A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Sights and insights: Vocational outdoor students’ learning

Outdoor leader and adventure sport education in the United Kingdom has been characterized by an over-emphasis on technical skills at the expense of equally important, but often marginalized intra- and inter-personal skills necessary for contemporary outdoor employment. This study examined the lived experience of vocational outdoor students in order, firstly, to identify what was learned about the workplace through using reflective practice and, secondly, what was learned about reflective practice through this experience. The study used a purposive sample of students (n=15) who were invited to maintain reflective journals during summer work experience, and this was followed up with semi-structured interviews. Manual Interpretative Phenomenological Analysis (IPA) revealed that in the workplace setting students used reflective practice to understand and develop technical proficiency, support awareness of the value of theory, and acted as a platform to express emergent concepts of ‘professionalism’. Lessons about reflective practice emphasized its value in social settings, acknowledging different ways of reflection, and understanding and managing professional life beyond graduation

Hydrogeol. J.

The protection of environmental flows, as a management objective for a regulating agency, needs to be consistent with the aquifer water balance and the degree of resource renewability. A stylized hydro-economic model is used where natural recharge, which sustains environmental flows, is considered both in the aquifer water budget and in the welfare function as ecosystem damage. Groundwater recharge and the associated natural drainage may be neglected for aquifers containing fossil water, where the groundwater is mined. However, when dealing with an aquifer that constitutes a renewable resource, for which recharge is not negligible, natural drainage should explicitly appear in the water budget. In doing so, the optimum path of net extraction rate does not necessarily converge to the recharge rate, but depends on the costs associated with ecosystem damages. The optimal paths and equilibrium values for the water volume and water extraction are analytically derived, and numerical simulations based on the Western La Mancha aquifer (southwest Spain) illustrate the theoretical results of the study