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.
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.
The Routledge Handbook Of Modality
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Author : Otávio Bueno
language : en
Publisher: Routledge
Release Date : 2020-12-29
The Routledge Handbook Of Modality written by Otávio Bueno and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Philosophy categories.
Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts: worlds and modality essentialism, ontological dependence, and modality modal anti-realism epistemology of modality modality in science modality in logic and mathematics modality in the history of philosophy. Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity. The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.
Set Theory Logic And Their Limitations
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Author : Moshé Machover
language : en
Publisher:
Release Date : 1998
Set Theory Logic And Their Limitations written by Moshé Machover and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Foundations Of Set Theory
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Author : Abraham Adolf Fraenkel
language : en
Publisher:
Release Date : 1958
Foundations Of Set Theory written by Abraham Adolf Fraenkel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Logic, Symbolic and mathematical categories.
Set Theory Logic And Their Limitations
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Author : Moshe Machover
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-23
Set Theory Logic And Their Limitations written by Moshe Machover 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 1996-05-23 with Mathematics categories.
In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory.
Mathematical Logic And Foundations Of Set Theory
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Author : Yehoshua Bar-Hillel
language : en
Publisher:
Release Date : 1970
Mathematical Logic And Foundations Of Set Theory written by Yehoshua Bar-Hillel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Set theory categories.