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.     

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.     

The Effects of Censorship on Attitude Change: The Influence of Censor and Communication Characteristics1

The effects of censor characteristics and audiences' initial agreement with a censored communication on attitude change and desire to hear a communication were investigated. Subjects were informed that a communication taking a position with which they had originally agreed or disagreed had been censored. The censor was either an attractive or unattractive agent and his expertise on the topic of the speech was either high or low. The results indicated that in all cases except one, censorship led to an increased desire to hear the communication and attitude change toward the position of the communication. In the one exceptional case, when an attractive expert censor forbade a communication with which the audience disagreed, the subjects decreased their desire to hear the speech and did not change their attitudes on the topic of the communication. The results were interpreted as indicating that censorship arouses both reactance and balancing attempts but that balancing will be observed only in limited situations.