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: 9513

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.
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Feferman on Foundations

Logic, Mathematics, Philosophy

Author: Gerhard Jäger,Wilfried Sieg

Publisher: Springer

ISBN: 3319633341

Category: Mathematics

Page: 551

View: 7780

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.
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Philosophy and Model Theory

Author: Tim Button,Sean Walsh

Publisher: Oxford University Press

ISBN: 0198790392

Category: Mathematics

Page: 544

View: 9112

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.
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Formal Theories of Truth

Author: Jc Beall,Michael Glanzberg,David Ripley

Publisher: Oxford University Press

ISBN: 0192547658

Category: Philosophy

Page: 160

View: 9558

Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth.
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Computer Vision

Algorithms and Applications

Author: Richard Szeliski

Publisher: Springer

ISBN: 9781848829466

Category: Computers

Page: 812

View: 9723

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.
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Theories, Sites, Toposes

Relating and studying mathematical theories through topos-theoretic 'bridges'

Author: Olivia Caramello

Publisher: Oxford University Press

ISBN: 0191076759

Category: Philosophy

Page: 336

View: 4846

According to Grothendieck, the notion of topos is "the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures". It is what he had "conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an "essence" which is common to situations most distant from each other, coming from one region or another of the vast universe of mathematical things". The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.
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Transcultural Performance

Negotiating Globalized Indigenous Identities

Author: Michele Back

Publisher: Springer

ISBN: 1137412437

Category: Social Science

Page: 160

View: 9420

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.
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Finite Element Procedures

Author: Klaus-Jürgen Bathe

Publisher: Klaus-Jurgen Bathe

ISBN: 9780979004902

Category: Engineering mathematics

Page: 1037

View: 2691

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English as a Global Language

Author: David Crystal

Publisher: Cambridge University Press

ISBN: 1107611806

Category: Language Arts & Disciplines

Page: 212

View: 8224

David Crystal's classic English as a Global Language considers the history, present status and future of the English language, focusing on its role as the leading international language. English has been deemed the most 'successful' language ever, with 1500 million speakers internationally, presenting a difficult task to those who wish to investigate it in its entirety. However, Crystal explores the subject in a measured but engaging way, always backing up observations with facts and figures. Written in a detailed and fascinating manner, this is a book written by an expert both for specialists in the subject and for general readers interested in the English language.
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Man and His Symbols

Author: C. G. Jung

Publisher: Dell

ISBN: 0307800555

Category: Social Science

Page: 320

View: 2292

Man and His Symbols owes its existence to one of Jung's own dreams. The great psychologist dreamed that his work was understood by a wide public, rather than just by psychiatrists, and therefore he agreed to write and edit this fascinating book. Here, Jung examines the full world of the unconscious, whose language he believed to be the symbols constantly revealed in dreams. Convinced that dreams offer practical advice, sent from the unconscious to the conscious self, Jung felt that self-understanding would lead to a full and productive life. Thus, the reader will gain new insights into himself from this thoughtful volume, which also illustrates symbols throughout history. Completed just before his death by Jung and his associates, it is clearly addressed to the general reader. Praise for Man and His Symbols “This book, which was the last piece of work undertaken by Jung before his death in 1961, provides a unique opportunity to assess his contribution to the life and thought of our time, for it was also his firsat attempt to present his life-work in psychology to a non-technical public. . . . What emerges with great clarity from the book is that Jung has done immense service both to psychology as a science and to our general understanding of man in society, by insisting that imaginative life must be taken seriously in its own right, as the most distinctive characteristic of human beings.”—Guardian “Straighforward to read and rich in suggestion.”—John Barkham, Saturday Review Syndicate “This book will be a resounding success for those who read it.”—Galveston News-Tribune “A magnificent achievement.”—Main Currents “Factual and revealing.”—Atlanta Times
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The Palgrave Handbook of Slavic Languages, Identities and Borders

Author: Tomasz Kamusella,Motoki Nomachi,Catherine Gibson

Publisher: Palgrave Macmillan

ISBN: 1137348402

Category: Language Arts & Disciplines

Page: 528

View: 8866

Languages are artefacts of culture, meaning they are created by people. They are often used for identity building and maintenance, but in Central and Eastern Europe they became the basis of nation building and national statehood maintenance. The recent split of the Serbo-Croatian language in the wake of the break-up of Yugoslavia amply illustrates the highly politicized role of languages in this region, which is also home to most of the world's Slavic-speakers. This volume presents and analyzes the creation of languages across the Slavophone areas of the world and their deployment for political projects and identity building, mainly after 1989. The overview concludes with a reflection on the recent rise of Slavophone speech communities in Western Europe and Israel. The book brings together renowned international scholars who offer a variety of perspectives from a number of disciplines and sub-fields such as sociolinguistics, socio-political history and language policy, making this book of great interest to historians, sociologists, political scientists and anthropologists interested in Central and Eastern Europe and Slavic Studies.
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The Garden

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Gardening

Page: N.A

View: 8927

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An Introduction to Sociolinguistics

Author: Ronald Wardhaugh,Janet M. Fuller

Publisher: John Wiley & Sons

ISBN: 1118732405

Category: Language Arts & Disciplines

Page: 448

View: 4446

Fully updated to reflect the most recent scholarship in the field and revised to include many more pedagogical features, An Introduction to Sociolinguistics, 7th Edition builds on its foundation as the most preeminent textbook in sociolinguistics, updated for today’s students. • Significantly revised discussions throughout each of the book’s four key parts reflect the state of the field today • Includes new chapters on Pragmatics, Discourse Analysis, and Sociolinguistics and Education • Incorporates innovative new perspectives drawn from linguistic anthropology • Provides an accessible history of the development of sociolinguistic thought and how this fast-moving field is integral to our lives • Includes numerous opportunities for students to engage with ideas presented in the text through a new glossary, new Explorations and end-of-chapter exercises, links, and key concepts • New companion website includes links and resources for students
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Pedagogy of the Oppressed

50th Anniversary Edition

Author: Paulo Freire

Publisher: Bloomsbury Publishing USA

ISBN: 1501314149

Category: Education

Page: 232

View: 8311

First published in Portuguese in 1968, Pedagogy of the Oppressed was translated and published in English in 1970. Paulo Freire's work has helped to empower countless people throughout the world and has taken on special urgency in the United States and Western Europe, where the creation of a permanent underclass among the underprivileged and minorities in cities and urban centers is ongoing. This 50th anniversary edition includes an updated introduction by Donaldo Macedo, a new afterword by Ira Shor and interviews with Marina Aparicio Barberán, Noam Chomsky, Ramón Flecha, Gustavo Fischman, Ronald David Glass, Valerie Kinloch, Peter Mayo, Peter McLaren and Margo Okazawa-Rey to inspire a new generation of educators, students, and general readers for years to come.
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Folk Devils and Moral Panics

Author: Stanley Cohen

Publisher: Taylor & Francis

ISBN: 1136807047

Category: Social Science

Page: 328

View: 2974

'Richly documented and convincingly presented' -- New Society Mods and Rockers, skinheads, video nasties, designer drugs, bogus asylum seeks and hoodies. Every era has its own moral panics. It was Stanley Cohen’s classic account, first published in the early 1970s and regularly revised, that brought the term ‘moral panic’ into widespread discussion. It is an outstanding investigation of the way in which the media and often those in a position of political power define a condition, or group, as a threat to societal values and interests. Fanned by screaming media headlines, Cohen brilliantly demonstrates how this leads to such groups being marginalised and vilified in the popular imagination, inhibiting rational debate about solutions to the social problems such groups represent. Furthermore, he argues that moral panics go even further by identifying the very fault lines of power in society. Full of sharp insight and analysis, Folk Devils and Moral Panics is essential reading for anyone wanting to understand this powerful and enduring phenomenon. Professor Stanley Cohen is Emeritus Professor of Sociology at the London School of Economics. He received the Sellin-Glueck Award of the American Society of Criminology (1985) and is on the Board of the International Council on Human Rights. He is a member of the British Academy.
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Upper Motor Neurone Syndrome and Spasticity

Clinical Management and Neurophysiology

Author: Michael P. Barnes,Garth R. Johnson

Publisher: Cambridge University Press

ISBN: 1139471422

Category: Medical

Page: N.A

View: 1177

Spasticity is a disabling problem for many adults and children with a variety of neurological disorders such as multiple sclerosis, stroke, cerebral palsy and traumatic brain injury. A practical guide for clinicians involved in the management of spasticity, this book covers all aspects of upper motor neurone syndrome from basic neurophysiology and measurement techniques to practical therapy and the use of orthoses. Surgical techniques are also covered, as well as the particular problems of management of spasticity in childhood. In the second edition of this key text, all chapters have been thoroughly updated, with additional coverage of new techniques and new drugs and therapies, whilst continuing the format that has made the first edition the core text in its field. This guide will be invaluable to physicians, physiotherapists, surgeons, orthotists, clinical engineers and health professionals.
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What Caused the Big Bang?

Author: Rem Blanchard Edwards

Publisher: Rodopi

ISBN: 9789042014077

Category: Philosophy

Page: 412

View: 2607

This book critically explores answers to the big question, What produced our universe around fifteen billion years ago in a Big Bang? It critiques contemporary atheistic cosmologies, including Steady State, Oscillationism, Big Fizz, Big Divide, and Big Accident, that affirm the eternity and self-sufficiency of the universe without God. This study defends and revises Process Theology and arguments for God's existence from the universe's life-supporting order and contingent existence.
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From Gestalt Theory to Image Analysis

A Probabilistic Approach

Author: Agnès Desolneux,Lionel Moisan,J.-M. Morel

Publisher: Springer Science & Business Media

ISBN: 0387726357

Category: Computers

Page: 276

View: 8238

This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The book is mathematically self-contained, needing only basic understanding of probability and calculus. The text includes more than 130 illustrations, and numerous examples based on specific images on which the theory is tested. Detailed exercises at the end of each chapter help the reader develop a firm understanding of the concepts imparted.
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