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)
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)
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.
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)
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.
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).
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)
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 . Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T . 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 . Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema . 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)
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)
(2011). The Normativity of Logic in the History of Ideas. Intellectual History Review: Vol. 21, Post-Analytic Hermeneutics: Themes from Mark Bevir's Philosophy of History, pp. 3-13. doi: 10.1080/17496977.2011.546631.
Geraldine Brady, "From Peirce to Skolem. A Neglected Chapter in the History of Logic", Studies in the History and Philosophy of Mathematics, vol. 4, Elsevier (imprint: North-Holland), 2000, ISBN-13: 978-0444503343, ISBN-10: 0-444-50334-X, 625~pp.
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)
The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical (...) development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided: 1. What were the reasons for the philosophers' lack of interest in formal logic? 2. What were the reasons for the mathematicians' interest in logic? 3. What did "logic reform" mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic? 4. Was mathematical logic regarded as art, as science or as both? (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.
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)
: 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.
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)
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 is meant to be a study in the philosophy of history of science as well as in informal logic. From the point of view of the latter, It is shown how the logical dimension of galileo's "two chief world systems" has been neglected by some of the best scholars, Through logically insensitive commentary, Transcription, And translation. From the point of view of the former, It is shown concretely how logical analysis can be relevant to history-Of-Science scholarship (...) by helping it solve its own problems. From the point of view of galilean studies, A re-Examination of this crucial work is suggested. (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)
This paper offers a refutation of J. C. Pinto de Oliveira's recent critique of revisionist Carnap scholarship as giving undue weight to two brief letters to Kuhn expressing his interest in the latter's work. First an argument is provided to show that Carnap and Kuhn are by no means divided by a radical mismatch of their conceptions of the rationality of science as supposedly evidenced by their stance towards the distinction of the contexts of discovery and justification. This is followed (...) by an argument to the effect that the fact that Carnap's own work concentrated on formal aspects of scientific theories does not licence the conclusion that he thought historical investigations and concerns irrelevant for what we nowadays would rightly call "philosophy of science". (shrink)
Mark Bevir's The Logic of the History of Ideas has received considerable attention recently. This article highlights a new problem with his weak intentionalism. Bevir's weak intentionalism holds that on occasion the meanings readers ascribe to texts may trump the meanings the authors express in texts. The article uses the example of Hegel's theory of punishment. The received wisdom is that Hegel is a pure retributivist. Yet, this strays far from his text and stated views. We might think (...) we should keep to this text to uncover Hegel's views. However, Bevir's weak intentionalism has us side with how he has been read over what Hegel has said. This view is problematic as our meanings may well stray far from the texts, words or spirit. Thus, Bevir's weak intentionalism can fall victim to straying from the text when trying to interpret it. (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)
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 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)