A Logical Foundation For Potentialist Set Theory

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A Logical Foundation For Potentialist Set Theory

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Author : Sharon Berry
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-17

A Logical Foundation For Potentialist Set Theory written by Sharon Berry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Mathematics categories.

A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.

The Palgrave Companion To The Philosophy Of Set Theory

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Author : Carolin Antos
language : en
Publisher: Springer Nature
Release Date : 2025-04-17

The Palgrave Companion To The Philosophy Of Set Theory written by Carolin Antos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-17 with Mathematics categories.

This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity. Key features of this volume: • Explores new and interesting connections between philosophy, set theory, and the study of infinity. • Considers questions intended to appeal to a wider audience in both philosophy and mathematical logic. • Examines three key areas of study: Epistemology, Formal Theories, and Ontology. The book provides a key reference text for future debates and is ideal for both newcomers to the philosophy of set theory and established researchers in the field.

Evolutionary Debunking Arguments

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Author : Diego E. Machuca
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-09

Evolutionary Debunking Arguments written by Diego E. Machuca and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-09 with Philosophy categories.

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.

Defending The Axioms

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Author : Penelope Maddy
language : en
Publisher: Oxford University Press
Release Date : 2011-01-27

Defending The Axioms written by Penelope Maddy and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-27 with Mathematics categories.

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.

Reconsidering Logical Positivism

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Author : Michael Friedman
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-28

Reconsidering Logical Positivism written by Michael Friedman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-28 with Philosophy categories.

A reinterpretation of the enduring significance of logical positivism.

Thin Objects

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Author : Øystein Linnebo
language : en
Publisher: Oxford University Press
Release Date : 2018-05-23

Thin Objects written by Øystein Linnebo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Philosophy categories.

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.

Critical Views Of Logic

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Author : Mirja Hartimo
language : en
Publisher: Taylor & Francis
Release Date : 2023-10-31

Critical Views Of Logic written by Mirja Hartimo and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-31 with Philosophy categories.

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.

Naturalism In Mathematics

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Author : Penelope Maddy
language : en
Publisher: Clarendon Press
Release Date : 1997-11-13

Naturalism In Mathematics written by Penelope Maddy and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-13 with Philosophy categories.

Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Set Theory

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Author : Charles C. Pinter
language : en
Publisher:
Release Date : 1971

Set Theory written by Charles C. Pinter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

Digitising The Industry Internet Of Things Connecting The Physical Digital And Virtual Worlds

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Author : Peter Friess
language : en
Publisher: River Publishers
Release Date : 2016-07-07

Digitising The Industry Internet Of Things Connecting The Physical Digital And Virtual Worlds written by Peter Friess and has been published by River Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-07 with Computers categories.

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