Logic and the Modalities in the Twentieth Century

Author: Dov M. Gabbay,John Woods

Publisher: Elsevier

ISBN: 9780080463032

Category: Mathematics

Page: 732

View: 4275

Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. · Detailed and comprehensive chapters covering the entire range of modal logic. · Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic.

Brill’s Companion to George Grote and the Classical Tradition

Author: Kyriakos N. Demetriou

Publisher: BRILL

ISBN: 9004280499

Category: History

Page: 432

View: 2018

In Brill’s Companion to George Grote and the Classical Tradition, Kyriakos Demetriou leads a team of prominent scholars to contextualize, unravel and explore Grote's works as well as provide a critical assessment of his posthumous legacy.

Logic from Russell to Church

Author: Dov M. Gabbay,John Woods

Publisher: Elsevier

ISBN: 0080885470

Category: Mathematics

Page: 1068

View: 9664

This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

Greek, Indian and Arabic Logic

Author: Dov M. Gabbay,John Woods

Publisher: Elsevier

ISBN: 9780080532868

Category: Mathematics

Page: 628

View: 560

Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas.

Handbook of the History of Logic: Sets and extensions in the twentieth century

Author: Dov M. Gabbay,John Hayden Woods,Akihiro Kanamori

Publisher: Elsevier

ISBN: 0444516212

Category: Reference

Page: 865

View: 8331

"Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-nineteenth century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the eleventh and sixteenth centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to enquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece." -- Publisher's website.

Agency and Deontic Logic

Author: John F. Horty

Publisher: Oxford University Press

ISBN: 9780198030768

Category: Philosophy

Page: 208

View: 5641

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point of view.

Logical Modalities from Aristotle to Carnap

Author: Max Cresswell,Edwin Mares,Adriane Rini

Publisher: Cambridge University Press

ISBN: 1107077885

Category: Mathematics

Page: 366

View: 6058

Introduces readers to the history of necessity and possibility, two modal concepts which play a key role in philosophy.

Logic for Applications

Author: Anil Nerode,Richard Shore

Publisher: Springer Science & Business Media

ISBN: 9780387948935

Category: Computers

Page: 456

View: 8695

In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

Empirical Logic and Public Debate

Essays in Honour of Else M. Barth

Author: Erik C. W. Krabbe,Renée José Dalitz,Pier A. Smit

Publisher: Rodopi

ISBN: 9789051835922

Category: Philosophy

Page: 337

View: 4857

Empirical Logic and Public Debate supplies a large number of previously unpublished papers that together make up a survey of recent developments in the field of empirical logic. It contains theoretical contributions, some of a more formal and some of an informal nature, as well as numerous contemporary and historical case studies. The book will therefore be attractive both to those who wish to focus upon the theory and practice of discussion, debate, arguing, and argument, as well as to those readers who are primarily interested in applications to a particular field, such as ethics, political philosophy, feminist philosophy, or the history of philosophy.

The Is-Ought Problem

An Investigation in Philosophical Logic

Author: G. Schurz

Publisher: Springer Science & Business Media

ISBN: 9780792344100

Category: Philosophy

Page: 332

View: 9167

Can OUGHT be derived from IS? This book presents a systematic investigation of this time-honored philosophical problem by means of modern alethic-deontic predicate logic. Two comprehensive introductory chapters into the philosophical and logical foundations make the text understandable also for non-logicians ethicists, social scientists and students of philosophy. New in this study are two leitmotifs: relevance and metalogical generality. It turns out that is-ought inferences indeed exist, but they are all irrelevant in a precise logical sense. New proof techniques allow to establish this result for very broad classes of logics. A profound philosophical investigation of the question of analytical or strongly intersubjective is-ought bridge principles supplements the logical study. The final results imply incisive limitations for the justifiability of ethics as opposed to empirical science.

Paraconsistent logic

essays on the inconsistent

Author: Graham Priest,Richard Sylvan

Publisher: Philosophia Verlag Gmbh


Category: Philosophy

Page: 715

View: 1025


Content and Modality

Themes from the Philosophy of Robert Stalnaker

Author: Judith Thomson,Alex Byrne

Publisher: Clarendon Press

ISBN: 0191515736

Category: Language Arts & Disciplines

Page: 312

View: 3921

Eleven distinguished philosophers have contributed specially written essays on a set of topics much debated in recent years, including physicalism, qualia, semantic competence, conditionals, presuppositions, two-dimensional semantics, and the relation between logic and metaphysics. All these topics are prominent in the work of Robert Stalnaker, a major presence in contemporary philosophy, in honour of whom the volume is published. It also contains a substantial new essay in which Stalnaker replies to his critics, and sets out his current views on the topics discussed. Contributors: Richard Heck, Frank Jackson, William Lycan, Vann McGee, John Perry, Paul Pietroski, Sydney Shoemaker, Scott Soames, Daniel Stoljar, Timothy Williamson, and Stephen Yablo.

New Studies in Deontic Logic

Norms, Actions, and the Foundations of Ethics

Author: R. Hilpinen

Publisher: Springer Science & Business Media

ISBN: 9400984847

Category: Philosophy

Page: 262

View: 1720

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings (D. Reidel Publishing Company, Dordrecht 1971): its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts of obligation, permission and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic' (1951). Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities.

The Analytic Tradition in Philosophy, Volume 1

The Founding Giants

Author: Scott Soames

Publisher: Princeton University Press

ISBN: 1400850452

Category: Philosophy

Page: 680

View: 5647

This is the first of five volumes of a definitive history of analytic philosophy from the invention of modern logic in 1879 to the end of the twentieth century. Scott Soames, a leading philosopher of language and historian of analytic philosophy, provides the fullest and most detailed account of the analytic tradition yet published, one that is unmatched in its chronological range, topics covered, and depth of treatment. Focusing on the major milestones and distinguishing them from the dead ends, Soames gives a seminal account of where the analytic tradition has been and where it appears to be heading. Volume 1 examines the initial phase of the analytic tradition through the major contributions of three of its four founding giants—Gottlob Frege, Bertrand Russell, and G. E. Moore. Soames describes and analyzes their work in logic, the philosophy of mathematics, epistemology, metaphysics, ethics, and the philosophy of language. He explains how by about 1920 their efforts had made logic, language, and mathematics central to philosophy in an unprecedented way. But although logic, language, and mathematics were now seen as powerful tools to attain traditional ends, they did not yet define philosophy. As volume 1 comes to a close, that was all about to change with the advent of the fourth founding giant, Ludwig Wittgenstein, and the 1922 English publication of his Tractatus, which ushered in a "linguistic turn" in philosophy that was to last for decades.

European Philosophy of Science - Philosophy of Science in Europe and the Viennese Heritage

Author: Maria Carla Galavotti,Elisabeth Nemeth,Friedrich Stadler

Publisher: Springer Science & Business Media

ISBN: 331901899X

Category: Science

Page: 403

View: 325

This volume combines the theoretical and historical perspective focusing on the specific features of a European philosophy of science. On the occasion of the 20th anniversary of the Institute Vienna Circle the Viennese roots and influences will be addressed, in addition. There is no doubt that contemporary philosophy of science originated mainly in Europe beginning in the 19th century and has influenced decisively the subsequent development of globalized philosophy of science, esp. in North America. Recent research in this field documents some specific characteristics of philosophy of science covering the natural, social, and also cultural sciences in the European context up to the destruction and forced migration caused by Fascism and National Socialism. This European perspective with the integration of history and philosophy of science and the current situation in the philosophy of science after the transatlantic interaction and transformation, and the “return” after World War II raises the question of contemporary European characteristics in the philosophy of science. The role and function of the renowned Vienna Circle of Logical Empiricism and its impact and influence on contemporary philosophy of science is on the agenda, too. Accordingly, the general topic is dealt with in two parallel sessions representing systematic-formal as well as genetic-historical perspectives on philosophy of science in a European context up to the present.​

Displaying Modal Logic

Author: Heinrich Wansing

Publisher: Springer

ISBN: 9780792352051

Category: Philosophy

Page: 252

View: 1880

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.

Formal Methods

An Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logic

Author: E.W. Beth

Publisher: Springer

ISBN: 9027700699

Category: Philosophy

Page: 170

View: 1459

Many philosophers have considered logical reasoning as an inborn ability of mankind and as a distinctive feature in the human mind; but we all know that the distribution of this capacity, or at any rate its development, is very unequal. Few people are able to set up a cogent argument; others are at least able to follow a logical argument and even to detect logical fallacies. Nevertheless, even among educated persons there are many who do not even attain this relatively modest level of development. According to my personal observations, lack of logical ability may be due to various circumstances. In the first place, I mention lack of general intelligence, insufficient power of concentration, and absence of formal education. Secondly, however, I have noticed that many people are unable, or sometimes rather unwilling, to argue ex hypothesi; such persons cannot, or will not, start from premisses which they know or believe to be false or even from premisses whose truth is not, in their opinion, sufficient ly warranted. Or, if they agree to start from such premisses, they sooner or later stray away from the argument into attempts first to settle the truth or falsehood of the premisses. Presumably this attitude results either from lack of imagination or from undue moral rectitude. On the other hand, proficiency in logical reasoning is not in itself a guarantee for a clear theoretic insight into the principles and foundations of logic.

The Development of Modern Logic

Author: Leila Haaparanta

Publisher: Oxford University Press

ISBN: 9780199722723

Category: Philosophy

Page: 1008

View: 649

This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.

Temporal Logic

From Ancient Ideas to Artificial Intelligence

Author: Peter Øhrstrøm,Per Hasle

Publisher: Springer Science & Business Media

ISBN: 0585374635

Category: Philosophy

Page: 416

View: 9925

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.