The Foundations Of Modality
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The Foundations Of Modality
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Author : Peter Fritz
language : en
Publisher: Oxford University Press
Release Date : 2024-01-25
The Foundations Of Modality written by Peter Fritz 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 2024-01-25 with Mathematics categories.
The notions of necessity and possibility, as well as the notion of a possible world, are ubiquitous in philosophy. Nevertheless, these notions remain controversial. This book develops a general framework for theorizing about these notions using the tools of higher-order logic.
The Foundations Of Modality
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Author : Peter Fritz
language : en
Publisher: Oxford University Press
Release Date : 2023-10-03
The Foundations Of Modality written by Peter Fritz 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 2023-10-03 with Philosophy categories.
The notions of necessity and possibility, as well as the notion of a possible world, are ubiquitous in philosophy. Nevertheless, these notions remain controversial. It also remains controversial whether metaphysics requires notions drawing distinctions which are finer than those which can be drawn in terms of necessity and possibility, such as the recently much-discussed notion of grounding. In order to make progress on these debates, this book develops a general framework for theorizing about such intensional notions using the tools of higher-order logic. The Foundations of Modality begins by motivating the use of higher-order logic, and introduces a particularly simple form of higher-order logic. Progress is made on well-trodden territory concerning modality and possible worlds by considering first the question how fine propositions are individuated. Peter Fritz uses both logical results and philosophical arguments to motivate a relatively coarse-grained individuation of propositions. Fritz shows that a number of putative metaphysical notions are ruled out by this theory of individuation. Furthermore, the theory allows the controversial notion of (metaphysical) necessity to be delineated as the broadest necessity, which applies just to the single tautologous proposition. This book also vindicates appeals to possible worlds: First, it shows that if anything plays the theoretical role of possible worlds, then certain propositions do so. Second, it argues that there are in fact the required propositions playing the role of possible worlds; this is shown using the notion of plural quantification over propositions in higher-order logic.
The Foundations Of Modality
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Author : Peter Fritz
language : en
Publisher:
Release Date : 2023
The Foundations Of Modality written by Peter Fritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Modality (Logic) categories.
The notions of necessity and possibility, as well as the notion of a possible world, are ubiquitous in philosophy. Nevertheless, these notions remain controversial. This book develops a general framework for theorizing about these notions using the tools of higher-order logic.
Mathematics Models And Modality
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Author : John P. Burgess
language : en
Publisher: Cambridge University Press
Release Date : 2008-02-21
Mathematics Models And Modality written by John P. Burgess 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 2008-02-21 with Science categories.
John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.
Many Dimensional Modal Logics Theory And Applications
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Author : A. Kurucz
language : en
Publisher: Elsevier
Release Date : 2003-10-21
Many Dimensional Modal Logics Theory And Applications written by A. Kurucz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-21 with Computers categories.
Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables
The Actual And The Possible
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Author : Mark Sinclair
language : en
Publisher: Oxford University Press
Release Date : 2017
The Actual And The Possible written by Mark Sinclair 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 2017 with Mathematics categories.
The Actual and the Possible presents new essays by leading specialists on modality and the metaphysics of modality in the history of modern philosophy from the seventeenth to the twentieth centuries. It revisits key moments in the history of modern modal doctrines, and illuminates lesser-known moments of that history. The ultimate purpose of this historical approach is to contextualise and even to offer some alternatives to dominant positions within the contemporary philosophy of modality. Hence the volume contains not only new scholarship on the early-modern doctrines of Baruch Spinoza, G. W. F. Leibniz, Christian Wolff and Immanuel Kant, but also work relating to less familiar nineteenth-century thinkers such as Alexius Meinong and Jan Lukasiewicz, together with essays on celebrated nineteenth- and twentieth-century thinkers such as G. W. F. Hegel, Martin Heidegger and Bertrand Russell, whose modal doctrines have not previously garnered the attention they deserve. The volume thus covers a variety of traditions, and its historical range extends to the end of the twentieth century, addressing the legacy of W. V. Quine's critique of modality within recent analytic philosophy.
Essays In The Metaphysics Of Modality
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Author : Alvin Plantinga
language : en
Publisher: Oxford University Press
Release Date : 2003-03-27
Essays In The Metaphysics Of Modality written by Alvin Plantinga 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 2003-03-27 with Philosophy categories.
Perhaps no one has done more in the last 30 years to advance thinking in the metaphysics of modality than has Alvin Plantinga. Collected here are some of his most important essays on this influential subject. Dating back from the late 1960's to the present, they chronicle the development of Plantinga's thoughts about some of the most fundamental issues in metaphysics: what is the nature of abstract objects like possible worlds, properties, propositions, and such phenomena? Are there possible but non-actual objects? Can objects that do not exist exemplify properties? Plantinga gives thorough and penetrating answers to all of these questions and many others. This volume contains some of the best work in metaphysics from the past 30 years, and will remain a source of critical contention and keen interest among philosophers of metaphysics and philosophical logic for years to come.
The Foundation Of Reality
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Author : David Glick
language : en
Publisher: Oxford University Press
Release Date : 2020-04-29
The Foundation Of Reality written by David Glick 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 2020-04-29 with Philosophy categories.
Are space and time fundamental features of our world or might they emerge from something else? The Foundation of Reality brings together metaphysicians and philosophers of physics working on space, time, and fundamentality to address this timely question. Recent developments in the interpretation of quantum mechanics and the understanding of certain approaches to quantum gravity have led philosophers of physics to propose that space and time might be emergent rather than fundamental. But such discussions are often conducted without engagement with those working on fundamentality and related issues in contemporary metaphysics. This book aims to correct this oversight. The diverse contributions to this volume address topics including the nature of fundamentality, the relation of space and time to quantum entanglement, and space and time in theories of quantum gravity. Only through consideration of a range of different approaches to the topic can we hope to get clear on the status of space and time in our contemporary understanding of physical reality.
The Foundation Grammar Dictionary
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Author : Gordon Winch
language : en
Publisher: New Frontier Publishing
Release Date : 2005
The Foundation Grammar Dictionary written by Gordon Winch and has been published by New Frontier Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Language Arts & Disciplines categories.
The essential grammar handbook for students.
Modality
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Author : Yitzhak Y. Melamed
language : en
Publisher: Oxford University Press
Release Date : 2024
Modality written by Yitzhak Y. Melamed 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 2024 with Philosophy categories.
Modality: A History provides readers a sweeping study of the history of philosophical work on modal concepts. Everyday discourse is saturated with appeals to what might be the case or to what must be true or to what cannot happen. Possibility, necessity, and impossibility are modal terms, and philosophers have long wondered how to best understand them. This volume traces the history of some of the most prominent and important contributions to our understanding of possibility and necessity over the past two and half millennia of western philosophy, from ancient Greek philosophers through current debates in the 21st century. Over the course of nine chapters from prominent scholars, this volume traces a history of modal theorizing that begins with extended discussions of Aristotle and the Stoics. Several chapters discuss insights and disagreements among Latin, Arabic, and Jewish medieval scholastics, such as Al-GhazâlÃ(R), Scotus, and Crescas. Three chapters center on early modern philosophers, whose modal views were deeply shaped by this conceptual inheritance but also departed from it in significant ways: Descartes, Malebranche, Locke, Spinoza, Leibniz, and Hume. Kant and Hegel's modal contributions are presented in their own chapter, and another chapter traces the legacy of Kant's account on early-to-mid 20th century modal views, including Husserl, Heidegger, Russell, and Quine. The revival of modal metaphysics in the more recent work of Kripke, Marcus, and Lewis has led to a new flourishing of modal theories, including in recent debates among neo-Aristotelians, as the final chapter illustrates. Although modal concepts are interesting and important on their own, theories of modality often intersect with other significant philosophical topics, such as time, freedom, and God. Modal concepts also extend beyond metaphysics. To illustrate the role of modality in other domains, several small-scale studies, or Reflections, are dispersed among these main chapters on modality in cosmology, religion, music, literature, and logic. Readers will learn how a seemingly timeless and changeless cluster of modal concepts have undergone significant revisions and enjoy a rich developmental history.