"The role of logic in the Middle Ages. Regarding the role of logic within the framework of arts and sciences during the Middle Ages, we have to distinguish two related aspects, one institutional and the other scientific. As to the first aspect, we have to remember that the medieval educational system was based on the seven liberal arts, which were divided into the trivium, i.e., three arts of language, and the quadrivium, i.e., four mathematical arts. The so-called trivial arts (...) were grammar, rhetoric, and logic, and during a period of several centuries virtually every educated person, at least every university graduate, received a training in these matters, especially in logic. Students in the medieval faculty of arts probably spent more time studying logic than any other discipline. This first -- institutional -- aspect concerning the role of logic is explained by the second -- scientific -- aspect. The trivial disciplines provided techniques of analysis and a technical vocabulary that permeate philosophical, scientific and theological writings. Logic, as mentioned before, was referred to and was generally regarded as the art of arts and the science of sciences. The increasing cultural dominance of the universities with their obligatory disputationes and their hierarchy of examinations on the one hand and the outstanding status of logic on the other were corresponding features of the educational world of the 13th century. The core of the logic curriculum from the 12th century onwards was provided by the logical works of Aristotle. These represented the material for the study of types of predication, the analysis of simple propositions or statements (2) and their relations of inference and equivalence, the analysis of modal propositions, of the structure and the types of the syllogism, dialectical topics, fallacies and scientific reasoning as based on the demonstrative syllogism. Medieval logicians, however, realized that there were other, non-Aristotelian, approaches to logical subjects, questions and methods that could be investigated.. (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 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)
Epistemic logic is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the twentieth century. Epistemic Logic in the Later Middle Ages provides the first comprehensive study of the subject. Ivan Boh explores the contrast between epistemic and alethic conceptions of consequence, the general epistemic rules of consequence, the search for conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, (...) the considerations of epistemic/doxastic iterated modalities, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. Boh concludes with a comparison between medieval endeavors and the epistemic logic of our own times. Written in a clear and readable style with minimal symbolic apparatus, this book employs modern symbolism and conceptual frameworks, and complements the studies of the syntacticand semantic dimensions of medieval logic. (shrink)
This study is the first modern account of the development of philosophy during the Carolingian Renaissance. In the late eighth century, Dr Marenbon argues, theologians were led by their enthusiasm for logic to pose themselves truly philosophical questions. The central themes of ninth-century philosophy - essence, the Aristotelian Categories, the problem of Universals - were to preoccupy thinkers throughout the Middle Ages. The earliest period of medieval philosophy was thus a formative one. This work is based on a fresh (...) study of the manuscript sources. The thoughts of scholars such as Alcuin, Candidus, Fredegisus, Ratramnus of Corbie, John Scottus Eriugena and Heiric of Auxerre is examined in detail and compared with their sources; and a wide variety of evidence is used to throw light on the milieu in which these thinkers flourished. Full critical editions of an important body of early medieval philosophical material, much of it never before published, are included. (shrink)
The Consolations of Philosophy by Boethius, whose English translators include King Alfred, Geoffrey Chaucer, and Queen Elizabeth I, ranks among the most remarkable books to be written by a prisoner awaiting the execution of a tyrannical death sentence. Its interpretation is bound up with his other writings on mathematics and music, on Aristotelian and propositional logic, and on central themes of Christian dogma. -/- Chadwick begins by tracing the career of Boethius, a Roman rising to high office under the Gothic (...) King Theoderic the Great, and suggests that his death may be seen as a cruel by-product of Byzantine ambitions to restore Roman imperial rule after its elimination in the West in AD 476. Subsequent chapters examine in detail his educational programme in the liberal arts designed to avert a threatened collapse of culture and his ambition to translate into Latin everything he could find on Plato and Aristotle. -/- Boethius has been called `last of the Romans, first of the scholastics'. This book is the first major study in English of a writer who was of critical importance in the history of thought. (shrink)
Introduction Since my work in medieval logic has concentrated on dialectic. I have tried to trace scholastic treatments of dialectic to discussions of it in ...
Medieval logicians advanced far beyond the logic of Aristotle, and this book shows how far that advance took them in two central areas. Broadie focuses upon the work of some of the great figures of the fourteenth century, including Walter Burley, William Ockham, John Buridan, Albert of Saxony, and Paul of Venice, and deals with their theories of truth conditions and validity conditions. He reveals how much of what seems characteristically twentieth-century logic was familiar long ago. Broadie has extensively (...) revised his text for this second edition, while preserving the character of the first. There are now fuller accounts of supposition, of intentional contexts, and of medieval syllogistic, and the conclusion has been substantially expanded. (shrink)
The specialized essays in this collection study whether non-Aristotelian traditions of ancient logic had a role for medieval logicians. Special attention is given to Stoic logic and semantics, and to Neoplatonism.
This study of the interpretations of Aristotle's "Categories" in the thirteenth century provides an introduction to some main themes of medieval philosophical ...
HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ...
0. Introduction: Mereology, Metaphysics, and Speculative Grammar 0.1 Mereology, Ancient and Contemporary 0.11 Mereology is, strictly speaking, the theory of ...
The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an examination (...) of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis ) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)
This is the first of a three-volume anthology intended as a companion to The Cambridge History of Later Medieval Philosophy. Volume 1 is concerned with the logic and the philosophy of language, and comprises fifteen important texts on questions of meaning and inference that formed the basis of Medieval philosophy. As far as is practicable, complete works or topically complete segments of larger works have been selected. The editors have provided a full introduction to the volume and (...) detailed introductory headnotes to each text; the volume is also indexed comprehensively. (shrink)
William of Auvergne and His Treatise De Anima I. Introduction William of Auvergne, Bishop of Paris from until his death in, is of interest to us chiefly ...
Sir Anthony Kenny here continues his fascinating account of the history of philosophy, focusing on the thousand-year-long medieval period. This is the second volume of a four-book set in which Kenny will unfold a magisterial new history of Western philosophy, the first major single-author history of philosophy to appear in decades. In this volume, Kenny takes us on a fascinating tour through more than a millennium of thought from 400 AD onwards, charting the story of philosophy (...) from the founders of Christian and Islamic thought through to the Renaissance. The Middle Ages saw a great flourishing of philosophy, and the intellectual endeavor of the era reaches its climax in the thirteenth and fourteenth centuries, with the systems of the great schoolmen such as Thomas Aquinas and John Duns Scotus. With Kenny as guide, we see these major philosophers through the eyes of a man who has spent a lifetime contemplating their work. Thus we do not simply get an overview of philosophy, but also a penetrating and insightful critique of it. Kenny offers an illuminating account of various thinkers and schools of thought, from Augustine to Maimonides and from Grosseteste to Pomponazzi. And he offers much insight into medieval thinking about logic and language, knowledge, physics, metaphysics, the mind, the soul, and God. Vividly written, but serious and deep enough to offer a genuine understanding of the great philosophers, Kenny's lucid and stimulating history will become the definitive work for anyone interested in the people and ideas that shaped the course of Western thought. (shrink)
This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the (...)medieval traditions in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)
PART ONE ELEMENTS OF SCHOLASTIC LOGIC I THE LEGACY OF SCHOLASTIC LOGIC "\ T 7E MAY safely describe the initial scholastic contri- VV bution to logical ...
This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schroder, Leopold Lowenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.
In 1980 L. M. de Rijk edited some texts connected with medieval disputation ( Die mittelaterlichen Traktate De modo opponendi et respondendi ), towards which he showed a strikingly contemptuous attitude. The reason for his contempt was that the treatises did not fit the obligationes and sophismata tradition. In this article I focus on the original version, the Thesaurus Philosophorum , to highlight the distinction of this family of treatises with respect to the “modern“ tradition. First, I study the (...) features of the disputation that can be recognised through the collection of fallacious arguments contained in the Thesaurus . Second, I briefly examine the contents of the treatise and their arrangement, showing that they are closely related to the kind of disputation in question. I hope to support the idea that neither the technique of disputation nor the contents and their arrangement deserve a straightforward rejection. (shrink)
The Hegel Lectures Series -/- Series Editor: Peter C. Hodgson -/- Hegel's lectures have had as great a historical impact as the works he himself published. Important elements of his system are elaborated only in the lectures, especially those given in Berlin during the last decade of his life. The original editors conflated materials from different sources and dates, obscuring the development and logic of Hegel's thought. The Hegel Lectures series is based on a selection of extant and recently discovered (...) transcripts and manuscripts. The original lecture series are reconstructed so that the structure of Hegel's argument can be followed. Each volume presents an accurate new translation accompanied by an editorial introduction and annotations on the text, which make possible the identification of Hegel's many allusions and sources. -/- Hegel's interpretation of the history of philosophy not only played a central role in the shaping of his own thought, but also has had a great influence on the development of historical thinking. In his own view the study of the history of philosophy is the study of philosophy itself. This explains why such a large proportion of his lectures, from 1805 to 1831, the year of his death, were about history of philosophy. The text of these lectures, presented here in the first authoritative English edition, is therefore a document of the greatest importance in the development of Western thought: they constitute the very first comprehensive history of philosophy that treats philosophy itself as undergoing genuine historical development. And they are crucial for understanding Hegel's own systematic works such as the Phenomenology, the Logic, and the Encyclopedia, for central to his thought is the theme of spirit as engaged in self-realization through the processes of historical change. Furthermore, they played a crucial role in one of the determining events of modern intellectual history: the rise of a new consciousness of human life, culture, and intellect as historical in nature. This third volume of the lectures covers the medieval and modern periods, and includes fascinating discussion of scholastic, Renaissance, and Reformation philosophy, and of such great modern thinkers as Descartes, Locke, Leibniz, and especially Kant. (shrink)
INTRODUCTION If Roger Bacon is known for anything today it is for his association with the medieval beginnings of what we now call experimental science, ...
The contributions in this volume examine these questions on the basis of key texts, thus shedding new light on the problematic relationship between logic and theology.
Whatever its merits and difficulties, the concept of logic embedded in much of the ?new philosophy? of the early modern period was then understood to supplant contemporary views of formal logic. The notion of compiling a natural history of the understanding constituted the basis of this new concept of logic. The following paper attempts to trace this view of logic through some of the major and numerous minor texts of the period, centering on the development and influence of John (...) Locke's understanding of the analysis of the cognitive faculties as the discipline of logic. (shrink)
This paper introduces the reader to the medieval Hebrew tradition of logic by considering its treatment of Aristotelian syllogistic. Starting in the thirteenth century European Jews translated Arabic and Latin texts into Hebrew and produced commentaries and original compendia.Because they stood culturally and geographically at the cross-roads of two great traditions they were influenced by both.This is clearly seen in the development of syllogistic theory, where the Latin tradition ultimately replaces, though never entirely, its Arabic counterpart.Specific attention is devoted (...) to the debate about the so-called Galenian fourth figure.In medieval Hebrew logic one finds both defenders and detractors of the figure, the former appearing towards the beginning of the period in question.With the ascendancy of scholastic logic the fourth figure virtually disappears from Hebrew texts. (shrink)
By using examples drawn from the periodical Nature, I show that research into the history of logic in the nineteenth century involves journals and periodicals which are normally not considered as standard sources for logic or its history.
The Deutsche Forschungsgemeinschaft (DFG)is supporting a research project entitled ?Case studies towards the establishment of a social history of logic? with a grant, initially for two years. The project is being carried out by a team of five members under the direction of Professor Christian Thiel in the Institut für Philosophie and the Interdisziplinäres Institut für Wissenschaftstheorie und Wissenschaftsgeschichte (IIWW) of the University of Erlangen-Nürnberg.
The paper begins by taking seriously Heidegger's provocative claims concerning Hegel's relationship to the Greeks. Most notably, the enigmatic assertion that Hegel, as the "last Greek," brings Greek philosophy to its completion through a historical thinking is considered in terms of the strange sense of repetition it opens up: the Hegelian presentation of Greek philosophy must both present that philosophy, repeat its movement, but also, in the repetition, present the truth of that movement for the first time. It thus must (...) remain undecided whether Hegel's presentation only opens up a necessity already at work in Greek philosophical history or whether that presentation, in fact, first grants such necessity to that history. The singularity of Hegel's relation to the Greeks is then explored through an examination of Hegel's own statements concerning the singularity of Aristotle. In this way, it becomes apparent that Hegel's own thought, in its entirety, asserts itself as nothing other that a decisive repetition of the Aristotelian speculative thought of actuality. This exceptional position of Aristotle in Hegel's logic of history suggests that there is a need for another sense of history's movement, in which that movement does not simply progress but unfolds as the sin- gular dialogue between one Greek and one German. (shrink)
Different conceptions of social philosophy were divided and polarized in different variants: from biological reductionism (the attempt to explain social phenomena in terms of biology) to sociocentrism. The approach V. A. Vazulin’s conception of “The Logic of History” makes it possible to concretize the dialectic of the natural (including the biological) and the social. The creative development of the method of scientific investigation made it possible to reveal the inner systematic interconnection of laws and categories of social theory which (...) reflect the structure of developed society; it also made it possible to outline thetheoretical periodization of human history (the objective laws of its “ascent” from the very beginning, emergence, formation, to maturity) through a prism of interconnections of natural and social factors. The conception of “The Logic of History” opens a stage in the successive dialectical development of social philosophy by sublating historical materialism and the formation approach. The structure of society as a whole is a multi‐level, hierarchical and subordinated system, the organic whole of interconnected elements, relations and processes. The historical process is regarded as a gradual transformation of the natural (including the biological) by the social, i.e., as a social “sublation” of the latter by the former. The stages in the process of development are analyzed here: as theunity of the natural (including the biological) and the social; as a process of emergence of the social from the natural; as the transformation of thenatural by the social. (shrink)
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 topic of history-of-science explanation is first briefly introduced as a generally important one for the light it may shed on action theory, on the logic of discovery, and on philosophy''s relations with historiography of science, intellectual history, and the sociology of knowledge. Then some problems and some conclusions are formulated by reference to some recent relevant literature: a critical analysis of Laudan''s views on the role of normative evaluations in rational explanations occasions the result that one must (...) make aconceptual distinction between evaluations and explanations of belief, and that there are at leastthree subclasses of the latter, rational, critical, and theoretical; I then discuss the problem of whether explanations of discoveries are self-evidencing and predictive by focusing on views of Hempel and Nickles, and I attempt a formalization of some aspects of the problem. Finally, a more systematic and concrete analysis is undertaken by using as an example the explanation of Galileo''s rejection of space-proportionality, and it is argued that the historical explanation of scientific beliefs is a type of logical analysis. (shrink)
The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (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)
The impact of social factors upon the philosophical investigations in a broad sense is quite evident. Nevertheless their impact upon epistemology as a branch of philosophy, logic, and history of science as fields of research with noticeable philosophical content is not evident enough. We are keen to claim that this impact exists within some limits, although it is not so overtly evident. Moreover in the case of Marxism it is of a paradoxical nature. Marxism always puts the accent on (...) the role of social and economic factors in the development, development of science included. To a large extent due to Marxism, externalism emerged; the key idea of externalism may be expressed through the statement that social and economic reasons are the main sources of development of science. B.M. Hessen declared and did his best in 1931 to justify this statement through the example of the emergence of classical mechanics. Meanwhile the social milieu of Marxist countries placed a taboo on the externalist approach towards epistemology, the interpretation of logic, and history of science. All these fields of knowledge were evolved in the Marxist era in the USSR and Eastern Europe - despite the spirit of Marxism - within strict internalist boarders. We offer the explanation of this contradiction. (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)
"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..
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)
Machine generated contents note: Introduction; Part I. Truth, Falsehood and Self-Refutation: 1. Preliminaries; 2. A modern approach: Mackie on the absolute self-refutation of 'nothing is true'; 3. Setting the ancient stage: Dissoi Logoi 4.6; 4. Self-refutation and dialectic: Plato; 5. Speaking to Antiphasis: Aristotle; 6. Introducing peritroph: Sextus Empiricus; 7. Augustine's turn; 8. Interim conclusions; Part II. Pragmatic, Ad Hominem and Operational Self-Refutation: 9. Epicurus against the determinist: blame and reversal; 10. Anti-sceptical dilemmas: pragmatic or ad hominem self-refutations?; 11. (...) Must we philosophise? Aristotle's protreptic argument; 12. Augustine's 'Si fallor, sum': how to prove one's existence by Consequentia Mirabilis; 13. A step back: operational self-refutations in Plato; Part III. Scepticism and Self-Refutation: 14. Self-bracketing Pyrrhonism: Sextus Empiricus; 15. Scepticism and self-refutation: looking backwards; Conclusion. (shrink)
: Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.
Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must be supplemented (...) by a transcendental logic that will in fact study nothing other than thought's content. Once this feature of Kant's views is brought to light, a much deeper accord emerges between the two thinkers than has hitherto been appreciated, on both the nature of the content that is at issue in logic and the sense of logic's generality and formality. (shrink)
: This essay is an attempt to see how some of Galison's ideas and analyses look from the vantage of art history. If there's to be dialogue between the history of science and the history of art, it will be necessary to find historically recognizable senses for words like "logic" and "homologous." I also propose how Galison's kinds of images might fit into larger classifications of images known to the history of art.
This paper is a brief history of natural logic at the interface of logic, linguistics, and nowadays also other disciplines. It merely summarizes some facts that deserve to be common knowledge.
Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches (...) to such sentences. I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (shrink)
A venerable story in the history of medieval philosophy has it that the eleventh century saw a debate between certain 'dialecticians', who exalted the role of reason and disdained theological authority, and 'anti-dialecticians', who carefully limited—or even rejected—the application of dialectical reasoning to Christian doctrine. A number of authors have called into question certain details of this story, but in..
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)
This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of (...) consequence analyzed with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)
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).
Volume 9 of the Routledge History of Philosophy surveys ten key topics in the Philosophy of Science, Logic and Mathematics in the Twentieth Century. Each article is written by one of the world's leading experts in that field. The papers provide a comprehensive introduction to the subject in question, and are written in a way that is accessible to philosophy undergraduates and to those outside of philosophy who are interested in these subjects. Each chapter contains an extensive bibliography of (...) the major writings in the field. Among the topics covered are the philosophy of logic; Ludwig Wittgenstein's Tractatus; a survey of logical positivism; the philosophy of physics and of science; probability theory and cybernetics. (shrink)
Jean van Heijenoort was best known for his editorial work in the history of mathematical logic. I survey his contributions to model-theoretic proof theory, and in particular to the falsifiability tree method. This work of van Heijenoort’s is not widely known, and much of it remains unpublished. A complete list of van Heijenoort’s unpublished writings on tableaux methods and related work in proof theory is appended.
This book presents a comprehensive critical survey of all the logical doctrines of the well-known but little understood Catalan philosopher and theologian, Ramon Llull (1232-1316). The highly idiosyncratic character of Llull's writings has long frustrated the efforts of general medieval historians to define his contribution to later scholastic culture, and has resisted attempts by specialists to explain exactly how his methods and procedures worked. This new study--the first book-length treatment in English of Llull's philosophy to appear in over fifty (...) years--seeks to resolve both of these difficulties. The author argues that Llull's peculiar logical doctrines result from his reinterpretation of the use of commonplace scholastic teachings according to his own preferred ethical and spiritual ideals. (shrink)
Written by a team of distinguished scholars, this is an authoritative and comprehensive history of Western philosophy from its earliest beginnings to the present day. Illustrated with over 150 color and black-and-white pictures, chosen to illuminate and complement the text, this lively and readable work is an ideal introduction to philosophy for anyone interested in the history of ideas. From Plato's Republic and St. Augustine's Confessions through Marx's Capital and Sartre's Being and Nothingness, the extraordinary philosophical dialogue between (...) great Western minds has flourished unabated through the ages. Dazzling in its genius and breadth, the long line of European and American intellectual discourse tells a remarkable story--a quest for truth and wisdom that continues to shape our most basic ideas about human nature and the world around us. That quest is brilliantly brought to life in The Oxford History of Western Philosophy. With spectacular illustrations--including sixteen pages of full-color plates--this splendidly written volume takes the reader on a magnificient chronological tour through the revolutions of thought that have forged the Western philosophical tradition from ancient times to the present. Throughout, the six contributors--an internationally renowned team of philosophers including Roger Scruton, Anthony Quinton, and Anthony Kenny--bring the astonishingly diverse, wide-ranging landscape of intellectual history into sharp focus, emphasizing how notions seen today as part of an inevitable march of ideas were in their own time often considered radical, if not revolutionary. Thus we are treated, for example, to lively accounts of how Plato's "theory of forms" and Aristotle's pioneering exercises in logic broke with the past to irrevocably alter the course of Western thought. The authors also reveal the relationships between landmark thinkers, and the ways they drew on their intellectual heritage. They show, for instance, how St. Augustine and Aquinas, though advancing the cause of Christian doctrine, picked up where their pagan Greek forebears had left off. We witness how, during the Renaissance, the profound empiricist ideas underlying Descarte's famous utterance--"I think, therefore I exist"--lived in a tense but complementary relationship with Locke's rationalist theories. Moving into the eighteenth and nineteenth centuries, the book explores how Hume greatly influenced Kant's conception of the "transcendental aesthetic," and how Hegel drew upon the lesser known (but groundbreaking) work of Fichte and Schelling. The authors bring the story up to our own time, vividly recounting the existential trend from Nietzsche ("God is dead") to Sartre, along with other increasingly fractious schools of thought. Along the way, we not only encounter the vast intellectual riches of the Western mind, but we also meet the personalities behind the great thoughts, from the saintly Hume (described by Adam Smith as having "come as near to perfection as anybody could") to the ill-mannered outcast Fichte. And the hundreds of maps and striking illustrations (including full-color reproductions of art ranging from medieval manuscripts to the works of Raphael, Ingres, and Magritte) form an integral part of the book, revealing the interweaving of art and ideas through the ages, as artists have striven to give visual immediacy to philosophical concepts. The Oxford History of Western Philosophy is the most authoritative single-volume account ever written for the general reader. Engagingly written and astonishingly far-reaching, it provides the consummate introduction to the intellectual bedrock upon which Western civilization is built. (shrink)
