Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language

Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language PDF

Author: Alessandro Torza

Publisher:

Published: 2015

Total Pages:

ISBN-13: 9783319183633

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This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology, and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth's notion of implicit definition, and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings, and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.

Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language

Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language PDF

Author: Alessandro Torza

Publisher: Springer

Published: 2015-07-23

Total Pages: 526

ISBN-13: 3319183621

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This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.

Quantifiers in Language and Logic

Quantifiers in Language and Logic PDF

Author: Stanley Peters

Publisher: Oxford University Press

Published: 2006-04-27

Total Pages: 549

ISBN-13: 019929125X

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Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment of meaning. It presents a broad view of the semantics and logic of quantifier expressions in natural languages and, to a slightly lesser extent, in logical languages. The authors progress carefully from a fairly elementary level to considerable depth over the course of sixteen chapters; their book will be invaluable to a broad spectrum of readers, from those with a basicknowledge of linguistic semantics and of first-order logic to those with advanced knowledge of semantics, logic, philosophy of language, and knowledge representation in artificial intelligence.

The Routledge Handbook of Philosophy of Relativism

The Routledge Handbook of Philosophy of Relativism PDF

Author: Martin Kusch

Publisher: Routledge

Published: 2019-12-06

Total Pages: 582

ISBN-13: 1351052292

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Relativism can be found in all philosophical traditions and subfields of philosophy. It is also a central idea in the social sciences, the humanities, religion and politics. This is the first volume to map relativistic motifs in all areas of philosophy, synchronically and diachronically. It thereby provides essential intellectual tools for thinking about contemporary issues like cultural diversity, the plurality of the sciences, or the scope of moral values. The Routledge Handbook of Philosophy of Relativism is an outstanding major reference source on this fundamental topic. The 57 chapters by a team of international contributors are divided into nine parts: Relativism in non-Western philosophical traditions Relativism in Western philosophical traditions Relativism in ethics Relativism in political and legal philosophy Relativism in epistemology Relativism in metaphysics Relativism in philosophy of science Relativism in philosophy of language and mind Relativism in other areas of philosophy. Essential reading for students and researchers in all branches of philosophy, this handbook will also be of interest to those in related subjects such as politics, religion, sociology, cultural studies and literature.

The Semantic Conception of Logic

The Semantic Conception of Logic PDF

Author: Gil Sagi

Publisher: Cambridge University Press

Published: 2021-09-09

Total Pages: 316

ISBN-13: 1108529828

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This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.

Objects and Modalities

Objects and Modalities PDF

Author: Tero Tulenheimo

Publisher: Springer

Published: 2017-03-14

Total Pages: 208

ISBN-13: 3319531190

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This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs.

Everything, more or less

Everything, more or less PDF

Author: J. P. Studd

Publisher: Oxford University Press

Published: 2019-04-04

Total Pages: 256

ISBN-13: 019103035X

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Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things regardless of their kind. But how general can we be and do we ever succeed in theorizing about absolutely everything? Not according to generality relativism. In its most promising form, this kind of relativism maintains that what 'everything' and other quantifiers encompass is always open to expansion: no matter how broadly we may generalize, a more inclusive 'everything' is always available. The importance of the issue comes out, in part, in relation to the foundations of mathematics. Generality relativism opens the way to avoid Russell's paradox without imposing ad hoc limitations on which pluralities of items may be encoded as a set. On the other hand, generality relativism faces numerous challenges: What are we to make of seemingly absolutely general theories? What prevents our achieving absolute generality simply by using 'everything' unrestrictedly? How are we to characterize relativism without making use of exactly the kind of generality this view foreswears? This book offers a sustained defence of generality relativism that seeks to answer these challenges. Along the way, the contemporary absolute generality debate is traced through diverse issues in metaphysics, logic, and the philosophy of language; some of the key works that lie behind the debate are reassessed; an accessible introduction is given to the relevant mathematics; and a relativist-friendly motivation for Zermelo-Fraenkel set theory is developed.

Quantifiers and Cognition: Logical and Computational Perspectives

Quantifiers and Cognition: Logical and Computational Perspectives PDF

Author: Jakub Szymanik

Publisher: Springer

Published: 2016-02-19

Total Pages: 211

ISBN-13: 3319287494

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This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science.

The Language of Ontology

The Language of Ontology PDF

Author: J. T. M. Miller

Publisher: Oxford University Press

Published: 2021-06-10

Total Pages: 240

ISBN-13: 0192648535

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Metaphysical and ontological debates, concerning what exists and the nature of reality, are perennial features of the philosophical landscape. However, some have argued that ontological debates are non-substantive, pointless, trivial, incoherent, or impossible. Debates about whether tables exist, for example, or about the nature of reality, are taken to be in some way deficient. This has led to a burgeoning literature studying the nature of metaphysical and ontological disputes themselves. One major debate within this context concerns the language of ontology. The central question is whether the nature of language influences or limits our ability to engage productively in ontological disputes. While we typically think that our language describes the world, or at least can accurately describe the world, there have been many who have argued that the nature of language inherently influences and limits our attempts to understand the nature of reality-that our claims about what exists are, in fact, merely a reflection of how we happen to speak or think. The Language of Ontology collects chapters from established participants in the debate alongside new voices, to explore the range of issues relating to our ability or inability to get beyond the limits of our language.

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