who completed them. To provide a more adequate way of assessing “faith,” a term here encompassing both religious and nonreligious attitudes, a new assessment device was developed that incorporates the singular advantages of Q methodology. The Faith Q‐Sort consists of 101 statements that respondents sort on a nine‐category continuum, indicating the degree to which each statement describes himself or herself. Factor analysis based on correlations of the sorts rather than individual items yielded, for the initial group of participants, three major prototypes and five minor ones, accounting for 67 percent of the variance. Of the 42 participants, 31 proved to be exemplars of one or another of the eight prototypes. Subsequent explorations illustrate the wealth of possibilities the FQS offers, both as a research instrument and a counseling tool.     

Features and investigative implications of muti murder in South Africa

Drawing upon anthropological, legal and forensic publications, an interview with a South African Zulu traditional healer and direct information gained during homicide investigations, the nature of Muti murder is discussed. Muti murder is defined as a murder in which body parts are removed from a live victim for the sole purpose of using the victim's body parts medicinally. These body parts are then often mixed with other ingredients or used alone to make a medicine called muti. Muti is a Zulu (umuthi) word meaning medicine. The victim usually dies as a result of blood loss from the wounds. While muti murders have occurred throughout history in South African culture, little is known about them and little research exists on the phenomenon. The term muti murder has been used interchangeably with the term ritual or sacrificial murder, often adding to confusion in terminology and definitions regarding these types of cases. This paper provides an overview of muti murder, explains the context in which these types of murder occur, defines the offenders and victims involved, and provides guidelines for investigating these types of murders. Two cases where muti murder was suspected are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Interpreting Self-Directed Search profiles: Validity of the “Rule of Eight”

Based on the standard error of measurement, Holland (1985) suggested the “rule of eight” for determining the meaningfulness of differences between two summary scores on the Self Directed Search. The present study empirically examined the rule's validity for practice. The participants were 2397 (1497 females and 900 males) undergraduate students enrolled in the exploratory major at a large Midwestern university. The results strongly supported the interpretive rule of eight. For those participants who scored a primary-code distinction of eight or more points, the hit rate was 55% with a kappa of .38. This compared to a hit rate of 40% with a kappa of .21 for those participants with less than eight-point distinction between their top two scores. The authors also discuss the practical implications for interpreting SDS results using the “rule of eight.”