Varieties of Continua

From Regions to Points and Back

Author: Geoffrey Hellman,Stewart Shapiro

Publisher: Oxford University Press

ISBN: 019871274X

Category: Mathematics

Page: 224

View: 8710


Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be composed of points, to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-to-late-twentieth century revival of pre-limit methods in analysis and geometry using infinitesimals, non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. Hellman and Shapiro develop a systematic comparison of these and related alternatives (including constructivist and predicative conceptions), balancing various trade-offs, helping articulate a modern pluralist perspective. A second main goal of the book is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent (inter-reducible) to the currently standard, punctiform accounts of modern texts. The theories developed by Hellman and Shapiro offer a more streamlined, unified and comprehensive study than others in the contemporary literature.

Feferman on Foundations

Logic, Mathematics, Philosophy

Author: Gerhard Jäger,Wilfried Sieg

Publisher: Springer

ISBN: 3319633341

Category: Mathematics

Page: 551

View: 5808


This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

Language Policies and (Dis)Citizenship

Rights, Access, Pedagogies

Author: Prof. Vaidehi Ramanathan

Publisher: Multilingual Matters

ISBN: 1783090219

Category: Language Arts & Disciplines

Page: 272

View: 4180


This volume explores the concept of 'citizenship', and argues that it should be understood both as a process of becoming and the ability to participate fully, rather than as a status that can be inherited, acquired, or achieved. From a courtroom in Bulawayo to a nursery in Birmingham, the authors use local contexts to foreground how the vulnerable, particularly those from minority language backgrounds, continue to be excluded, whilst offering a powerful demonstration of the potential for change offered by individual agency, resistance and struggle. In addressing questions such as 'under what local conditions does "dis-citizenship" happen?'; 'what role do language policies and pedagogic practices play?' and 'what kinds of margins and borders keep humans from fully participating'? The chapters in this volume shift the debate away from visas and passports to more uncertain and contested spaces of interpretation.

Transcultural Performance

Negotiating Globalized Indigenous Identities

Author: Michele Back

Publisher: Springer

ISBN: 1137412437

Category: Social Science

Page: 160

View: 6626


Featuring interviews, conversations and observations from a multi-sited ethnography of Ecuadorean musicians and their families, this book offers an innovative response to previous analyses of globalization and indigenous languages, demonstrating how transcultural practices can enhance the use and maintenance of indigenous and minority languages.

Plato's Timaeus as cultural icon

Author: Gretchen J. Reydams-Schils,Plato

Publisher: Univ of Notre Dame Pr

ISBN: 9780268038717

Category: Philosophy

Page: 334

View: 1110


In recent years, Plato's Timaeus has recaptured the interest of scholars, sparking an exploration of the astonishing influence this work has had on a wide range of intellectual traditions. Plato's Timaeus as Cultural Icon brings together a group of leading experts from Canada, the United States, and Europe to examine the reception of Plato's Timaeus throughout history, as well as its impact on major intellectual and cultural traditions.Gretchen J. Reydams-Schils's enlightening introduction tackles the issue of why the Timaeus has enjoyed such tremendous cultural status, and sets the stage for the many topics covered in this volume, which include an assessment of the Timaeus' influence on Plato's successors, an examination of how it became connected to traditions of sacred texts, an analysis of the "mind-body problem, " the tradition of music and its relation to philosophy, the cultural impact of Calcidius' Latin translation of the work, and the interaction between the Timaeus and Islamic philosophy. As a,collaborative effort of expert philosophers, classicists, and historians, this remarkable book serves as a wonderful starting point and research tool for anyone with an interest in Plato's Timaeus.