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).

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.

Excerpt from A History of Formal Logic In this edition of the most considerable history Of formal logic yet published, the Opportunity has Of course been taken to make some adjustments seen to be necessary in the original, with the author's full concurrence. Only in 36, however, has the numeration of cited passages been altered owing to the introduction of new matter. Those changes are as follows. About the Publisher Forgotten Books publishes hundreds of thousands of (...) rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, (...) the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics. (shrink)

We take into account two areas of the logical research of the Lvov-Warsaw School. First, we consider a new approach to research in the history of logic introduced and practiced by Łukasiewicz and some of his followers. In this style of doing history of logic, the knowledge of original philosophical and logical texts was combined with competence in modern logic. This method resulted in many important discoveries both in history and in logic and (...) philosophy. At the same time, we pay attention to contemporary historical research devoted to the logic created by the School itself. In this context, we present an overview of the six papers included in the special issue ‘Logic and its History in the Lvov-Warsaw School’. These papers were presented at an international symposium, ‘History in/of the Lvov-Warsaw School’, held in October 2022 in Warsaw, and they cover various aspects of historical-logical and logical achievements of the School. They concern topics from history of ancient logic, history of modern proof theory, and the issues of applying logic to philosophy and theology in the same way as the one implemented at the Lvov-Warsaw School. (shrink)

AbstractŁukasiewicz introduced a new methodological approach to the history of logic. It consists of the use of modern formal logic in the research of the history of logic. Although he was not the first to use formal logic in his historical research, Łukasiewicz was the first who used it consistently and formulated it as a requirement for a historian of logic. The aim of this paper is to present Łukasiewicz's contribution and the (...) class='Hi'>history of its formulation. In addition, the paper will present its reception. There are two main themes in Łukasiewicz’s work on the history of logic. He discussed Stoic logic and Aristotle’s syllogistic. The second part of the paper focuses on current reception of Łukasiewicz’s contribution and on the question of whether there is a difference between knowledge about his contribution to Stoic logic and to Aristotle’s syllogistic, given that it has been hypothesised that Łukasiewicz’s contribution is currently more known among Aristotelian scholars than among those who focus on Stoic logic. Based on the papers that have appeared in the last five years at Web of Science and Scopus this hypothesis has not been confirmed. (shrink)

Johannes Steuchius’ disputatio uses Arabic logic to present an historical account of the development of philosophical thought in Arabia before and after the emergence of Islam. Steuchius first proposes that philosophy drew its origins from the East. His evidence for this claim is that many of the Greek philosophers, considered the forefathers of European philosophy, began cultivating their philosophical thinking as a result of exposure to ancient Eastern philosophy. After the introduction of Greek philosophy, it is agreed that dialectic (...) was among the first of the arts the Arabs practiced. (shrink)

Logical positivism is often characterized as a set of naive doctrines on meaning, method, and metaphysics. In recent decades, however, historians have dismissed this view as a gross misinterpretation. This new scholarship raises a number of questions. When did the standard reading emerge? Why did it become so popular? And how could commentators have been so wrong? This essay reconstructs the history of a “caricature” and rejects the hypothesis that it was developed by ill-informed Anglophone scholars who failed to (...) appreciate the subtleties of European scientific philosophy. It argues that the received view has a more complicated history and was frequently promoted by the European positivists themselves. The essay shows that the view has roots in both American and European scientific philosophy and emerged as a result of the complex interplay between the two communities in the years before the intellectual migration. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd 1 Gabbay and Woods, eds., The Rise of Modern Logic from Leibniz to Frege, Vol. 3 of the Handbook of the History of Logic (Amsterdam, etc.: North-Holland, 2004). russell: the Journal of Bertrand Russell Studies n.s. 29 (winter 2009–10): 167–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 eviews BERTRAND (...) RUSSELL IN RECENT BOOKS ON LOGIC HISTORY Irving Anellis Peirce Edition / Indiana U.–Purdue U. Indianapolis, in 46202–5157, usa [email protected] Dov M. Gabbay and John Woods, eds. Logic from Russell to Church. Vol. 5 of The Handbook of the History of Logic. Amsterdam, etc.: North-Holland, 2009. Pp. xii + 1056. us$260; £157.99; ¤185.95. Leila Haaparanta, ed. The Development of Modern Logic. Oxford and New York: Oxford U. P., 2009. Pp. x + 904. us$150.00. The essay “Bertrand Russell’s Logic” by Andrew D. Irvine in Volume 5 of the Handbook of the History of Logic is one of the shortest in the volume (pp. 1–28). But something of Russell pervades many of the other essays as well, as we might expect given the centrality that Principia Mathematica has occupied in the historiography of logic through much of the twentieth century. This is especially evident in the lengthiest of the essays, Andrea Cantini’s “Paradoxes, Self-reference and Truth in the 20th Century” (pp. 875–1013), and more than tangentially in Dale Jacquette’s “Logic for Meinongian Object Theory Semantics” (pp. 29–76) and Michael Potter’s “The Logic of the Tractatusz” (pp. 255–304). In their preface, the editors of the Handbook explain (p. vii) the rationale for treating Frege and Russell in separate volumes.1 One reason is that it was a matter of simple conveniencez—zto keep the volume covering logic from Leibniz to Frege of manageable size. The other is historical: while admitting that Frege and Russell shared important goals and the philosophical position of logicism, it is noted that Frege’s most important work in logic and foundations was carried out prior to his learning of Russell’s paradox, whereas the entire corpus of Russell’s work, Principiaz included, was designed to a considerable extent in eTorts to deal with the paradox, as was much of the work in logic, set theory, and philosophy of logic that came as a consequence of the discovery of that paradox. Gabbay April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd 168 Reviews and Woods also make explicit the philosophical diTerences between Frege and Russell regarding the epistemological status of axioms as one of the signiWcant diTerences between these two. More particularly, the editors assert (p. viii) that, in the very brief period between publication of the second volume of Frege’s Grundgesetze (1903) and Russell’s Principles of Mathematics (1903), there was a pronounced shift initiated in the goals of mathematical logic, away from naïve apriority of axiom systems, towards study of the limits and properties of formal systems.Thecontributors to these metalogical concerns, Herbrand, Hilbert, and Gödel, among others, are the subject of the bulk of the essays included in Volume 5 of the Handbook. The task that Irvine undertakes is initiated by the eTort to understand the unity of Russell’s technical body of work in mathematics, logic, metaphysics, and epistemology. Thus the discrepancy between the neo-Hegelian concept of relations, inherited from Bradley, with certain types of relationsz—zlogical, spatial, temporal, for examplez—zwith the mathematical understanding of relations, is given as the ground for Russell’s abandonment of idealism in favour of realism (pp. 4–5). For example, there is nothing inherent in two relata, say Abelard and Héloise, which contributes to the relation of love between the pair; rather, its root is found in the mental states of one or the other of the lovers, so that the relation itself is not an intrinsic property of one of the pair. Likewise, Russell reaches this position... (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)

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that (...) they are founded on only one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today. (shrink)

The author has in this work clearly marked the principal stages of Indian logic in the vast period of about two thousand years beginning from 640 and has traced how from Anviksiki the science of debate Indian logic developed into the science of knowledge Pramanasastra and then into the science of dialectics Prakarana of Tarkasastra.The treatment of the subject is both historical and critical. The author has traced some Greek influence on indian logic. For instance he has (...) shown how the five membered syllogism of Aristotle found its way through Alexandria Syria and other countries into Taxila and got amalgamated with the Nyaya doctrine of inference.The book is one of the pioneer works on the subjects. It has drawn on original sources exhaustively. Besides the preface introduction, foreword and table of contents the work contains several appendices and indexes. (shrink)

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)

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)

In this paper we present an overview, with historical and critical remarks, of two articles by S. Jaśkowski ([20, 21] 1948 and [22, 23] 1949), which contain the oldest known formulation of a paraconsistent logic. Jaśkowski has built the logic – he termed discussive (D2) – by defining two new connectives and by introducing a modal translation map from D2 systems into Lewis’ modal logic S5. Discussive systems, for their formal details and their original philosophical justification, have (...) attracted discrete attention among experts. Indeed, in what follows, after having introduced Jaśkowski methodology of building D2 and his main philosophical motivations for providing such a system, we will explore some of the main contributions to the development of D2. (shrink)

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)

A Short History of Logic by William Ritchie Sorley, first published in 1911, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent (...) damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. (shrink)

This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.

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)

This book provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. Its fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

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)

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.

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book (...) appeared under the title _Natural Deduction_. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration. (shrink)

In the first decades of the twentieth century, many philosophers and philosophical movements attempted to make philosophy scientific by analogy with science. Such attempts vary with respect to the strategies adopted for implementing the analogy. In this article, I single out the specificity of logical empiricism’s strategy, by comparing it to some of its most relevant contemporary scientific philosophies, such as Russell’s method of analysis, Husserl’s phenomenology, neo-Kantianism, and American pragmatism. Logical empiricism sees philosophy as continuous with science, by reducing (...) the problems of philosophy to problems in mathematical logic. The other scientific philosophies postulate a specificity of philosophy, by maintaining a special domain for it and also a specific methodology, while requiring this methodology to be scientific in a manner analogous to the general method of the special sciences. I argue that this distinction helps to revise and possibly to settle some of the debates concerning our understanding of both the genealogy and the development of the movement, such as the conjectural derivation of its scientific philosophy from Russell’s analytic philosophy or from a special brand of Austrian philosophy and the complex relationship with its German and American contemporaries. (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)

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)

"General Survey. The succession of thinkers and schools. The history of ancient philosophy covers about eleven centuries, from Thales who lived during the sixth century B.C. to Boethius and Simplicius who flourished at the beginning of the sixth A.D. From the point of view of the history of formal logic this long epoch may be divided into three periods. (1) The pre-Aristotelian period, from the beginnings to the time at which Aristotle..

From the start the better logicians found much to take exception to in Prantl. Peirce, for example, describes him as "a writer of little judgment and over-rated learning, whose useful history of logic is full of blunders, misappreciations, and insensate theories, and whose own Billingsgate justifies almost any tone toward him". As is indicated in this comment, Prantl attempted to judge and assess the value of the logical achievements that he made the object of his study. However, he (...) himself had little logical acumen. If not justified, this is to some extent excused by Heinrich Scholz, the first comprehensive historian of logic after Prantl. In his Abriß der Geschichte der Logik, which first appeared in 1931 and has now been translated, he maintains that no trustworthy conception of the history of logic was possible until modern and mathematical logic provided a precise criterion for formal logic. In particular he maintains that logic in the course of its history has assumed different Gestalten, which must be distinguished if sense is to be made of it. He is especially concerned to distinguish formal logic, whether in its ancient Aristotelian or its modern mathematical Gestalt, from its non-formal extensions into psychology, epistemology, and metaphysics. It is certainly true that the rise of mathematical logic has also witnessed a renewed interest in the history of logic. Scholars using the means provided by modern analysis have found much in the past of great logical interest, which had previously been dismissed as worthless extravagance. The logic of the Stoics and of the 14th-century scholastics are prime examples. (shrink)

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish (...) mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

In 1948, Stanis aw Ja kowski defined a logical system D2 of a discursive 1 sentential calculus. The aim of this paper is to introduce the reader to the basic ideas of the discursive logic and to show, in a historical perspective, its development originating from the two germ papers [19] and [20]. We intend to present some problems connected with it and outline the solutions they have received up to the present day.