This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students (...) learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future. (shrink)

Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...) conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable 'tests' are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as "Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.". (shrink)

Reviewers of this book have praised Christina Hoff Sommer's well-reasoned argument against many feminists' reliance on misleading, politically motivated 'facts' about how women are victimised.

Contemporary ethicists largely ignore the recent, revolutionary findings of psychodynamic psychology. The author argues that ethicists have been dissuaded from taking psychodynamic psychology seriously by hostile attacks on the credibility of the psychodynamic paradigm, and confusion about the contribution that clinical findings can make to ethics. With respect to these obstacles, the credibility of the psychodynamic paradigm is vouchsafed by a growing body of empirical studies that support the main psychodynamic hypotheses, particularly those of interest to ethicists. This new research (...) points toward the need to expand the range of issues covered by contemporary ethics by retrieving and updating the ancient tradition of askesis, involving thought-exercises oriented towards cultivation of habits of mind conducive to acting morally in one's daily activities. The paper concludes by sketching several ways in which self-reflection may improve moral decision-making. (shrink)

ArgumentTwo simultaneous episodes in late nineteenth-century mathematical research, one by Karl Hermann Brunn and another by Hermann Minkowski, have been described as the origin of the theory of convex bodies. This article aims to understand and explain how and why the concept of such bodies emerged in these two trajectories of mathematical research; and why Minkowski's – and not Brunn's – strand of thought led to the development of a theory of convexity. Concrete pieces of Brunn's and Minkowski's mathematical work (...) in the two episodes will, from the perspective of the above questions, be presented and analyzed with the use of the methodological framework of epistemic objects, techniques, and configurations as adapted from Hans-Jörg Rheinberger's work on empirical sciences to the historiography of mathematics by Moritz Epple. Based on detailed descriptions and a comparison of the objects and techniques that Brunn and Minkowski studied and used in these pieces it will be concluded that Brunn and Minkowski worked in different epistemic configurations, and it will be argued that this had a significant influence on the mathematics they developed for those bodies, which can provide answers to the two research questions listed above. (shrink)

In this study, 10 hematologists and 10 lung oncologists were interviewed regarding the information they provide to patients in four situations of uncertainty: determining the treatment that is in the patient’s best interest; recurrence or progression of the patient’s disease; determining when to withdraw life-prolonging treatment; discussing death, addressing questions such as whether the patient will die from the disease, and when. The primary finding is that delivery of information to patients with low survival rates can be improved by more (...) and better disclosure by physicians at an earlier stage. The crucial point for physicians is to ascertain the wishes of patients, to learn what to reveal about what patients should expect, short term and long term, as death approaches. (shrink)

_An account of Hegel's political insights and their contemporary relevance._.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

These forms would result regularly from the longer forms, audivisti, etc. The v drops out between two like vowels, and these then contract immediately . Both the long and the short forms are used, but the intervening forms audiisti, etc., do not occur in early Latin, just as diitis is not found.