In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of (...) base event pairs, it costs no more to elicit estimates on all combinations of these base events. (shrink)

It is well known that, for example, the Continuum Hypothesis can’t be proved or disproved from the standard axioms of set theory or their familiar extensions. Some think it follows that CH has no determinate truth value; others insist that this conclusion is false, not because there is some objective world of sets in which CH is either true or false, but on logical grounds. Claims of indeterminacy have also been made on the basis of such considerations as the existence (...) of non-standard models of arithmetic, with similar rejoinders. We’ll read some representative examples of the various positions and replies. (For background on second-order logic, see Stewart Shapiro. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 15.2 (2007) 177-179MuseSearchJournalsThis JournalContents[Access article in PDF]Reviewed byLise Vaugeois University of TorontoHildegard C. Froehlich, Sociology for Music Teachers:Perspectives for Practice (Upper Saddle River, NJ: Pearson Prentice Hall, 2007)Hildegard Froehlich's book, Sociology for Music Teachers, provides an important and much needed resource for undergraduate and advanced music education programs. Music students tend to see their interests and goals within a narrow framework, one (...) that is reinforced by the intensely personal nature of music-making as well as the material and psychological separation that inheres from our location in physically detached faculties of music. Froehlich's book provides a resource that directly addresses this tendency towards narrowness by inviting students to engage with sociological questions as they affect us personally, professionally, and in the context of questions much larger than ourselves.The book is organized into eight chapters, each of which explores a particular set of questions and introduces related studies and resources. She recommends that students actively engage with the material and provides suggestions for group discussion throughout the book. Each chapter introduces a comprehensive survey of related questions and the body of literature that investigates these questions. Thus, it can be used as the basis to structure an undergraduate course as well as a literature guide for graduate students.Undergraduate students are often resistant to exploring ideas beyond their [End Page 177] immediate conceptions of themselves as musicians and Froehlich addresses this resistance by discussing concepts about identity formation in the first chapter. Students are thus asked to consider a series of questions they can easily recognize as relevant to their own lives. She begins with the personal and the familiar and then brings in ideas that broaden the range of inquiry, gradually introducing concepts that challenge many of our assumptions about the meaning of music in different people's lives; the range of meanings possible within sounds and musical practices; the role of public education and various ways that music education functions within this larger system, and important questions about how we might conceive of ourselves as transmitters of extant cultural values or transformers of values and social relations.The chapter headings give an indication of the range of material introduced in her text: "The Performer and Teacher in You: A Matter of Identity"; "Teaching as Work: What Educational Sociologists Tell Us"; "Music Learning and Teaching as Socially Situated Acts"; "Music and Social Context: Macro, Micro, and Interactive Perspectives in Selected Texts on the Sociology of Music"; "Musical Meaning and Social Context: Thoughts by Selected Ethnomusicologists and Cultural Theorists"; "Sociology of Education: Major Theories and Their Connection to School Practice"; "Application of Sociological Constructs in Education to Music Schooling"; "Conclusion: You and the Big Picture." Each chapter gives a historical survey of the literature pertaining to the area of inquiry plus an introduction to contemporary writing. Competing discourses are introduced throughout.Froehlich's survey of disciplines that intersect with sociology is quite comprehensive. Amongst other disciplines, she includes foundational literature from musicology, philosophy of music education, sociology of education, and social psychology. The book is thus valuable as a resource for its bibliography alone. She also includes a glossary of terms, another feature that makes the book particularly helpful to undergraduate students. One writer I was surprised not to see included is Jacques Attali. His theoretical arguments on the relations of musical culture to economy provide a significant lens for considering the influence of music on social development and would have been an appropriate addition to the chapter on "Music and Social Context." I also missed work by musicologists and human geographers who have explored the role of race in music and music education.Related to these missing discourses, I have a major concern that is less a critique of Froehlich than an acknowledgement that this position has not yet been given sufficient consideration in our field, and to which Deborah Bradley refers as the "normative centering of whiteness."1 Froehlich bases her work on the assumption that her audience consists of a... (shrink)

review of Philosophy of Economics by C. Dyke.