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, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.

The study of human reasoning and the study of human language have been closely connected in European philosophical thought. Except for the Buddhist thinker Dignāga, these two areas of study have not been connected in classical India. The connection which Dignāga made between inference and meaning in his theory of exclusion is a distinguishing feature of Buddhist philosophical thought in classical India and, for that reason, it is useful to treat the Indian Buddhist views of reasoning and meaning together. (...) Logic, seeks to distinguish good reasoning from bad. Since reasoning is often communicated and, to that extent, expressed in a language, it is natural to use the forms of language to identify the forms of reasoning. (shrink)

This book focuses on two primary concerns, language and philosophical thinking. The first part of the book examines the ways that language, particularly the English language, shapes and channels our thoughts. The second part considers the three basic processes in concept formation: abstracting, imagining and generalizing. Lastly, the rational process itself is examined, looking at definition, rational inquiry and philosophical system building. First published in 1967, this edition is a reprint of the 1972 enlarged edition published by (...) University of New Mexico Press. (shrink)

HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ...

The chapter considers the relation between language and logic in early Daoism. It explains the Daoist experience of language, which is closely related to the Daoist experience of the Way (dao). It is shown how Daoist logic differs from the Confucian logic of correctness and the Mohist logic of naming. Even if Daoist discourse does not follow these more familiar forms of logic, it does not negate the law of non-contradiction nor does it (...) fall into the performative contradiction. Through readings of significant Daoist stories the Daoist logic beyond logic is brought to view. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, (...) and different approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

'This sentence is false' - is that true? The 'Liar paradox' embodied in those words exerted a particular fascination on the logicians of the Western later Middle Ages, and, along with similar 'insoluble' problems, forms the subject of the first group of articles in this volume. In the following parts Professor Spade turns to medieval semantic theory, views on the relationship between language and thought, and to a study of one particular genre of disputation, that known as 'obligationes'. The (...) focus is on the Oxford scholastics of the first half of the 14th century, and it is the name of William of Ockham which dominates these pages - a thinker with whom Professor Spade finds himself in considerable philosophical sympathy, and whose work on logic and semantic theory has a depth and richness that have not always been sufficiently appreciated. (shrink)

This paper investigates Wittgenstein’s account of the relation between elementary and molecular propositions (and thus, also, the propositions of logic) in the Tractatus Logico-Philosophicus. I start by sketching a natural reading of that relation – which I call the “bipartite reading” – holding that the Tractatus gives an account of elementary propositions, based on the so-called picture theory, and a different account of molecular ones, based on the principle of truth- functionality. I then show that such a reading cannot (...) be attributed to Wittgenstein, because he holds the view that an explanation of logical complexity is already given by a correct account of the (pictorial) nature of elementary propositions; this is implied in his claim that “an elementary proposition contains all logical constants/operations in itself”. After clarifying Wittgenstein’s notion of an operation from the Notes on Logic to the Tractatus, I finally explain why Wittgenstein claims that an elementary proposition contains all logical operations in itself, and hence why he can be said to provide a unified (and thus not bipartite) account of language and logic. (shrink)

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

This thesis discusses some central aspects of Wittgenstein's conception of language and logic in his Tractatus Logico-Philosophicus and brings them into relation with the philosophies of Frege and Russell. The main contention is that a fruitful way of understanding the Tractatus is to see it as responding to tensions in Frege's conception of logic and Russell's theory of judgement. In the thesis the philosophy of the Tractatus is presented as developing from these two strands of criticism and (...) thus as the culmination of the philosophy of logic and language developed in the early analytic period. Part one examines relevant features of Frege's philosophy of logic. Besides shedding light on Frege's philosophy in its own right, it aims at preparing the ground for a discussion of those aspects of the Tractatus' conception of logic which derive from Wittgenstein's critical response to Frege. Part two first presents Russell's early view on truth and judgement, before considering several variants of the multiple relation theory of judgement, devised in opposition to it. Part three discusses the development of Wittgenstein's conception of language and logic, beginning with Wittgenstein's criticism of the multiple relation theory and his early theory of sense, seen as containing the seeds of the picture theory of propositions presented in the Tractatus. I then consider the relation between Wittgenstein's pictorial conception of language and his conception of logic, arguing that Wittgenstein's understanding of sense in terms of bipolarity grounds his view of logical complexity and of the essence of logic as a whole. This view, I show, is free from the internal tensions that affect Frege's understanding of the nature of logic. (shrink)

In the current version of Mozi, there are six special chapters on knowledge, language, logic, ethics, politics and science. They include “Canon I ” and “Canon Explanation I ”, “Canon II ” and “Canon Explanation II ”, and “Major Illustrations” and “Minor Illustrations”. Later scholars give the names “Mohist Canons ” for the first four chapters and “Mohist Dialectical Chapters” for all the six. The content of these six chapters indicates that the later Mohists follow Mozi’s cognitive spirit (...) in dealing with ethical and socio-political issues and,most importantly, apply an analytic approach to investigate philosophical problems, especially, in knowledge, language and logic. (shrink)

This is a sequel to the author's The Language and Logic of the Bible: The Earlier Middle Ages. The period of the reformation saw immense changes of approach to the study of the Bible, which in turn brought huge consequences. This book, seeking to show the direction of endeavour of such study in the last medieval centuries, examines the theory of exegesis, practical interpretation, popular Bible study and preaching, and looks especially at the areas of logic and (...) language in which the scholars of the period had considerable expertise. The condemnation of the scholastics has tended to sink with them a proper recognition of what they achieved. In looking forward to the reformation, Dr Evans demonstrates a greater continuity of attitude than has often been allowed and describes how the enquiries of later medieval scholars opened out into the explorations of the sixteenth century made by Protestant and Roman Catholic thinkers alike. (shrink)

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, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.

Although the two volumes of _Logic, Language, and Meaning _can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions.

This book focuses on two primary concerns, language and philosophical thinking. The first part of the book examines the ways that language, particularly the English language, shapes and channels our thoughts. The second part considers the three basic processes in concept formation: abstracting, imagining and generalizing. Lastly, the rational process itself is examined, looking at definition, rational inquiry and philosophical system building. First published in 1967, this edition is a reprint of the 1972 enlarged edition published by (...) University of New Mexico Press. (shrink)

The German debates concerning the need for a reform of logic in post-Hegelian times took place under the label “The logical question”, a label introduced by Friedrich Adolf Trendelenburg. The main objective of these debates was to overcome the Hegelian identification of logic and metaphysics without re-establishing the old Aristotelian-scholastic formal logic. This paper presents the positions developed by Friedrich Adolf Trendelenburg, Otto Friedrich Gruppe, and Carl v. Prantl, each of whom advocated the importance of language (...) in logic in order to introduce a more dynamical element into the alleged static character of formal logic. (shrink)

The essays in this collection are by some of the leading figures in their fields and they touch on the most recent turnings in Quine's work.

Candrakīrti is known for his commentaries on the major works of Nāgārjuna and Āryadeva. This chapter examines how Candrakīrti uses language and logic to undermine people's confidence in cherished beliefs about a self and point them towards the Buddha's path and its goal the peace of nirvana that transcends the limitations of language and logic. Candrakīrti first sets out his view on the two truths in the Madhyamakāvatāra. He associates both truths with the soteriological goal of (...) Nāgārjuna's path: the peaceful state of nirvana. Madhyamaka teaching amounts to nihilism. Candrakīrti responds that the charge of nihilism is wrong because there is no repudiation of moral actions. Emptiness is also related to the concept of intrinsic nature, and Candrakīrti uses this term in more than one sense. (shrink)

The content of this book provides a unified and coherent treatment of a number of important issues in the philosophy of language and logical theory.

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such (...) self-referential sentences? The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

Recent commentators on Nietzsche’s philosophy have paid careful attention to his reflections on truth. While this issue has generated significant dispute, one prominent school of thought is in tacit agreement about the view of language that underlies Nietzschean truth. This view holds that certain linguistic entities can capture precise, distinct units of propositional content and static, rigidly designated conceptual meanings. A closer look at Nietzsche’s various analyses of language and logic reveals not only that he does not (...) subscribe to such a position, but that he offers a sustained critique against the possibility of any form of atomism of language. It was only in the 1880s, after Nietzsche overcame his dualistic commitments to Kant and Schopenhauer and embraced a philosophy of becoming, that the full power of his critique is made manifest. (shrink)

For Proclus, like other Platonists, logic, epistemology, and philosophy of language are not distinct as a tool and parts of philosophy respectively, but are all part of dialectic. This chapter first briefly addresses Proclus’ logic, specifically the ‘rule of obversion’ ascribed to him, and his naturalist philosophy of language, and thereafter moves on to epistemology. The author discusses Proclus’ top-down psychology, where the highest faculty is the paradigm for the lower ones; the Iamblichean principle that knower (...) determines knowledge; the essential reason-principles, or lower forms constituting the soul’s essence; Proclus’ rich notion of recollection; his solutions to two challenges to his epistemology: the knowledge of things of which there is no Form, and the use of images in cognition. Finally, in the conclusion the author assesses Proclus’ originality and discusses the fact that for late Neoplatonists knowledge is not an end in itself. (shrink)

This is the first critical study of The Logic of Sense, Gilles Deleuze's most important work on language and ethics, as well as the main source of his vital philosophy of the event.James Williams explains the originality of Deleuze's work with careful definitions of all his innovative terms and a detailed description of the complex structure he constructs. This reading makes connections to his ground-breaking work on literature, to his critical but also progressive relation to the sciences, and (...) to his controversial denial of the priority of standard logics, human values and 'meaning' in thinking.This book will open new debates and develop current ones around Deleuze's work in philosophy, politics, literature, linguistics, cultural studies and sociology. (shrink)

The main purpose of Alexander’s book is "to lay a foundation for modes of philosophical thinking and many of the traditional problems of philosophy by an examination of the manner in which ideas are constructed." Toward this end, the book is divided into three parts. The first part deals mainly with language and its constituent questions. The mechanics of communication are presented including a detailed breakdown of its elements and the reasons for its success and failure. With respect to (...) the study of language, Alexander explores such questions as the learning of a language, the study of grammar, the nature of words, and the relation of thought to language. In his section on symbols, the author considers the nature of symbols, the relationship of symbols to their referents, and the distinction between and uses of signs and symbols. The fourth major topic in this section, the concept of meaning, centers around the kinds of referential meaning and the relation of existential variability to class relations. Views mentioned range from Plato to Chomsky, Piaget, and Austin. This first part serves as a backdrop to the more central part dealing with processes of thinking. Analyzed are three basic processes: abstracting, imagining, and generalizing. Three varieties of abstractions: qualities, relations, and functions, are deemed sufficiently important to warrant sustained treatment. Imagining, "the altering of abstractions," is of primary importance in the understanding of the nature of thought. His account of the process of generalizing explicates, among other issues, the concept of universals and their existential status. This section is neatly tied together by an examination of the interrelationships between these three processes in which he appropriately draws upon the major figures of Greek and modern philosophy. Throughout the presentation, the ways in which these processes are expressed linguistically is never lost sight of. The final part of the book, dealing with the nature of rational inquiry, centers upon the concepts of defining, inferring, and systematizing. While the book was designed as an introductory text, its usefulness is certainly not limited to this purpose.—B. G. H. (shrink)

RESUMEN Este trabajo pretende relacionar dos debates emparentados sobre cómo la lógica y el lenguaje influyen sobre el pensamiento. Existe un eje de discusión en relación a si hay una pluralidad de lógicas o un único sistema lógico como criterio de evaluación para cualquier contexto de razonamiento. En lingüística, el debate surgido a partir de las interpretaciones fuertes y débiles de la hipótesis Sapir-Whorf ha centralizado la discusión en torno al grado de influencia o determinación del lenguaje sobre el pensamiento. (...) Desde perspectivas y marcos teórico-conceptuales diferentes, lógica y lingüística delimitan y problematizan un campo de indagación y reflexión. El artículo, desde una mirada transdisciplinar, pretende dar cuenta y postular vasos comunicantes entre estos debates atendiendo a los matices de cada enfoque, así como proponer una hipótesis propia sobre la problemática planteada. ABSTRACT This paper aims to relate two debates about how logic and language influence thought. There is an axis of discussion about whether there exists a plurality of logic or a single logical system as an evaluation criterion for any reasoning context. In linguistics, the debate arising from the strong and weak interpretations of the Sapir-Whorf hypothesis has centralized the discussion around the degree of influence or determination of language on thought. From different perspectives and theoretical-conceptual frameworks, logic, and linguistics delimit and problematize a field of inquiry and reflection. The article, from a transdisciplinary perspective, intends to account for and postulate communicating vessels between these debates, considering the nuances of each approach. It also seeks to propose its own hypothesis on the problem raised. (shrink)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when (...) the language is enriched with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

Although the two volumes of _Logic, Language, and Meaning_ can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, _Introduction to Logic_, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach (...) to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained. (shrink)