Definitions are traditionally seen as abbreviations, as tools for notational convenience that do not increase inferential power. From a Philosophy of Mathematical Practice point of view, however, there is much more to definitions. For example, definitions can play a role in problem solving, definitions can contribute to understanding, sometimes equivalent definitions are appreciated differently, and so on. This chapter reviews the literature on definitions and (to a certain extent) concepts in mathematical practice. It is structured according to four themes through (...) which definitions (and concepts) in mathematical practice have been studied. These themes concern (1) the nature of definitions, (2) whether and how concepts evolve, (3) definitions and concepts from a communal perspective, and (4) different values relating to definitions and concepts. (shrink)

In the philosophy of mathematical practice, the aim is to understand the various aspects of this practice. Even though definitions are a central element of mathematical practice, the study of this aspect of mathematical practice is still in its infancy. In particular, there is little empirical evidence to substantiate claims about definitions in practice. In this article, we address this gap by reporting on an empirical investigation on how mathematicians create definitions and which roles and properties they attribute to them. (...) On the basis of interviews with thirteen research mathematicians, we provide a broad range of relevant aspects of definitions. In particular, we address various roles of definitions and show that definitions are not just a product of mathematical factors, but also of social and contingent factors. Furthermore, we provide concrete examples of how mathematicians interact and think about definition. This broad empirical basis with a variety of examples provides an optimal starting point for future investigations into definitions in mathematical practice. (shrink)

Environmental Sound Artists: In Their Own Words is an incisive and imaginative look at the international environmental sound art movement, which emerged in the late 1960s. The term environmental sound art is generally applied to the work of sound artists who incorporate processes in which the artist actively engages with the environment. While the field of environmental sound art is diverse and includes a variety of approaches, the art form diverges from traditional contemporary music by the conscious and strategic integration (...) of environmental impulses and natural processes. This book presents a current perspective on the environmental sound art movement through a collection of personal writings by important environmental sound artists. Dismayed by the limitations and gradual breakdown of contemporary compositional strategies, environmental sound artists have sought alternate venues, genres, technologies, and delivery methods for their creative expression. Environmental sound art is especially relevant because it addresses political, social, economic, scientific, and aesthetic issues. As a result, it has attracted the participation of artists internationally. Awareness and concern for the environment has connected and unified artists across the globe and has achieved a solidarity and clarity of purpose that is singularly unique and optimistic. The environmental sound art movement is borderless and thriving. (shrink)

For over a century and certainly since single-unit recordings in the 1960s the theory of perception that has dominated thinking and research, with implications for the understanding of all other cognitive domains, entails a neocortical process of progressive assembly from V-1 to V-4 leading to object-construction and secondary spatial updating and recognition. In recent years, however, difficulties with the theory have emerged in neurophysiological research though a compelling alternative has not been forcefully argued. It is the purpose of this paper (...) to review the main features of the microgenetic account of perception, which inverts standard theory 180 degrees, and aligns the perceptual process with patterns of evolutionary growth. This theory developed on clinical study, and perhaps for this reason has not received sufficient attention, in mainstream cognitive and affective neuroscience, though it provides an account not only of perception but of stages in memory, imagery, the present moment, and the mind/brain state. (shrink)

In this article, an ethical analysis of an educational programme on renal replacement therapy options for patients and their social network is presented. The two main spearheads of this approach are: (1) offering an educational programme on all renal replacement therapy options ahead of treatment requirement and (2) a home-based approach involving the family and friends of the patient. Arguments are offered for the ethical justification of this approach by considering the viewpoint of the various stakeholders involved. Finally, reflecting on (...) these ethical considerations, essential conditions for carrying out such a programme are outlined. The goal is to develop an ethically justified and responsible educational programme. (shrink)

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: In this commentary, I address the viability of conducting constructivist teaching experiments to develop models of students’ conceptualizations. I also discuss how this research tradition has been adapted by researchers to conduct classroom teaching experiments. In my concluding remarks, I address the need for researchers to develop models for teacher (...) learning. (shrink)

© 2016 Regents of the University of California.The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous (...) tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group. The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.