Counterfactuals and the applications of mathematics

Conclusion It has been argued that the attempt to meet indispensability arguments for realism in mathematics, by appeal to counterfactual statements, presupposes a view of mathematical modality according to which even though mathematical entities do not exist, they might have existed. But I have sought to defend this controversial view of mathematical modality from various objections derived from the fact that the existence or nonexistence of mathematical objects makes no difference to the arrangement of concrete objects. This defense of the controversial view of mathematical modality obviously falls far short of a full endorsement of the counterfactual approach, but I hope my remarks may serve to help keep such an approach a live option.     

Should a school honor a student's DNR order? A physician/ethicist responds: a student's rights are not so simple.

...S.A. has a right to refuse treatment, but the school has a responsibility to others as well as S.A. By insisting on activating 911, the school risks violating her rights. But by agreeing to a rigid demand not to call 911, the school risks harming S.A., her schoolmates, and teachers. S.A. could be harmed in two ways: by having to endure a prolonged and painful death or by not being treated for an acute, reversible event that further compromises her life without ending it. Her fellow schoolmates and teachers could be harmed by being put in a position to exercise judgments and accept responsibilities for which they are neither professionally nor emotionally equipped....     

Sensible reasoning in two tasks: Rule discovery and hypothesis evaluation

The hypothesis testing skills of undergraduates were measured in two tasks: the 2-4-6 rule discovery task in which students generate and assess hypotheses, and a hypothesis evaluation task, which requires only the assessment of hypotheses. The results of Experiments 1 and 2 show that the students consistently employed a disconfirmation strategy when assessing hypotheses, but employed a counterfactual inference strategy when they also were required to generate the hypotheses. The results of Experiment 3 suggest that the selection of the hypothesis testing strategy reflected a balance between the logical requirements of the task and the desirability of possible outcomes. Taken together, the findings support a more consistent picture of human rationality across tasks, and suggest alternatives to accounts of confirmation bias.     

Countering perfectionism in research on clinical practice I: Surveying rationality changes after a single intensive ret intervention

The failure of controlled experimental research on therapy out-come to produce findings of clinical as well as statistical significance seems at least partly due to irrational, perfectionistic, beliefs about how research can be used to infer causes of therapeutic change. Irrational beliefs about controlled experimental designs and about incomplete sampling, in particular, appear to prevent appropriate consideration of probatively valuable quasi-experimental research. Models of more rational alternatives are identified, and an example of the functional advantages of adopting these rational beliefs is explicated. The example demonstrates that single-shot pre-post survey data from self-selected catch-as-catch-can samples can permit legitimate, but not absolutely certain, conclusions about the efficacy and efficiency of RET.Albert Ellis, Ph.D. is executive director of the Institute for Rational-Emotive Therapy in New York City.     

Programs for visual psychophysics on the Amiga: A tutorial

A typical psychophysical experiment presents a sequence of visual stimuli to an observer and collects and stores the responses for later analysis. Although computers can speed up this process, paint programs that allow one to prepare visual stimuli without programming cannot read responses from the mouse or keyboard, whereas BASIC and other programming languages that allow one to collect and store observer’s responses unfortunately cannot handle prepainted pictures. A new programming language called The Director provides the best of both worlds. Its BASIC-like commands can manipulate prepainted pictures, read responses made with the mouse and keyboard, and save these on disk for later analysis. A dozen sample programs are provided.     

Preventive group psychotherapy for at-risk infants and their mothers

There is increased evidence that infants who receive poor quality social stimulation from their primary caregiver are at risk for later developmental difficulties. This paper describes a preventive intervention for mother-infant dyads exhibiting impaired patterns of social interaction. An impaired relationship with the primary caregiver has been found to be associated with social and emotional deficits in early childhood as well as with significant psychopathology in adulthood. The intervention consisted of group treatment of mothers and their infants. Each group session has 4 subsections which, together, were directed towards improving the mothers' ability to relate in a stimulating and nurturant manner to their children. Types of intervention included didactic instruction, modeling, and interpretation of the infant's behavior. Qualitative data suggested that the group intervention has positive effects on the mother-infant dyads.     

Cognitive mechanisms mediating the biasing effects of leader sex on ratings of leader behavior

The present study examined the effects of the sex of the leader, the sex of the rater, and the temporal position of leader performance information on ratings of leader behavior. Male and female subjects listened to an audiotape of a male or female leader and then rated the leader's initiating structure and consideration behaviors. The position of the leader performance information was manipulated by describing the leader as successful before or after raters listened to the audiotape or not presenting raters with the performance information. Analyses indicated that the sex of the leader and/or sex of the rater biased ratings of initiating structure when the performance information was presented after the audiotape and when no leader performance information was presented. Consideration ratings were affected only by the position of the leader performance information. The results are interpreted within a cognitive/implicit sex theory framework. Implications for leadership research are also discussed.Portions of the data analyzed in this study were collected by the second author as part of a master's thesis directed by Joseph A. Sgro.