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  • Englisch  (4)
  • TH Wildau  (4)
  • Woods, John  (4)
  • 1
    Online-Ressource
    Online-Ressource
    Amsterdam : Elsevier
    UID:
    b3kat_BV039830212
    Umfang: 1 Online-Ressource (1 online resource)
    Ausgabe: 1st ed
    ISBN: 9780444516114 , 0444516115
    Serie: Handbook of the history of logic v. 3
    Anmerkung: With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. , The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. , Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegel make clear. , Of the two, Hegel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century , Preface (D.M. Gabbay, J. Woods) -- List of Contributors -- Leibniz's Logic (W. Lenzen) -- Kant: From General to Transcendental Logic (M. Tiles) -- Hegel's Logic (J.W. Burbidge) -- Bolzano as Logician (P. Rusnock, R. George) -- Husserl's Logic (R. Tieszen) -- Algebraical Logic 1685-1900 (T. Hailperin) -- The Algebra of Logic (V.S. Valencia) -- The Mathematical Turn in Logic (I. Grattan-Guinness) -- Schrder's Logic (V. Peckhaus) -- Peirce's Logic (R. Hilpinen) -- Frege's Logic (P. Sullivan) -- Index , Includes bibliographical references and index
    Sprache: Englisch
    Fachgebiete: Mathematik , Philosophie
    RVK:
    RVK:
    Schlagwort(e): Mathematische Logik ; Mathematik ; Geschichte ; Logik ; Geschichte
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Online-Ressource
    Online-Ressource
    Amsterdam : Elsevier
    UID:
    b3kat_BV039830186
    Umfang: 1 Online-Ressource (1 online resource)
    Ausgabe: 1st ed
    ISBN: 9780444504661 , 0444504664
    Serie: Handbook of the history of logic v. 1
    Anmerkung: 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 Gdel, 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 , Contents -- Preface (D.M. Gabbay, J. Woods) -- List of Contributors -- Logic before Aristotle: Development or Birth? (J. Moravcsik) -- Aristotle's Early Logic (J. Woods, A. Irvine) -- Aristotle's Underlying Logic (G. Boger) -- Aristotle's Modal Syllogisms (F. Johnson) -- Indian Logic (J. Ganeri) -- The Megarians and the Stoics (R.R. O'Toole, R.E. Jennings) -- Arabic Logic (T. Street) -- The Translation of Arabic Works on Logic into Latin in the Middle Ages and Renaissance (C. Burnett) -- Index , Includes bibliographical references and index
    Sprache: Englisch
    Fachgebiete: Mathematik , Philosophie
    RVK:
    RVK:
    Schlagwort(e): Logik ; Geschichte
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Online-Ressource
    Online-Ressource
    Amsterdam : North Holland
    UID:
    b3kat_BV039834067
    Umfang: 1 Online-Ressource (1 online resource)
    ISBN: 9780444516237 , 0444516239 , 9780080549392 , 008054939X
    Serie: Handbook of the history of logic v. 8
    Anmerkung: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. , A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. In some instances, our two themes coincide. , Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs. The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic , Preface -- List of Contributors -- Chapter 1. Many-valued Logic (Grzegorz Malinowski) -- Chapter 2. Paraconsistent Logic: Preservationist Variations (Bryson Brown) -- Chapter 3. Paraconsistent Logic: Dialethic Variations (Graham Priest) -- Chapter 4. Quantum Logic (M. Dalla Chiara, Roberto Giuntini and Miklos Rdei) -- Chapter 5. Logic of Vagueness (Dominic Hyde) -- Chapter 6. Fuzzy Logic (Didier Dubois, Henri Prade and Lluis Godo) -- Chapter 7. Non-monotonic Logic (Karl Schlechta) -- Chapter 8. Default Logic (Grigoris Antoniou and Kewen Wang) -- Chapter 9. Non-monotonic Reasoning and Belief Change (Alexander Bochman) -- Chapter 10. Free Logic (Carl Posy) -- Index , Includes bibliographical references and index
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Online-Ressource
    Online-Ressource
    Amsterdam : Elsevier North Holland
    UID:
    b3kat_BV039830213
    Umfang: 1 Online-Ressource (1 online resource)
    ISBN: 9780444516220 , 0444516220
    Serie: Handbook of the history of logic v. 7
    Anmerkung: Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas. This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logics long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration. Detailed and comprehensive chapters covering the entire range of modal logic. Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic , Preface -- List of Authors -- 1. Mathematical Modal Logic: A View of its Evolution (Rob Goldblatt) -- 2. Epistemic Logic (Paul Gochet and Pascal Gribomont) -- 3. Deontic Logic (Paul McNamara) -- 4. Relevant and Substructural Logics (Greg Restall) -- 5. A.N. Prior's Logic (Peter hrstrm and Per F.V. Hasle) -- 6. Modern Temporal Logic: The Philosophical Background (Peter hrstrm and Per F.V. Hasle) -- 7. The Gamut of Dynamic Logics (Jan van Eijck and Martin Stockhof) -- 8. Situation Theory and Situation Semantics (Keith Devlin) -- 9. Dialogue Logic (Erik Krabbe) -- Index
    Sprache: Englisch
    Schlagwort(e): Logik ; Geschichte
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