On Certainty,Change, and “Mathematical Hinges”

Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, “Are there mathematical hinges?” I argue here, against Coliva’s own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts on mathematics. For example, a view of how mathematical hinges relate to Wittgenstein’s well-known river-bed analogy enables us to see how his way of thinking about mathematics can account nicely for a “dynamics of change” within mathematical research—something his philosophy of mathematics has been accused of missing (e.g., by Robert Ackermann (Wittgenstein’s city, The University of Massachusetts Press, Amherst, 1988) and Mark Wilson (Wandering significance: an essay on conceptual behavior, Oxford University Press, Oxford, 2006). Finally, the perspective on mathematical hinges ultimately arrived at will be seen to provide us with illuminating examples of how our conceptual choices and theories can be ungrounded but nevertheless the right ones (in a sense to be explained).

     

Risking Everything in Obsessive–Compulsive Disorder: An Analogue Decision-Making Study

An experiment examined decision-making processes among nonclinical participants with low or high levels of OCD symptomatology (N?=?303). To better simulate the decision environments that are most likely to be problematic for clients with OCD, we employed decision tasks that incorporated “black swan” options that have a very low probability but involve substantial loss. When faced with a choice between a safer option that involved no risk of loss or a riskier alternative with a very low probability of substantial loss, most participants chose the safer option regardless of OCD symptom level. However, when faced with choices between options that had similar expected values to the previous choices, but where each option had some low risk of a substantial loss, there was a significant shift towards riskier decisions. These effects were stronger when the task involved a contamination based, health-relevant decision task as compared to one with financial outcomes. The results suggest that both low and high symptom OC participants approach decisions involving risk-free options and decisions involving risky alternatives in qualitatively different ways. There was some evidence that measures of impulsivity were better predictors of the shift to risky decision making than OCD symptomatology.

     

A Neuropsychological Model of Mentally Tough Behavior

Four studies were conducted with two primary objectives: (a) to conceptualize and measure mental toughness from a behavioral perspective and (b) to apply relevant personality theory to the examination of between‐person differences in mentally tough behavior. Studies 1 (N = 305 participants from a range of different sports) and 2 (N = 110 high‐level cricketers) focused on the development of an informant‐rated mental toughness questionnaire that assessed individual differences in ability to maintain or enhance performance under pressure from a wide range of stressors. Studies 3 (N = 214) and 4 (N = 196) examined the relationship between reinforcement sensitivities and mentally tough behavior in high‐level cricketers. The highest levels of mental toughness reported by coaches occurred when cricketers were sensitive to punishment and insensitive to reward. Study 4 suggested that such players are predisposed to identify threatening stimuli early, which gives them the best possible opportunity to prepare an effective response to the pressurized environments they encounter. The findings show that high‐level cricketers who are punishment sensitive, but not reward sensitive, detect threat early and can maintain goal‐directed behavior under pressure from a range of different stressors.     

Predictable Mispredictions in the Context of Physical Activity and Sport: A Review

Theoretical models and research that aim to identify antecedents of participation in physical activities or sport can measure antecedents of physical activity behaviour through instruments that involve subjective predictions. In this article, we argue that such instruments may not reflect physical activity experiences or behaviour accurately because people are not very good predictors of future states. Additionally, we propose that mispredictions may be predictable because they are “caused” by tendencies to neglect processes related to hedonic adaptation and competing alternatives. We also suggest that it may be possible to improve measurement of antecedents through methods that focus respondents' attention on factors that cause mispredictions or through experiential sampling methods.