The papers in this volume present some of the most recent results of the work about contradictions in philosophical logic and metaphysics; examine the history of contradiction in crucial phases of philosophical thought; consider the relevance of contradictions for political and philosophical actuality. From this consideration a common question emerges: the question of the irreducibility, reality and productive force of (some) contradictions.

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).

In selecting the papers for this volume I have excluded all physics papers proper. I have further omitted all book rev.iews. Instead, I have included two papers not published previously; they are marked by an asterisk in the table of contents. Since many of the papers were occasioned by Symposia or similar gatherings their chronological order is rather accidental. Hence I have tried to group the papers thematically into four parts. Within each part the order of sequence is from the (...) more general to the more special, or from a more popular to a more technical treatment. The same principle has been applied to the sequential order of the parts. The foundational papers on quantum mechanics have been arranged in a somewhat dif ferent manner. Chapters XVI-XIX are concerned with the logic of complementarity while in Chapters XX-XXII a more radical recon ceptualization is carried out. Two of the older papers have been revised to bring them more into line with present terminology. Other papers have been corrected by additions and omissions. Additions are marked by square brackets [ ], while double square brackets [[ II signify omis sions or parts to be omitted. Hence [[A]] [B] means that 'A' should be replaced by 'B'. The heading of one paper has been changed to make it more descriptive. (shrink)

This book traces the development of Dialectical Logic within the history of modern western philosophy, culminating in Marx s materialist dialectics. It brings out the essential contours of Logic through a detailed exposition of the ontological and epistem.

Analytic philosophy is sometimes said to have particularly close connections to logic and to science, and no particularly interesting or close relation to its own history. It is argued here that although the connections to logic and science have been important in the development of analytic philosophy, these connections do not come close to characterizing the nature of analytic philosophy, either as a body of doctrines or as a philosophical method. We will do better to understand analytic (...) philosophy—and its relationship to continental philosophy—if we see it as a historically constructed collection of texts, which define its key problems and concerns. It is true, however, that analytic philosophy has paid little attention to the history of the subject. This is both its strength—since it allows for a distinctive kind of creativity—and its weakness—since ignoring history can encourage a philosophical variety of “normal science.”. (shrink)

The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the (...) set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base (...) of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

This paper provides a short summary of Mark Bevir, The Logic of the History of Ideas (Cambridge: Cambridge University Press, 1999). Logic stands here as a subset of Wittgenstein’s notion of philosophy as a matter of the grammar of our concepts. It studies the forms of reasoning appropriate to a discipline, rather than the material of that discipline. Hence, the logic of the history of ideas considers the nature of meaning, the way we should justify (...) our knowledge of past meanings, and how we should explain things such as the existence of meanings, the beliefs people held, and conceptual change. (shrink)

In 1934 a most singular event occurred. Two papers were published on a topic that had (apparently) never before been written about, the authors had never been in contact with one another, and they had (apparently) no common intellectual background that would otherwise account for their mutual interest in this topic.1 These two papers formed the basis for a movement in logic which is by now the most common way of teaching elementary logic by far, and indeed is (...) perhaps all that is known in any detail about logic by a number of philosophers (especially in North America). This manner of proceeding in logic is called ‘natural deduction’. And in its own way the instigation of this style of logical proof is as important to the history of logic as the discovery of resolution by Robinson in 1965, or the discovery of the logistical method by Frege in 1879, or even the discovery of the syllogistic by Aristotle in the fourth century BC. (shrink)

The Conciliatory Character of Jaina Logic. In the previous pages there has been given an indication of the services rendered by the Jainas and N° Brihrna^1 H,e the Buddhists in the formation of the Mediaeval School of Indian Logic. Since the  ...

The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages The early modern period High modern period Early 20th century Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and (...) look at historical arguments in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic. (shrink)

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the (...) language of relating logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue. (shrink)

A 'self-refutation argument' is any argument which aims at showing that a certain thesis is self-refuting. This study was the first book-length treatment of ancient self-refutation and provides a unified account of what is distinctive in the ancient approach to the self-refutation argument, on the basis of close philological, logical and historical analysis of a variety of sources. It examines the logic, force and prospects of this original style of argumentation within the context of ancient philosophical debates, dispelling various (...) misconceptions concerning its nature and purpose and elucidating some important differences which exist both within the ancient approach to self-refutation and between that approach, as a whole, and some modern counterparts of it. In providing a comprehensive account of ancient self-refutation, the book advances our understanding of influential and debated texts and arguments from philosophers like Democritus, Plato, Aristotle, Epicurus, the Stoics, the Academic sceptics, the Pyrrhonists and Augustine. (shrink)

In Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy , edited by Admir Skodo, an array of historical and philosophical chapters decenter the idea of formal logic as the most accurate, timeless, and abstract description of all thought and reasoning.

This book reveals the rational basis for historians' descriptions, interpretations and explanations of past events. C. Behan McCullagh defends the practice of history as more reliable than has recently been acknowledged. Historians, he argues, make their accounts of the past as fair as they can and avoid misleading their readers. He explains and discusses postmodern criticisms of history, providing students and teachers of history with a renewed validation of their practice. McCullagh takes the history debate to (...) a new stage with bold replies to the major questions historians face today. (shrink)

Is logic masculine? Is women's lack of interest in the "hard core" philosophical disciplines of formal logic and semantics symptomatic of an inadequacy linked to sex? Is the failure of women to excel in pure mathematics and mathematical science a function of their inability to think rationally? Andrea Nye undermines the assumptions that inform these questions, assumptions such as: logic is unitary, logic is independenet of concrete human relations, and logic transcends historical circumstances as well (...) as gender. In a series of studies of the logics of historical figures--Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege--she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, or scientists. (shrink)

The study of literary texts appears at the moment to stand at a decisive juncture. Trends in critical thinking over the last decades have questioned the possibility of recovering a text's historical meaning. At the same time, there is a newly insistent plea for a return to “history” in the interpretation of literature. Before a rapprochement can occur, however, we need to have a clearer understanding of how both historians and critics understand “history” and of the ways in (...) which postmodernist thought positions history and the role of the historian with respect to issues of literary interpretation at the forefront of contemporary critical debate. (shrink)

In the tree-like representation of Time, two histories are undivided at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with an indistinguishability function, a generalization of (...) the notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper. (shrink)

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, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in (...) class='Hi'>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. (shrink)

This essay presents a theoretical construct upon which to base a working - "pragmatic" - definition of the History of Present Illness (HPI). The major thesis of this essay is that analysis of both the logic of hypothesis formation and literary narrative - especially detective stories - facilitates understanding of the diagnostic process. The essay examines three elements necessary to a successful development of a patient's HPI: the logic of hypothesis formation, based upon the work of the (...) philosopher-logician, Charles Sanders Peirce; the organization of knowledge in relation to structures of narrative; and the feedback necessary to the successful physician-interviewer. It concludes with a systematic description of the design of hypothesis formation within diagnoses. (shrink)

History based models suggest a process-based approach to epistemic and temporal reasoning. In this work, we introduce preferences to history based models. Motivated by game theoretical observations, we discuss how preferences can dynamically be updated in history based models. Following, we consider arrow update logic and event calculus, and give history based models for these logics. This allows us to relate dynamic logics of history based models to a broader framework.

Many philosophers affiliated with the analytic school contend that the history of philosophy is not relevant to their work. The present study challenges this claim by introducing a strong variant of the philosophical history of philosophy termed the “logical–contextual history of philosophy.” Its objective is to map the “logical geography” of the concepts and theories of past philosophical masters, concepts and theories that are not only genealogically, but also logically related. Such history of philosophy cannot be (...) set in opposition to the traditional “systematic philosophy.” Rather, the logical–contextual history of philosophy is, like the traditional school philosophies, systematic, although it develops along different lines. (shrink)

History of Logic and Semantics offers a collection of studies on the development of the Aristotelian and terminist approaches to language, from the Boethian reception of Aristotle to the post-medieval terminism. These articles were also published in Vivarium, Volume 53, Nos. 2-4.

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all (...) dispel the many fallacious ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

Much attention has been given to Arabic thought in the history of philosophy, however, Arabic contributions to logic have been greatly overlooked. In the ten essays of this book, Nicholas Rescher presents substantial material on the history, progression and major trends of Arabic logic from the eighth through the sixteenth century. Rescher finds that, like much of Western thought, Arabic logic had its basis in Greek philosophy, and specifically in Hellenistic Aristotelian logic.

Outlines a systematic historical account of the developments of Hegel's logic, both in his own works and those of his most significant followers. This study then provides an interpretation and internal criticism from an idealistic-transcendental philosophical perspective.

Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...