Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. The book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. Anyone interested in ancient philosophy, or in logic and its history, will find much to learn and enjoy here.
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).
"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..
Clashes between bits of non-homogeneous theories inherited from antiquity were an important factor in the formation of medieval theories in logic and grammar, but the traditional categories of Aristotelianism, Stoicism and Neoplatonism are not quite adequate to describe the situation. Neoplatonism is almost irrelevant in logic and grammar, while there might be reasons to introduce a new category, LAS = Late Ancient Standard, with two branches: (1) logical LAS = Aristotle + Boethius, and (2) grammatical LAS = Stoics (...) &c. → Apollonius → Priscian. (shrink)
ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians.
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)
Susanne Bobzien (1996). Logic. In Simon Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary, 3rd edition. Oxford University Press.score: 45.0
ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).
Original and penetrating, this book investigates of the notion of inference from signs, which played a central role in ancient philosophical and scientific method. It examines an important chapter in ancient epistemology: the debates about the nature of evidence and of the inferences based on it--or signs and sign-inferences as they were called in antiquity. As the first comprehensive treatment of this topic, it fills an important gap in the histories of science and philosophy.
This book uncovers and examines the confusion in antiquity between Aristotle's hypothetical syllogistic and Stoic logic, and offers a fresh perspective on the ...
ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.
Ways into the Logic of Alexander of Aphrodisias is intended to give an overview of the logic of Alexander of Aphrodisias (fl. early third century A D). Since ...
Boethius, the Roman philosopher, was executed for treason and pilloried by modern scholars for misinterpreting Aristotle to the West. This book examines his semantics and logic, attempting to clear his name and lend him new credence.
In this essay, I examine the nature of Chinese logic and Chinese sciences in the history of China. I conclude that Chinese logic is essentially analogical, and that the Chinese did not have theoretical sciences. I then connect these together and explain why the Chinese failed to develop theoretical sciences, even though they enjoyed an advanced civilization and great scientific and technological innovations. This is because a deductive system of logic is necessary for the development of theoretical sciences, and analogical (...) logic cannot provide the deductive connections between a theory and empirical observations required by a theoretical science. This also offers a more satisfactory answer to the long-standing Needham Problem. (shrink)
ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; 4. (...) Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)
ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can be found (...) in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)
ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s Topics and (...) Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)
ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.
Following strict rules of interpretation, this book focuses on the ideas in Plato's early and middle dialogues that lie within the fields now called logic and methodology, specifically elenchus and dialectic and the method of hypothesis.
ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness.2 In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)
This work provides some interesting new results on the notion of the topos and the theory of hypothetical syllogisms in Aristotle based on an incisive ...
He was the author or translator of many books, most recently The Argument of the Action, Plato's "Laws," and Plato's "Symposium," all published by the University of Chicago Press.
them. Though Aristotle does not say so, presumably the questioner who conceals in this way must be prepared, when challenged, to show that the conclusion ...
This collection of articles and review essays, including many hard to find pieces, comprises the most important and fundamental studies of Indian logic and linguistics ever undertaken. Frits Staal is concerned with four basic questions: Are there universals of logic that transcend culture and time? Are there universals of language and linguistics? What is the nature of Indian logic? And what is the nature of Indian linguistics? By addressing these questions, Staal demonstrates that, contrary to the general assumption among Western (...) philosophers, the classical philosophers of India were rationalists, attentive to arguments. They were in this respect unlike contemporary Western thinkers inspired by existentialism or hermeneutics, and like the ancient Chinese, Greeks, and many medieval European schoolmen, only--as Staal says--more so. Universals establishes that Asia's contributions are not only compatible with what has been produced in the West, but a necessary ingredient and an essential component of any future human science. (shrink)
This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.
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)
ABSTRACT: ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor (...) did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)
Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers (...) by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99 -/- Website: http://www.c-s-p.org/Flyers/Logic-and-Knowledge1-4438-3008-9.htm. 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A Companion to Ancient Philosophy provides a comprehensive and current overview of the history of ancient Greek and Roman philosophy from its origins until late antiquity. Comprises an extensive collection of original essays, featuring contributions from both rising stars and senior scholars of ancient philosophy Integrates analytic and continental traditions Explores the development of various disciplines, such as mathematics, logic, grammar, physics, and medicine, in relation to ancient philosophy Includes an illuminating introduction, bibliography, chronology, maps and (...) an index. (shrink)
Sir Anthony Kenny here tells the fascinating story of the birth of philosophy and its remarkable flourishing in the ancient Mediterranean world. This is the initial 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. Ancient Philosophy spans over a thousand years and brings to life the great minds of the past, from Thales, Pythagoras, and Parmenides, to Socrates, Epictetus, (...) Marcus Aurelius, and Augustine. The book's great virtue is that it is written by one of the world's leading authorities on the subject. Instead of an uncritical, straightforward recitation of known facts--Plato and his cave of shadows, Aristotle's ethics, Augustine's City of God--we see the 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 Aristotle, for example, but a penetrating and insightful critique of his thought. Kenny offers an illuminating account of the various schools of thought, from the Pre-Socratics to the Epicureans. He examines the development of logic and reason, ancient ideas about physics ("how things happen"), metaphysics and ethics, and the earliest thinking about 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)
Geoffrey Lloyd engages in a wide-ranging exploration of what we can learn from the study of ancient civilizations that is relevant to fundamental problems, both intellectual and moral, that we still face today. These include, in philosophy of science, the question of the incommensurability of paradigms, the debate between realism and relativism or constructivism, and between correspondence and coherence conceptions of truth. How far is it possible to arrive at an understanding of alien systems of belief? Is it possible (...) to talk meaningfully of 'science' and of its various constituent disciplines, 'astronomy' 'geography' 'anatomy' and so on, in the ancient world? Are logic and its laws universal? Is there one ontology - a single world - to which all attempts at understanding must be considered to be directed? When we encounter apparently very different views of reality, how far can that be put down to a difference in conceptions of what needs explaining, or of what counts as an explanation, or to different preferred modes of reasoning or styles of inquiry? Do the notions of truth and belief represent reliable cross-cultural universals? In another area, what can ancient history teach us about today's social and political problems? Are the discourses of human nature and of human rights universally applicable? What political institutions do we need to help secure equity and justice within nation states and between them? Lloyd sets out to answer all these questions, and to argue that the study of the science and culture of ancient Greece and China provided a precious resource in order to advance a wealth of modern debates. (shrink)
Springer link: http://www.springer.com/philosophy/logic+and+philosophy+of+language/book/978-94-007-6090-5 -/- This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to (...) the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. -/- Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)
This book discusses key philosophical concepts and ideologies, including ontology, epistemology, logic, semantics, moral and political philosophy, theology and aesthetics during classical antiquity. Karsten Friis Johansen charts the history of ancient philosophy from the mythological oral tradition, Homer and early tragedy, to the giants of Plato and Aristotle through to paganism and the genesis of Christianity. A History of Ancient Philosophy also presents detailed analysis of individual ancient philosophers and interpretations and commentary on key philosophical passages.
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.
Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results (...) for the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among 'necessary', 'essential' and 'accidental'. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic. (shrink)
Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account of (...) negation as cancellation is intimately connected with connexivist principles such as ¬( ¬). Despite this, standard connexivist logics incorporate quite different accounts of negation. The second half of the paper shows how the cancellation account of negation of the first part gives rise to a semantics for a simple connexivist logic. (shrink)
reasons for the disappreciation as well as for the rehabilitation of Stoic logic; it is found in I. M. Bochenski's Ancient Formal Logic (Amsterdam, 1951), and it clearly portrays the difference in attitude of the logicians of the twentieth century towards the Stoic logical system.
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)
: Ancient Chinese logicians presupposed no fixed order in the world. Things are changing all the time. Time, then, plays a crucial role in the structure of Chinese logic. This article uses the concept of "subjective time" and the Leibnizian concept of "possible worlds" to analyze the structure of logic in the Later Mohist Canon and in the logical reasoning of other early Chinese philosophers. The author argues that Chinese logic is structured in the time of the now. This (...) time is subjective and "spreads out" to more than one possible world. Chinese logicians had to deal with relationships in not only a single world but also more than one "possible world." The aim of Chinese logical reasoning is not to represent any universal truth but to point out (zhi ) a particular-world-related truth, or, in other words, the harmony of relations among particulars in a particular field at a single moment. Therefore, a valid Chinese logical argument represents only the beauty of harmony among possible worlds at a given moment. The harmony represented by Chinese logic brings to light a high level of aesthetic order in a world that is always changing. (shrink)
G. Aldo Antonelli (2004). Logic. In Luciano Floridi (ed.), The Blackwell Guide to the Philosophy of Computing and Information. Blackwell.score: 21.0
Logic is an ancient discipline that, ever since its inception some 2500 years ago, has been concerned with the analysis of patterns of valid reasoning. Aristotle first developed the theory of the syllogism (a valid argument form involving predicates and quantifiers), and later the Stoics singled out patterns of propositional argumentation (involving sentential connectives). The study of logic flourished in ancient times and during the middle ages, when logic was regarded, together with grammar and rhetoric (the other two (...) disciplines of the trivium), as the foundation of humanistic education. (shrink)
Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend to be dull knives that mangle reality. If reality is a tomato and predicates are knives, then when these knives divide the tomato, plenty of mush remains unaccounted for. Of course some knives are sharper than others, just as some predicates are less vague than others. “x is water” is certainly sharper (...) than “x is beautiful.” But perfect sharpness, perfect boundaries, and perfect separation seem only to obtain in mathematics. The vagueness inherent in many predicates became particularly evident in the twentieth century. Quantum mechanics, the revival of certain ancient paradoxes, and the philosophy of science all contributed to a growing awareness that vagueness was ineliminable from many predicates. Quantum mechanical superposition seems to allow mutually exclusive simultaneous states. In searching for plausible interpretations of quantum mechanics, some researchers attempted to do away with classical bivalent logic. In its place they substituted multivalent quantum logics. Any logic with more than two values forces its predicates to slice reality into more than two parts. Ancient paradoxes involving heaps and baldness also pointed up the 1 Random Predicate Logic 2.. (shrink)
Every philosophical mode has a unique conceptual system. Qi has consistently been a fundamental part of ancient Chinese philosophy, and its significance is obvious. Guided by the idea of re-evaluating all values, Yan Fu, who was deeply influenced by Western philosophy and logic, used reverse analogical interpretation to present a new explanation of the traditional Chinese concept of qi. Qi thus evolved into basic physical particles. Yan’s philosophical effort has great significance: The logical ambiguity that had haunted qi was (...) overcome. However, qi gradually evolved into a particular existence as it was Westernized. It completely lost its internal flavor as indigenous Chinese philosophy. Its previous philosophical abstraction and universality diminished and at the same time it was not Westernized into the pure concept of Hegel’s philosophy. (shrink)
: Claus Oetke, in his "Ancient Indian Logic as a Theory of Non-monotonic Reasoning," presents a sweeping new interpretation of the early history of Indian logic. His main proposal is that Indian logic up until Dharmakirti was nonmonotonic in character-similar to some of the newer logics that have been explored in the field of Artificial Intelligence, such as default logic, which abandon deductive validity as a requirement for formally acceptable arguments; Dharmakirti, he suggests, was the first to consider that (...) a good argument should be one for which it is not possible for the property identified as the "reason" (hetu) to occur without the property to be proved (sadhya)-a requirement akin to deductive validity. Oetke's approach is challenged here, arguing that from the very beginning in India something like monotonic, that is, deductively valid, reasoning was the ideal or norm, but that the conception of that ideal was continually refined, in that the criteria for determining when it is realized were progressively sharpened. (shrink)
This paper discusses the topics, goals, values and methods of Chinese logic. It holds that the goal of the research in Chinese logic is to reveal its structure, content, rules, and essential character, as well as to reveal both similarities and differences between Chinese and foreign logic. The value of the research is to carry forward and develop the outstanding heritage of Chinese logic. Its method is to annotate original works of Chinese ancient logic with the tools of modern (...) language and logic in order to reveal both the particular nature and the universal qualities of Chinese logic. The method also explores the differences and similarities between Chinese and foreign logic. In recent years, research in Chinese logic has developed considerably; it has also logged many important achievements. But there are many different views about the complexity and long-term goals of the research. Future research will build on the merits of different kinds of logic, promote Chinese logic, and increase communication between Chinese logic and foreign logic. (shrink)
Dialogue theory, although it has ancient roots, was put forward in the 1970s in logic as astructure that can be useful for helping to evaluate argumentation and informal fallacies.Recently, however, it has been taken up as a broader subject of investigation in computerscience. This paper surveys both the historical and philosophical background of dialoguetheory and the latest research initiatives on dialogue theory in computer science. The main components of dialogue theory are briefly explained. Included is a classification of the (...) main types of dialogue that, it is argued, should provide the central focus for studying many important dialogue contexts in specific cases. Following these three surveys, a concluding prediction is made about the direction dialogue theory is likely to take in the next century, especially in relation to the growing field of communication studies. (shrink)
This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the (...) lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context. (shrink)
The ancient mythology could serve as an effective medium for metaphorically conveying complex concepts and principles to a broad spectrum of people. In this paper we show how the fuzzy logic approach can be used to translate the metaphoric language of ancient myths and legends into a 'soft' scientific paradigm which helps us to understand better the social complexity of our time.
The article mainly tries to discuss the dialogue between China and Western countries from the aspect of logic. There were three sources of logic, including formal logic in ancient Greek, logic in Early Qin of China as well as logic in ancient India. While, among all the schools in ancient China, Mohist and Virtuoso valued logic most. But as the rulers of Han Dynasty only paid their homage to Confucianism, the two schools gradually sank, logic in Early (...) Qin of China discontinued, without entering the main headstream of logic development worldwide. Later, logic in China had little influence on Chinese society although Indian logic was introduced in Tang Dynasty, a scholar-bureaucrat named Zhizao Li in Ming Dynasty, translated logic textbook Discussion of Name and Science, and German philosopher G.W. Leibniz explained Chinese changing theory with binary system. In the early 1900s, during the process of introducing western science, logic, regarded as the basis of science and a tool of scientific research, was highly valued by Chinese scholars, in fact, western logic entered China through two channels. After Chinese scholars learnt from western logic, they made their contribution to the development of logic. (shrink)
The Greek under the Latin and the Latin under the Greek -- Greek-Latin philosophical interaction -- The odyssey of semantics from the Stoa to Buridan -- The Chimera's diary -- Where were the stoics in the late Middle Ages? -- Theories of language in the Hellenistic age and in the twelfth and thirteenth centuries -- Late-ancient ancestors of medieval philosophical commentaries -- Boethius on Aristotle -- Boethius on the metaphysics of words -- Western and Byzantine approaches to logic -- (...) Greek and Latin medieval logic -- Philoponus, Alexander, and the origins of medieval logic -- Analyzing syllogisms or anonymus Aurelianensis III, the (presumably) earliest extant Latin commentary on the prior analytics, and its Greek model -- Fragments of Alexander's commentaries on Analytica posteriora and Sophistici elenchi. (shrink)
This offering in Routledge's acclaimed History of Philosophy series completes the acclaimed 10-volume collection. This work explores the schools of thought that developed in the wake of Platonism through the time of Augustine. The 11 separately authored in-depth articles include: Aristotle the scientist-- David Furley, Princeton University; Aristotle: logic and metaphysics-- Alan Code, Ohio State University; Aristotle: aesthetics and philosophy of mind -- David Gallop, Trent University, Ontario; Aristotle: ethics and politics-- Stephen White, University of Texas at Austin; The peripatetic (...) school-- Robert Sharples, University College, London; Hellenistic science and mathematics-- Alan C. Bowen, Institute for Research in Classical Philosophy and Science, New Jersey; Epicureanism-- Philip Mitsis, Cornell University; Stoicism-- Brad Inwood, University of Toronto; Ancient skepticism-- Michael Frede, Keble College, Oxford; Neo-Platonism-- Eyjdfur Kjalar Emilsson, University of Iceland; Augustine-- G.J.P. O'Daly, University College London. Order the entire Routledge History of Philosophy series and save 10% off each volume! (shrink)
The happy fish episode from the outer chapters of the Zhuangzi poses enormous difficulty for interpreters. While it may appear to surprisingly resemble the dialectic in Western philosophy, any attempt to analyse it in terms of the patterns of inference familiar to the West is often frustrated by the ostensible queerness that defies such treatment. The following examination of the dialogue in the episode is intended to address the difficulty and to provide a reasoned explanation for both the surface resemblance (...) and apparent queerness. I suggest that the dialogue becomes perfectly intelligible, if it is read against the backdrop of the disputations practiced in ancient China. My contention is that the real purpose of the dialogue is to expose the fundamental unreliability of the logic of the disputers by means of the logic itself. (shrink)
Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of (...) topics -- from Pythagoras's exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought -- Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations. This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits -- revealing them instead as dynamic and intrinsic to almost every human endeavor. (shrink)
This volume collects Late Ancient, Byzantine and Medieval appropriations of Aristotle's Posterior Analytics, addressing the logic of inquiry, concept formation, the question whether metaphysics is a science, and the theory of demonstration.
My personal odyssey -- Tripping the night fantastic. Who-and what-am I? -- The journey home. Take me to the river-- -- The being human -- White crows : mystics, savants, and other harbingers of human potential. Mystic mind (or how to crack open the cranium) -- Wake up! Greek philosophy breaks the trance -- The ultimate cage match : philosophy, science, and religion (or togas, Bibles, and microscopes : why can't we all just get along?) -- Homo anxious : I (...) think, therefore I worry. Mindfulness walk : "being" without thinking -- Why philosophy matters-and how it just might save your life! Am I a neuron in the mind of God? -- Reality bites -- The physical world : the tip of the reality iceberg. More to reality than meets the eye -- Real deal reality : beyond sense and beyond reason. Beyond logic : riddles and paradoxes. Pyramids, togas, and cosmic consciousness -- Pythagoras squared : who was this mystic mathemagician? Infinity : the ultimate mind trip -- Good vibrations : Pythagoras and the big beat. The cosmic symphony : music from the universal orchestra -- Escaping Plato's cave -- Plato's retreat-from the material world. the universe as one big thought -- On the nature of change : the more things change--. Change : the great illusion -- Death : the new birth. Incubation (or how death can transform your life) -- Yes, but what does it all mean? -- New science and old wisdom -- Musings from my dissertation -- Some final thoughts. (shrink)
A full account of the philosophy of the Greek and Roman worlds from the last days of Aristotle (c. 320 BC) until 100 BC. Hellenistic philosophy, for long relatively neglected and unappreciated, has over the last decade been the object of a considerable amount of scholarly attention. Now available in paperback, this volume is the first general reference work to pull the subject together and present an overview. The time has come for a general reference work which pulls the subject (...) together and presents an overview. The History is organised by subject, rather than chronologically or by philosophical school, with sections on logic, epistemology, physics and metaphysics, ethics and politics. It has been written by specialists but is intended to be a source of reference for any student of ancient philosophy, for students of classical antiquity and for students of the philosophy of later periods. Greek and Latin are used sparingly and always translated in the main text. (shrink)
By far the most detailed surviving examination by any ancient Greek sceptic of epistemology and logic, this work critically reviews the pretensions of non-sceptical philosophers, to have discovered methods for determining the truth, either through direct observation or by inference from the observed to the unobserved. A fine example of the Pyrrhonist sceptical method at work, it also provides extensive information about the ideas of other Greek thinkers, which in many instances, are poorly preserved in other sources.
