The Indispensability Argument and Multiple Foundations for Mathematics

One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set–theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects.     

Discounting in causality and covariation judgements

In two experiments, humans were asked to judge the strength of a moderate contingency between a cue and an outcome in the presence of a second strong contingency between another cue and the outcome. The first experiment replicated the discounting effect whereby a strong contingency causes subjects to reduce or discount judgements of a moderate contingency. This experiment used a video-game procedure in which subjects camouflaged a tank to make it safe from mines. The second causal cue was the presence or absence of a spotter plane. Experiment 1 also ruled out the possibility that judgements might be determined by the number of co-occurrences of the cue and outcome as opposed to the level of contingency. The second experiment used an abstract scenario in which discounting was demonstrated when subjects were asked to judge the relationship between the occurrence of geometric objects. The instructions were neutral to discourage causal hypotheses. These results support the notion that judgements result from associative or connectionist processes and not from a two-step cognitive retrospective process in which an estimate of covariation is calculated between cue and outcome and then in a second step this information is used in a normative manner when a decision is made.     

Velocity as a Predictor of Performance Satisfaction,Mental Focus,and Goal Revision

In a longitudinal study, the authors examined the role of students' rate of progress, or velocity, in goal‐striving over one semester of a college‐level Introductory Psychology course. At both mid‐course and near end‐of‐course time periods, results demonstrated that velocity uniquely contributed to the prediction of students' performance satisfaction, mental focus, and goal revision, above and beyond the influence of performance‐goal discrepancies and ability. Specifically, velocity demonstrated main effects on performance satisfaction and mental focus. Velocity significantly interacted with goal importance in the prediction of goal revision. The authors call for increased attention to the role of velocity in self‐regulation. Dans une étude longitudinale, les auteurs examinent le rôle du taux de progrès des étudiants ou leur rapiditéà atteindre des buts sur un semestre pour un cours d'introduction à la psychologie en faculté. Deux mesures ont été faites: l'une à la moitié du semestre et l'autre à la fin de ce même semestre. Les résultats montrent que uniquement la rapidité contribue à prédire la satisfaction de la performance des étudiants, la concentration, et la révision de l'objectif quels que soient les écarts entre le but de la performance et les capacités. Plus spécifiquement, la rapidité a des effets importants sur la satisfaction de la performance et la concentration. La rapidité interagit significativement avec l'importance des buts dans le cas où l'on envisage leur révision. Les auteurs soulignent le rôle de la rapidité sur l'auto‐régulation.     

Self-Efficacy for Enhancing Students’ Career and College Readiness: A Survey of Professional School Counselors

Grounded in Bandura’s (1997) self-efficacy theory and Savickas’s (2011) career construction theory, this study examined school counselors’ beliefs about whether they can perform specific tasks related to supporting students’ career and college readiness. A national sample of school counselors (N = 2,047) completed the School Counselor Self-Efficacy for Enhancing Student Career and College Readiness Scale (Baker, Parikh-Foxx, & Martinez, 2017). Findings from a survey research design indicated that the extent of related training and the challenges associated with implementation of career service delivery were of concern to participants. Recommendations for training, practice, and further research are presented.