Fractal Images of Formal Systems

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex value spaces, with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic.\looseness=-1     

Some correlates of health locus of control among multicultural individuals

The relationship of locus of control to depression, anxiety, hostility, and physical health was assessed in a sample of multicultural college students (N = 162). Powerful Others Health Locus of Control was correlated with depression, anxiety, hostility, and recent physical symptoms while Chance Health Locus of Control (CHLC) was correlated with all of the above as well as chronic physical symptoms and major health problems. When controlling for a variety of health risk factors (viz., age, sex, body mass, exercise, smoking, salt, alcohol, and caffeine), only CHLC remained significant in the physical health models. Results support the cognitive model of mental health which emphasize the importance of adaptive beliefs. Specifically, they suggest that issues about control are related to negative affect and indicate that the often-cited relationship of an external locus of control to depression and anxiety also holds for hostility. The findings do not, however, support the view that anxiety and depression are associated with different types of external locus of control but rather suggest a unified set of locus of control beliefs underlying the three types of negative affect. In addition, evidence is provided for the external validity of the Multidimensional Health Locus of Control (MHLC) Scales with respect to mental health. Further, the results indicate that belief about one’s health may play a significant role in one’s physical health and that the health behavior model of the relationship between locus of control and physical health is insufficient to explain the relationship. As the Chance and Powerful Others MHLC scales were not related to health habits in this sample but were related to mental health (viz., depression, anxiety, and hostility), locus of control beliefs may be related to physical health via their relationship with mental health.     

Positive and Negative Hypothesis Testing by Cooperative Groups

In a rule induction problem positive hypothesis tests select evidence that the tester expects to be an example of the correct rule if the hypothesis is correct, whereas negative hypothesis tests select evidence that the tester expects to be a nonexample if the hypothesis is correct. Previous research indicates the general effectiveness of a positive test strategy for individuals, but there has been very little research with cooperative groups. We extend the analysis of Klayman and Ha (Psychological Review, 1987) of ambiguous verification or conclusive falsification of five possible types of hypotheses by positive and negative tests by emphasizing the importance of further examples following hypothesis tests. In two experiments four-person cooperative groups solved rule induction problems by proposing a hypothesis and selecting evidence to test the hypothesis on each of four arrays on each trial. In different conditions the groups were instructed to use different combinations of positive and negative tests on the four arrays. Positive tests were more likely to lead to further examples than negative tests, and the proportion of correct hypotheses corresponded to the proportion of positive tests, in both experiments. We suggest that positive tests are more effective than negative hypothesis tests in generating further evidence, and thus in inducing the correct rule, in experimental rule induction tasks with a criterion of certainty imposed by the researcher.     

SEEING TWO AS ONE:

Abstract -Object tokens are episodic visual representations that mediate the ability to track visual events as they move about and change over time. Multiple tokens also allow the viewer to individuate multiple instances of a single type of object. In the present study, we established a functional link for object tokens in two seemingly disparate visual phenomena: apparent motion and repetition blindness [RB]. In RB, repeated items are more difficult to perceive than unre-peated items. Using displays in which two sets of alphanumeric characters streamed in opposite directions across a computer screen in apparent motion, we found increased RB for targets appearing within a single apparent motion stream, relative to targets in different apparent motion streams. The results are inconsistent with refractory period or memory retrieval accounts of RB and support the role of object tokens in both apparent motion and RB.     

The double bind of caregiving: Representation of gendered emotion in American advice literature

Parent advice books written for the traditional, intact biological family represent maternal and paternal emotion quite differently from one another [S. A. Shields and B. A. Koster (1989) Emotional Stereotyping of Parents in Child-Rearing Manuals, Social Psychology Quarterly, Vol. 52, pp. 44–55]. This study examined gender-specific references to emotion in advice books directed to adoptive parents, step-parents, single parents, and married couples in order to determine the relationship between beliefs about women's and men's emotional natures and beliefs about caregiving. The gendered representation of caregivers' emotion is remarkably consistent across time, parenting genre, and author characteristics. Books directed to parents portray women as at risk for excessive emotions (both positive and negative) that have negative developmental impact on the child. In contrast, men are largely encouraged to be emotionally expressive, and when they are cautioned about their emotional display, the caution is restricted to negative emotions that are elicited by external emotional hazards: the children, the spouse (or ex-spouse), or the situation. In contrast, marriage manuals portray spouses as mutually responsible for their own and their spouse's emotional well-being. Husbands and wives are encouraged to express unlimited positive emotion and to engage in moderated ventilation of negative emotion. In our discussion of these results we consider the role of emotion representation in promoting a culture of mother blaming.We are indebted to Diane Early, Diane Hayashino, Nancy Kohn, and Sonja Jensen for their assistance in collecting and interpreting the data. This research was supported by University of California, Davis, Faculty Research Grants to S. Shields.     

School Counseling: An Evolving Specialty

This article provides a review of school counseling as a specialty area of the counseling profession, including attention to historical development, training standards and accreditation, certification, and future trends and issues.     

Simulation and the Reproduction of Injustice: A Reply

Melinda Vadas rejects my claim that there are morally relevant differences between simulations of unjust events and actual unjust events on the ground that I overlook the connection between simulations and that which they simulate. I argue that this purported moral connection can only be understood as either the result of a necessary psychological disposition or as a “magical,” metaphysical attachment, neither of which is defensible or satisfactory.     

The holocaust of first nation people: Residual effects on parenting and treatment implications

The residential school experience was devastating for many First Nation (Indian) people. The lingering effects of this era have been far reaching and remain painfully evident throughout Native communities. One of the more obvious areas directly affected has been parenting. This paper discusses current parenting difficulties of Native clients who were formerly in residential schools. A connection is made between the abuse experienced by these individuals and their parental struggles. Along with addressing various sociopolitical issues, a number of clinical interventions designed to promote the healing process of these victims and their families are provided and discussed.     

Success,social comparison,and self-assessment: Parents' midlife evaluations of sons,daughters, and self

The literatures on sex-role socialization and social comparison theory were used to predict how parents would evaluate the life success of adult sons and daughters and how parents' assessments of themselves would be influenced by comparisons with these children. Although parents (N=215) did not report different levels of life success for 291 adult sons versus 251 adult daughters, parental well-being was more closely tied to assessments of sons' success. In addition, although parents' reported that both sons and daughters had exceeded their own life success, theparent-child comparison with daughters was the better predictor of parents' well-being. Findings are discussed in terms of parents' individual development, family processes at midlife, and cohort differences between parents and their children.