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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).
相似文献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.
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