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Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108998852
Category : Science
Languages : en
Pages : 250
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Book Description
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Author: Sharon Berry
Publisher: Cambridge University Press
ISBN: 1108998852
Category : Science
Languages : en
Pages : 250
Get Book Here
Book Description
In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.
Author: Diego E. Machuca
Publisher: Taylor & Francis
ISBN: 1000648605
Category : Philosophy
Languages : en
Pages : 425
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Book Description
Recent years have seen an explosion of interest in evolutionary debunking arguments directed against certain types of belief, particularly moral and religious beliefs. According to those arguments, the evolutionary origins of the cognitive mechanisms that produce the targeted beliefs render these beliefs epistemically unjustified. The reason is that natural selection cares for reproduction and survival rather than truth, and false beliefs can in principle be as evolutionarily advantageous as true beliefs. The present volume brings together fourteen essays that examine evolutionary debunking arguments not only in ethics and philosophy of religion, but also in philosophy of mathematics, metaphysics, and epistemology. The essays move forward research on those arguments by shedding fresh light on old problems and proposing new lines of inquiry. The book will appeal to scholars and graduate students interested in the possible skeptical implications of evolutionary theory in any of the above domains.
Author: Øystein Linnebo
Publisher: Oxford University Press
ISBN: 019255896X
Category : Philosophy
Languages : en
Pages : 232
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Book Description
Are there objects that are "thin" in the sense that not very much is required for their existence? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. Øystein Linnebo aims to do so by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. The result is a distinctive approach to ontology. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. And Linnebo also offers a novel approach to set theory which takes seriously the idea that sets are "formed" successively.
Author: Charles C. Pinter
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Author: Agustín Rayo
Publisher:
ISBN: 0199662622
Category : Mathematics
Languages : en
Pages : 241
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Book Description
Our conception of logical space is the set of distinctions we use to navigate the world. Agustín Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics.
Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 110863074X
Category : Science
Languages : en
Pages : 167
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Book Description
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.
Author: Mirja Hartimo
Publisher: Taylor & Francis
ISBN: 1000992322
Category : Philosophy
Languages : en
Pages : 235
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Book Description
This book examines positions that challenge the Fregean logic-first view. It raises critical questions about logic by examining various ways in which logic may be entangled with mathematics and metaphysics. Is logic topic-neutral and general? Can we take the application of logic for granted? This book suggests that we should not be dogmatic about logic but ask similar critical questions about logic as those Kant raised about metaphysics and mathematics. It challenges the Fregean logic-first view according to which logic is fundamental and hence independent of any extra-logical considerations. Whereas Quine assimilated logic and mathematics to the theoretical parts of empirical science, the present volume explores views that stop short of his thoroughgoing holism but instead take logic to be answerable to or entangled with some particular disciplines. The contributions provide views that assign primacy to mathematical reasons, Kantian metaphysical grounds, Husserlian transcendental phenomenological reflection, or normative considerations about how terms ought to be defined in various fields of empirical science or mathematics. Space is thereby carved out between a Fregean position on the one hand and Quinean holism on the other. Critical Views of Logic will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science, as well as those engaged in various fields of empirical science. The chapters in this book, except for chapter 4, were originally published in the journal Inquiry.
Author: Geoffrey Hellman
Publisher: Cambridge University Press
ISBN: 1316999602
Category : Science
Languages : en
Pages : 296
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Book Description
In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
Author: Peter Friess
Publisher: River Publishers
ISBN: 8793379811
Category : Computers
Languages : en
Pages : 362
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Book Description
This book provides an overview of the current Internet of Things (IoT) landscape, ranging from the research, innovation and development priorities to enabling technologies in a global context. A successful deployment of IoT technologies requires integration on all layers, be it cognitive and semantic aspects, middleware components, services, edge devices/machines and infrastructures. It is intended to be a standalone book in a series that covers the Internet of Things activities of the IERC - Internet of Things European Research Cluster from research to technological innovation, validation and deployment. The book builds on the ideas put forward by the European Research Cluster and the IoT European Platform Initiative (IoT-EPI) and presents global views and state of the art results on the challenges facing the research, innovation, development and deployment of IoT in the next years. The IoT is bridging the physical world with virtual world and requires sound information processing capabilities for the "digital shadows" of these real things. The research and innovation in nanoelectronics, semiconductor, sensors/actuators, communication, analytics technologies, cyber-physical systems, software, swarm intelligent and deep learning systems are essential for the successful deployment of IoT applications. The emergence of IoT platforms with multiple functionalities enables rapid development and lower costs by offering standardised components that can be shared across multiple solutions in many industry verticals. The IoT applications will gradually move from vertical, single purpose solutions to multi-purpose and collaborative applications interacting across industry verticals, organisations and people, being one of the essential paradigms of the digital economy. Many of those applications still have to be identified and involvement of end-users including the creative sector in this innovation is crucial. The IoT applications and deployments as integrated building blocks of the new digital economy are part of the accompanying IoT policy framework to address issues of horizontal nature and common interest (i.e. privacy, end-to-end security, user acceptance, societal, ethical aspects and legal issues) for providing trusted IoT solutions in a coordinated and consolidated manner across the IoT activities and pilots. In this, context IoT ecosystems offer solutions beyond a platform and solve important technical challenges in the different verticals and across verticals. These IoT technology ecosystems are instrumental for the deployment of large pilots and can easily be connected to or build upon the core IoT solutions for different applications in order to expand the system of use and allow new and even unanticipated IoT end uses. Technical topics discussed in the book include: IntroductionDigitising industry and IoT as key enabler in the new era of Digital EconomyIoT Strategic Research and Innovation Agenda IoT in the digital industrial context: Digital Single MarketIntegration of heterogeneous systems and bridging the virtual, digital and physical worldsFederated IoT platforms and interoperabilityEvolution from intelligent devices to connected systems of systems by adding new layers of cognitive behaviour, artificial intelligence and user interfaces. Innovation through IoT ecosystemsTrust-based IoT end-to-end security, privacy framework User acceptance, societal, ethical aspects and legal issuesInternet of Things Applications
Author: Michael Friedman
Publisher: Cambridge University Press
ISBN: 9780521624763
Category : Philosophy
Languages : en
Pages : 276
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Book Description
A reinterpretation of the enduring significance of logical positivism.
