Plural Logic

Second Edition, Revised and Enlarged
Author: Alex Oliver,Timothy Smiley
Publisher: OUP Oxford
ISBN: 0191644110
Category: Philosophy
Page: 352
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Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; in other words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The authors' approach is an attractive blend of no-nonsense argumentative directness and open-minded liberalism, and they convey the exciting and unexpected richness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book. This second edition includes a greatly expanded treatment of the paradigm empty term zilch, a much strengthened treatment of Cantorian set theory, and a new chapter on higher-level plural logic.

Logic & Natural Language

On Plural Reference and Its Semantic and Logical Significance
Author: Hanoch Ben-Yami
Publisher: Ashgate Publishing, Ltd.
ISBN: 9780754637431
Category: Language Arts & Disciplines
Page: 160
View: 3526
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Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus' place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in its treatment of reference and quantification, and that as a result the calculus is inadequate for the analysis of the semantics and logic of natural language.

Mereology: A Philosophical Introduction


Author: Giorgio Lando
Publisher: Bloomsbury Publishing
ISBN: 1472583671
Category: Philosophy
Page: 240
View: 2815
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Parthood and composition are everywhere. The leg of a table is part of the table, the word "Christmas" is part of the sentence "I wish you a merry Christmas", the 13th century is part of the Middle Ages. The Netherlands, Belgium, and Luxembourg compose Benelux, the body of a deer is composed of a huge number of cells, the Middle Ages are composed of the Early Middle Ages, High Middle Ages, and Late Middle Ages. Is there really a general theory covering every instance of parthood and composition? Is classical mereology this general theory? Are its seemingly counter-intuitive features serious defects? Mereology: A Philosophical Introduction addresses the multifaceted and lively philosophical debates surrounding these questions, and defends the idea that classical mereology is indeed the general and exhaustive theory of parthood and composition in the domain of concrete entities. Several examples of parthood and composition, involving entities of different kinds, are scrutinised in depth. Incidentally, mereology is shown to interact in a surprising way with metaontology. Presenting a well-organized and comprehensive discussion of parthood and related notions, Mereology: A Philosophical Introduction contributes to a better understanding of a subject central to contemporary metaphysics.

Modal Logic as Metaphysics


Author: Timothy Williamson
Publisher: OUP Oxford
ISBN: 0191057401
Category: Philosophy
Page: 480
View: 2452
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Are there such things as merely possible people, who would have lived if our ancestors had acted differently? Are there future people, who have not yet been conceived? Questions like those raise deep issues about both the nature of being and its logical relations with contingency and change. In Modal Logic as Metaphysics, Timothy Williamson argues for positive answers to those questions on the basis of an integrated approach to the issues, applying the technical resources of modal logic to provide structural cores for metaphysical theories. He rejects the search for a metaphysically neutral logic as futile. The book contains detailed historical discussion of how the metaphysical issues emerged in the twentieth century development of quantified modal logic, through the work of such figures as Rudolf Carnap, Ruth Barcan Marcus, Arthur Prior, and Saul Kripke. It proposes higher-order modal logic as a new setting in which to resolve such metaphysical questions scientifically, by the construction of systematic logical theories embodying rival answers and their comparison by normal scientific standards. Williamson provides both a rigorous introduction to the technical background needed to understand metaphysical questions in quantified modal logic and an extended argument for controversial, provocative answers to them. He gives original, precise treatments of topics including the relation between logic and metaphysics, the methodology of theory choice in philosophy, the nature of possible worlds and their role in semantics, plural quantification compared to quantification into predicate position, communication across metaphysical disagreement, and problems for truthmaker theory.

Unity and Plurality

Logic, Philosophy, and Linguistics
Author: Massimiliano Carrara,Alexandra Arapinis,Friederike Moltmann
Publisher: Oxford University Press
ISBN: 0191025623
Category: Philosophy
Page: 256
View: 3356
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Unity and Plurality presents novel ways of thinking about plurality while casting new light on the interconnections among the logical, philosophical, and linguistic aspects of plurals. The volume brings together new work on the logic and ontology of plurality and on the semantics of plurals in natural language. Plural reference, the view that definite plurals such as 'the students' refer to several entities at once (the individual students), is an approach favoured by logicians and philosophers, who take sentences with plurals ('the students gathered') not to be committed to entities beyond individuals, entities such as classes, sums, or sets. By contrast, linguistic semantics has been dominated by a singularist approach to plurals, taking the semantic value of a definite plural such as 'the students' to be a mereological sum or set. Moreover, semantics has been dominated by a particular ontological view of plurality, that of extensional mereology. This volume aims to build a bridge between the two traditions and to show the fruitfulness of nonstandard mereological approaches. A team of leading experts investigates new perspectives that arise from plural logic and non-standard mereology and explore novel applications to natural language phenomena.

Plural Predication


Author: Thomas McKay
Publisher: Oxford University Press on Demand
ISBN: 0199278148
Category: Language Arts & Disciplines
Page: 263
View: 3948
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Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. Yet the apparatus of predication and quantification in standard modern logic does not allow a place for such non-distributive predicates.Thomas McKay's book explores the enrichment of modern logic with plural predication and quantification. We can have genuinely non-distributive predication without relying on singularizing procedures from set theory and mereology. The fundamental 'among' relation can be understood in a way that does not generate any hierarchy of plurals analogous to a hierarchy of types or a hierarchy of higher-order logics. Singular quantification can be understood as a special case, with the general type beingquantifiers that allow both singular and plural quantification. The 'among' relation is formally similar to a 'part of' relation, but the relations are distinct, so that mass quantification and plural quantification cannot be united in the same way that plural and singular are united.Analysis of singular and plural definite descriptions follows, with a defense of a fundamentally Russellian analysis, but coupled with some new ideas about how to be sensitive to the role of context. This facilitates an analysis of some central features of the use of pronouns, both singular and plural.

Composition as Identity


Author: A. J. Cotnoir,Donald L. M. Baxter
Publisher: OUP Oxford
ISBN: 0191022160
Category: Philosophy
Page: 240
View: 7826
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Composition is the relation between a whole and its parts—the parts are said to compose the whole; the whole is composed of the parts. But is a whole anything distinct from its parts taken collectively? It is often said that 'a whole is nothing over and above its parts'; but what might we mean by that? Could it be that a whole just is its parts? This collection of essays is the first of its kind to focus on the relationship between composition and identity. Twelve original articles—written by internationally renowned scholars and rising stars in the field—argue for and against the controversial doctrine that composition is identity. An editor's introduction sets out the formal and philosophical groundwork to bring readers to the forefront of the debate.

Logic, Logic, and Logic


Author: George Boolos,Richard C. Jeffrey
Publisher: Harvard University Press
ISBN: 9780674537675
Category: Philosophy
Page: 443
View: 4704
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George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Plural Pronominal Anaphora in Context

Dynamic Aspects of Quantification
Author: Rick Nouwen
Publisher: N.A
ISBN: N.A
Category: Anaphora (Linguistics)
Page: 193
View: 4395
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From Discourse to Logic

Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory
Author: Hans Kamp,Uwe Reyle
Publisher: Springer Science & Business Media
ISBN: 9401716161
Category: Philosophy
Page: 717
View: 5527
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Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than that, it is about a particular way of dealing with those subjects, known as Discourse Representation Theory, or DRT. DRT is an approach towards natural language semantics which, some thirteen years ago, arose out of attempts to deal with two distinct problems. The first of those was the semantic puzzle that had been brought to contempo rary attention by Geach's notorious "donkey sentences" - sentences like If Pedro owns some donkey, he beats it, in which the anaphoric connection we perceive between the indefinite noun phrase some donkey and the pronoun it may seem to conflict with the existential meaning of the word some. The second problem had to do with tense and aspect. Some languages, for instance French and the other Romance languages, have two morphologically distinct past tenses, a simple past (the French Passe Simple) and a continuous past (the French Imparfait). To articulate precisely what the difference between these tenses is has turned out to be surprisingly difficult.

Plurals and Events


Author: Barry Schein
Publisher: MIT Press
ISBN: 9780262193344
Category: Language Arts & Disciplines
Page: 384
View: 8391
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Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of plurals without invoking "pluralobjects," with its attendant metaphysics, and also provide an absolute truth-theoreticcharacterization of the semantics of sentences with plurals in them.

Handbook of Logic and Language


Author: Johan F.A.K. van Benthem,Alice ter Meulen
Publisher: Elsevier
ISBN: 9780444537270
Category: Mathematics
Page: 1168
View: 1623
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The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. Completely revised and updated - includes over 25% new material Discusses the interface between logic and language Many of the authors are creators or active developers of the theories

The Construction of Logical Space


Author: Agustín Rayo
Publisher: Oxford University Press
ISBN: 0199662622
Category: Mathematics
Page: 220
View: 3375
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Our conception of logical space is the set of distinctions we use to navigate the world. Agustín Rayo defends the idea that one's conception of logical space is shaped by one's acceptance or rejection of 'just is'-statements: statements like 'to be composed of water just is to be composed of H2O'. The resulting picture is used to articulate a conception of metaphysical possibility that does not depend on a reduction of the modal to the non-modal, and todevelop a trivialist philosophy of mathematics, according to which the truths of pure mathematics have trivial truth-conditions.

Derrida Vis-à-vis Lacan

Interweaving Deconstruction and Psychoanalysis
Author: Andrea Margaret Hurst
Publisher: Fordham Univ Press
ISBN: 0823228754
Category: Philosophy
Page: 469
View: 2080
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Derrida and Lacan have long been viewed as proponents of two opposing schools of thought. This book argues, however, that the logical structure underpinning Lacanian psychoanalytic theory is a complex, paradoxical relationality that corresponds to Derrida's plural logic of the aporia.Andrea Hurst begins by linking this logic to a strand of thinking (in which Freud plays a part) that unsettles philosophy's transcendental tradition. She then shows that Derrida is just as serious and careful a reader of Freud's texts as Lacan. Interweaving the two thinkers, she argues that the Lacanian Real is another name for Derrida's diffrance and shows how Derrida's writings on Heidegger and Nietzsche embody an attitude toward sexual difference and feminine sexuality that matches Lacanian insights. Derrida's plural logic of the aporia, she argues, can serve as a heuristic for addressing prominent themes in Lacanian psychoanalysis: subjectivity, ethics, and language. Finally, she takes up Derrida's prejudicial reading of Lacan's Seminar on 'The Purloined Letter, 'which was instrumental in the antagonism between Derrideans and Lacanians. Although acknowledging the injustice of Derrida's reading, the author brings out the deep theoretical accord between thinkers that both recognize the power of psychoanalysis to address contemporary political and ethical issues

The Plural Actor


Author: Bernard Lahire
Publisher: Polity
ISBN: 0745646840
Category: Political Science
Page: 271
View: 2559
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The individual that the social sciences take as an object is most often studied in a particular context or from a single dimension. The actor is analysed as a student, worker, consumer, spouse, reader, sportsperson, a voter etc. However, in societies where individuals live often through simultaneously and successively heterogeneous and sometimes contradictory social experiences, each person inevitably carries a plurality of roles, ways of seeing, feeling and acting. The aim of this study is to consider the ways in which this plurality of worlds and experiences are incorporated into the being of each individual and to observe the individual's actions in a variety of settings. In addition to his sociological viewpoint, the author engages with psychology, history, anthropology and philosophy. His reflections lead him to embark on a program of psychological sociology to highlight the complexities of this plural view of the social.

First Person Plural

Multiple Personality and the Philosophy of Mind
Author: Stephen E. Braude
Publisher: Rowman & Littlefield
ISBN: 9780847679966
Category: Psychology
Page: 315
View: 2721
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Do people with multiple personalities have more than one self? The first full-length philosophical study of multiple personality disorder, First Person Plural maintains that even the deeply divided multiple personality contains an underlying psychological unity. Braude updates his work in this revised edition to discuss recent empirical and conceptual developments, including the charge that clinicians induce false memories in their patients, and the professional redefinition of "multiple personality disorder" as "dissociative identity disorder."

Plural Temporality

Transindividuality and the Aleatory Between Spinoza and Althusser
Author: Vittorio Morfino
Publisher: BRILL
ISBN: 9004270558
Category: Political Science
Page: 204
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Plural Temporality traces out a dynamic historical relationship between the texts of Spinoza and of Althusser. It interrogates Spinoza’s text through Althusser and vice versa regarding the question of materialism.

Worlds Apart

A Handbook on World Views; Second Edition
Author: Norman Geisler,William D. Watkins
Publisher: Wipf and Stock Publishers
ISBN: 1592441262
Category: Religion
Page: 308
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Those looking for a compendium of the major world views, written from a Christian perspective, need look no further. Comprehensive and readable, well organized and up to date, 'Worlds Apart' stands alone. After introducing the meaning and function of a world view, the authors explore the seven major world views of our day -- theism, atheism, pantheism, pantheism, deism, finite godism, and polytheism. They delineate the varieties within each view, analyze the beliefs of its major representatives, and outline and evaluate its basic tenets. The authors present the seven world views in such a way that one can compare and contrast these views. ÒIt is our hope,Ó they write, Òthat [readers] will carefully consider all the options and then decide, even if it means discarding the world view [they] now have.Ó In this revised edition the authors have updated the text and bibliography, rewritten several sections, and included suggested readings for each world view. Like the original edition, published in 1984, this volume contains a glossary of terms and an index of subjects and names.

Mathematics, Models, and Modality

Selected Philosophical Essays
Author: John P. Burgess
Publisher: Cambridge University Press
ISBN: 113947054X
Category: Science
Page: N.A
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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.

The Plural Event

Descartes, Hegel, Heidegger
Author: Andrew Benjamin
Publisher: Routledge
ISBN: 1134866925
Category: Philosophy
Page: 224
View: 3338
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Benjamin provides new and important readings of key canonical texts in the history of philosophy in his sustained philosophical reworking of ontology. Amongst texts included are Hegel's Difference Essay and the Shorter Logic and Heidegger's Time and Being and The Question of Being. The effective presence of ontology, defined as `an original difference', will be familiar to readers of his earlier writings. This book represents his most thorough and original contribution to contemporary philosophy to date.