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  • 1
    ISBN: 9789400749511
    Language: English
    Pages: Online-Ressource (XII, 259 p. 1 illus, digital)
    Series Statement: Studies in History and Philosophy of Science 32
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T.
    RVK:
    Keywords: Philosophy (General) ; Logic ; Science Philosophy ; Philosophy ; Philosophy (General) ; Logic ; Science Philosophy
    Abstract: This book is a radical reappraisal of the importance of Aristotelianism in Britain. Using a full range of manuscripts as well as printed sources, it provides an entirely new interpretation of the impact of the early-modern Aristotelian tradition upon the rise of British Empiricism, and reexamines the fundamental shift from a humanist logic to epistemology and facultative logic. The task is to reconstruct the philosophical background and framework in which the thought of philosophers such Locke, Berkeley and Hume originated: some aspects of their empiricism can be explained only in reference to the academic Aristotelian tradition, even if these authors established themselves as anti-scholastic, anti-Aristotelian philosophers outside the official institutions.
    Description / Table of Contents: 1 Introduction -- 2 Logic in the British Isles during the Sixteenth and Seventeenth Centuries -- 3 Logic in the Universities of the British Isles -- 4 Zabarella’s Empiricism 5 Early Aristotelianism between Humanism and Ramism -- the British School 7 Continental Aristotelians in the British Isles -- 8 The Empiricism of the Seventeenth-Century Aristotelianism -- 9. The Reformers of Aristotelian Logic -- 10 Late Seventeenth-Century Aristotelianism -- 11 Conclusion -- Bibliography.-Index ​.
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  • 2
    ISBN: 9789400744646
    Language: English
    Pages: Online-Ressource (X, 156 p, digital)
    Series Statement: Logic, Epistemology, and the Unity of Science 29
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T. Frápolli, María José, 1960 - The nature of truth
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    Keywords: Philosophy (General) ; Logic ; Linguistics Philosophy ; Pragmatism ; Semantics ; Philosophy ; Philosophy (General) ; Logic ; Linguistics Philosophy ; Pragmatism ; Semantics ; Truth ; Wahrheit ; Wahrheit
    Abstract: The book offers a characterization of the meaning and role of the notion of truth in natural languages and an explanation of why, in spite of the big amount of proposals about truth, this task has proved to be resistant to the different analyses. The general thesis of the book is that defining truth is perfectly possible and that the average educated philosopher of language has the tools to do it. The book offers an updated treatment of the meaning of truth ascriptions from taking into account the latest views in philosophy of language and linguistics.
    Abstract: The wealth of proposals about truth and its meaning in natural languages everywhere should open it to analysis and definition, but this book makes the startlingly rare assertion that we can define truth using the latest methods in linguistics and philosophy
    Description / Table of Contents: The Nature of Truth; Acknowledgements; Contents; Chapter 1: Some Preliminary Issues; 1.1 The General Purpose; 1.2 Some Features of the Proposal; 1.3 Required Philosophical Assumptions; 1.4 The Content of a Theory of Truth; 1.5 The Pragmatist Ingredient; 1.6 The Structure of the Book; Chapter 2: Syntax: Playing with Building Blocks; 2.1 Does Syntax Matter?; 2.2 The Truth Predicate; 2.3 The Truth Operator; 2.4 Truth and Identity; 2.5 Adverbs, Adjectives and Nouns; Chapter 3: The Meaning and Content of Truth Ascriptions; 3.1 The Distinction; 3.2 Kinds of Proforms; 3.3 Truth-Ascriptions
    Description / Table of Contents: 3.4 A Classification of Truth-Ascriptions3.5 Special Semantic Tasks; Chapter 4: What Do We Do with Truth Ascriptions?; 4.1 Pragmatics and Semantics; 4.2 Assertions; 4.3 Expressivism; 4.4 Particular Pragmatic Functions; Chapter 5: The Liar Paradox (And Other Logico-Semantic Issues); 5.1 Is There a Liar Paradox?; 5.2 Truth Bearers; 5.3 Logical Form; 5.4 The Paradox; Chapter 6: What Do You Mean by "Redundancy"?; 6.1 R amsey's View; 6.2 Redundancy, of What?; 6.3 Syntactic Redundancy; 6.4 Semantic Redundancy; 6.5 Pragmatic Redundancy; Chapter 7: Obvious Answers for Ready-Made Objections
    Description / Table of Contents: 7.1 Standard Objections7.2 The Epistemic Objections; 7.2.1 Definitions vs. Criteria; 7.2.2 The Causal Effect of Truth; 7.3 The Logical Objection; 7.4 The Semantic Objection; 7.5 Mathematical Truth and Other Metaphors; References; Index;
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  • 3
    ISBN: 9789400744387
    Language: English
    Pages: Online-Ressource (VIII, 375 p. 31 illus, digital)
    Series Statement: Logic, Epistemology, and the Unity of Science 26
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T. Tanaka, Kōji, 1965 - Paraconsistency
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    Keywords: Philosophy (General) ; Logic ; Linguistics Philosophy ; Computer science ; Artificial intelligence ; Philosophy ; Philosophy (General) ; Logic ; Linguistics Philosophy ; Computer science ; Artificial intelligence ; Aufsatzsammlung ; Parakonsistente Logik
    Abstract: A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics
    Abstract: A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.
    Note: Includes bibliographical references and index , Part 2. Applications ; An Approach to Human-Level Commonsense Reasoning , Paraconsistency: Introduction , Distribution in the Logic of Meaning Containment and in Quantum Mechanics , Wittgenstein on Incompleteness Makes Paraconsistent Sense , Pluralism and "Bad" Mathematical Theories: Challenging our Prejudices , Arithmetic Starred , Notes on Inconsistent Set Theory , Sorting out the Sorites , Are the Sorites and Liar Paradox of a Kind? , Vague Inclosures , Part 1. Logic ; Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic , On Discourses Addressed by Infidel Logicians , Information, Negation, and Paraconsistency , Noisy vs. Merely Equivocal Logics , Assertion, Denial and Non-classical Theories , New Arguments for Adaptive Logics as Unifying Frame for the Defeasible Handling of Inconsistency , Consequence as Preservation: Some Refinements , On Modal Logics Defining Jaśkowski's D2-Consequence , FDE: A Logic of Clutters , A Paraconsistent and Substructural Conditional Logic
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  • 4
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789400751378
    Language: English
    Pages: Online-Ressource (XVII, 161 p, digital)
    Series Statement: Logic, Epistemology, and the Unity of Science 31
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T.
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    Keywords: Philosophy (General) ; Chemistry ; Genetic epistemology ; Logic ; Philosophy ; Philosophy (General) ; Chemistry ; Genetic epistemology ; Logic
    Abstract: This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​
    Description / Table of Contents: Judgement and the Epistemic Foundation of Logic; Preface; Contents; Introduction; Bibliography; Part I: Constructivism, Judgement and Reason; Chapter 1: Verificationism Then and Now; Chapter 2: Demonstrations Versus Proofs, Being an Afterword to Constructions, Proofs, and the Meaning of the Logical Constants; Bibliography; Chapter 3: Containment and Variation; Two Strands in the Development of Analyticity from Aristotle to Martin-Löf; Bibliography; Part II: Judgement and Reason in the Seventeenth Century; Chapter 4: Descartes' Theory of Judgement: Warranted Assertions, the Key to Science*
    Description / Table of Contents: 1 Descartes' Debate with Scholastic Logic over the Foundations of Science2 The Rules for the Forming of True Judgements; 3 The Many Uses of the Concept of Judgement in Descartes' Mathesis; Bibliography; Chapter 5: Striving, Oomph, and Intelligibility in Spinoza; 1 Descartes and the Great Intelligibility Trade-Off; 2 Strengthening Intelligibility; 3 Weakening Intelligibility; Bibliography; I. Works by Descartes; II. Works by Spinoza; III. Works by Leibniz; IV. Works by Hume; V. Other Works; Part III: Kant, Neo-Kantianism, and Bolzano
    Description / Table of Contents: Chapter 6: The Role of Wolff's Analysis of Judgements in Kant's Inaugural Dissertation1 Wolff's Analysis of Judgements; 2 Meier's Notion of Condition; 3 The Strategy of Kant's Dissertation; 4 Three Classes of Subreption; Bibliography; Chapter 7: Windelband on Beurteilung; 1 Windelband's Definition of Judgement; 2 Windelband's Three-Step Argument; 3 Judgeable Content; 4 Assessing Under Assumption of Epistemic Values; 5 The Nature of Epistemic Assessment; Bibliography; I. Primary; II. Secondary; Chapter 8: A Priori Knowledge in Bolzano, Conceptual Truths, and Judgements
    Description / Table of Contents: 1 The Apriori in Bolzano1.1 Concepts and Conceptual Truths; 1.2 Conceptual Truths and Judgements A Priori; 1.2.1 Conceptual Truths and Analytic Truths; 1.2.2 Empirical Analytic Truths; 1.2.3 Synthetic Conceptual Truths; 1.3 How Are Synthetic Judgements A Priori Possible?; 2 Understanding (C1): Bolzano's Epistemology; 2.1 Judgements and Subjective Representations; 2.2 Bolzano's Analysis of the Concept of Knowledge; 2.2.1 Confidence; 2.2.2 How Much Confidence?; 3 Understanding (C2): Knowing a Concept; 3.1 The Correspondence Assumption; 3.2 Having a Representation, Clarity, and Distinctness
    Description / Table of Contents: 4 Definitions, Proofs, and Synthetic Truths4.1 Knowledge and Proof; 4.2 Two Remaining Problems; 4.3 The Case of Fundamental Truths; 5 Conclusion; Bibliography; Part IV: Husserl, Frege and Russell; Chapter 9: Immanent and Real States of Affairs in Husserl's Early Theory of Judgement: Reflections on Manuscripts from 1893/1894 and Their Background in the Logic of Brentano and Stumpf; 1 Introduction; 2 Brentano and Stumpf on Contents of Judgement; 2.1 Brentano; 2.2 Stumpf; 2.3 Excursus: Other Students of Brentano; 3 Husserl's Theory of Judgement (1893/1894)
    Description / Table of Contents: 3.1 Psychological Studies in Elementary Logic
    Description / Table of Contents: Preface -- Part 1. Constructivism, Judgement, and Reason -- Chapter 1. Verificationism then and now: Per Martin-Löf -- Chapter 2. Demonstrations versus Proofs, being an afterword to 'Constructions, Proofs and the meaning of Logical Constants': Göran Sundholm -- Chapter 3. Containment and Variation: Two Strands in the Development of Analyticity from Aristotle to Martin-Löf: Göran Sundholm -- Part 2. Judgement and Reason in the Seventeenth Century -- Chapter 4. Decartes' Theory of Judgement: Warranted Assertions, the Key to Science: Elodie Cassan -- Chapter 5. Striving, Oomph, and Intelligibility in Spinoza: Michael Della Rocca -- Part 3. Kant, Neo-Kantianism, and Bolzano -- Chapter 6. The Role of Wolff's Analysis of Judgments in Kant's Inaugural Dissertation: Johan Blok -- Chapter 7. Windelband on 'Beurteilung’: Arnaud Dewalque -- Chapter 8. A Priori Knowledge in Bolzano; Conceptual Truths and Judgements: Stefan Roski -- Part 4. Husserl, Frege and Russell -- Chapter 9. Immanent and Real States of Affairs in Husserl's Early Theory of Judgement: Robin Rollinger -- Chapter 10. Frege and Russell on Assertion: Jeremy Kelly.​.
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  • 5
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789400753570 , 1283936097 , 9781283936095
    Language: English
    Pages: Online-Ressource (VIII, 215 p. 23 illus, digital)
    Series Statement: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science 362
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T. Bayesian argumentation
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    Keywords: Philosophy (General) ; Genetic epistemology ; Computer simulation ; Applied linguistics ; Social sciences Methodology ; Applied psychology ; Philosophy ; Philosophy (General) ; Genetic epistemology ; Computer simulation ; Applied linguistics ; Social sciences Methodology ; Applied psychology ; Reasoning (Psychology) ; Congresses ; Logic ; Congresses ; Thought and thinking ; Congresses ; Probabilities ; Congresses ; Bayesian statistical decision theory ; Congresses ; Konferenzschrift ; Argumentationstheorie ; Bayes-Entscheidungstheorie
    Abstract: Relevant to, and drawing from, a range of disciplines, the chapters in this collection show the diversity, and applicability, of research in Bayesian argumentation. Together, they form a challenge to philosophers versed in both the use and criticism of Bayesian models who have largely overlooked their potential in argumentation. Selected from contributions to a multidisciplinary workshop on the topic held in Lund, Sweden, in autumn 2010, the authors count legal scholars and cognitive scientists among their number, in addition to philosophers. They analyze material that includes real-life court cases, experimental research results, and the insights gained from computer models.The volume provides a formal measure of subjective argument strength and argument force, robust enough to allow advocates of opposing sides of an argument to agree on the relative strengths of their supporting reasoning. With papers from leading figures such as Mike Oaksford and Ulrike Hahn, the book comprises recent research conducted at the frontiers of Bayesian argumentation and provides a multitude of examples in which these formal tools can be applied to informal argument. It signals new and impending developments in philosophy, which has seen Bayesian models deployed in formal epistemology and philosophy of science, but has yet to explore the full potential of Bayesian models as a framework in argumentation. In doing so, this revealing anthology looks destined to become a standard teaching text in years to come.
    Description / Table of Contents: Bayesian Argumentation; Foreword; Contents; Bayesian Argumentation: The Practical Side of Probability; 1 Introduction; 2 The Bayesian Approach to Argumentation; 3 Chapter Overview; 3.1 The Bayesian Approach to Argumentation; 3.2 The Legal Domain; 3.3 Modeling Rational Agents; 3.4 Theoretical Issues; References; Part I: The Bayesian Approach to Argumentation; Testimony and Argument: A Bayesian Perspective; 1 Introduction; 2 Testimony, Argumentation and the `Third Way´; 3 Some Problems for MAXMIN; 4 A Bayesian Perspective; 5 Message Content and Message Source: Exploring Norms and Intuitions
    Description / Table of Contents: 6 Rehousing Argumentation Schemes Within a Bayesian Framework7 Concluding Remarks; References; Why Are We Convinced by the Ad Hominem Argument?: Bayesian Source Reliability and Pragma-Dialectical Discussion Rules; 1 Types of the Argumentum Ad Hominem; 2 The Pragma-Dialectical Approach; 3 The Bayesian Approach; 4 An Experiment on the Argument Ad Hominem; 5 Method; 6 Results and Discussion; 7 Conclusion; Appendix: Experimental Materials; Abusive; Circumstantial; Tu Quoque; Control; References; 1 Introduction; 2 Survey of Relevant Uncertainties; Part II: The Legal Domain
    Description / Table of Contents: A Survey of Uncertainties and Their Consequences in Probabilistic Legal Argumentation2.1 The Example Case; 2.2 Factual Uncertainty; 2.3 Normative Uncertainty; 2.4 Moral Uncertainty; 2.5 Empirical Uncertainty; 2.6 Interdependencies; 3 Desirable Attributes for a Probabilistic Argument Model to Assist Litigation Planning; 3.1 Assessment of Utilities; 3.2 Easy Knowledge Engineering; 3.3 Conflict Resolution and Argument Weights; 4 Sample Assessment of Graphical Models; 4.1 A Graphical Structure of the Analysis; 4.2 Casting the Example into a Graphical Model; 4.3 Generic Bayesian Networks
    Description / Table of Contents: 5 Carneades5.1 A Brief Introduction to the Carneades Model; 5.2 Carneades Bayesian Networks; 5.3 Carneades Bayesian Networks with Probabilistic Assumptions; 5.4 Introduction to Argument Weights; 6 Extension of Carneades to Support Probabilistic Argument Weights; 7 Desiderata for Future Developments; 7.1 Weights Subject to Argumentation; 7.2 Inform Weights from Values; 8 Conclusions and Future Work; References; Was It Wrong to Use Statistics in R v Clark? A Case Study of the Use of Statistical Evidence in Criminal Courts; 1 Introduction; 2 Factual Background; 3 Existing Explanations
    Description / Table of Contents: 3.1 The Flaws in Meadow´s Calculation3.2 The Psychological Effect of the Statistical Evidence; 3.3 The Prosecutor´s Fallacy; 3.4 Bayes´ Theorem; 3.5 The Insignificance of the SIDS Statistics; 4 The Contrastive Explanation; 5 Conclusion; References; Part III: Modeling Rational Agents; A Bayesian Simulation Model of Group Deliberation and Polarization; 1 Introduction; 2 The Laputa Simulation Framework; 3 The Underlying Bayesian Model; 4 Interpreting Laputa; 5 Do Bayesian Inquirers Polarize?; 6 Conclusion and Discussion; Appendix; References
    Description / Table of Contents: Degrees of Justification, Bayes´ Rule, and Rationality
    Description / Table of Contents: Introduction: Frank Zenker.​- Part 1 -- The Bayesian Approach to Argumentation -- Chapter 1. Testimony and Argument: A Bayesian Perspective: Ulrike Hahn, Mike Oaksford and Adam J.L. Harris -- Chapter 2. Why are we convinced by the Ad Hominem Argument?: Source Reliability or Pragma-Dialectics: Mike Oaksford and Ulrike Hahn.- Part 2. The Legal Domain.-Chapter 3. A survey of uncertainties and their consequences in Probabilistic Legal Argumentation: Matthias Grabmair and Kevin D. Ashley -- Chapter 4. What went wrong in the case of Sally Clark? A case-study of the use of Statistical Evidence in Court: Amid Pundik -- Part 3. Modeling Rational Agents -- Chapter 5. A Bayesian Simulation Model of Group Deliberation: Erik J. Olsson -- Chapter 6. Degrees of Justification, Bayes' Rule, and Rationality: Gregor Betz -- Chapter 7. Argumentation with (Bounded) Rational Agents: Robert van Rooij and Kris de Jaeghery -- Part 4. Theoretical Issues -- Chapter 8. Reductio, Coherence, and the Myth of Epistemic Circularity: Tomoji Shogenji -- Chapter 9. On Argument Strength: Niki Pfeiffer -- Chapter 10 -- Upping the Stakes and the Preface Paradox: Jonny Blamey -- References.​.
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  • 6
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789400765344
    Language: English
    Pages: Online-Ressource (X, 393 p. 74 illus, online resource)
    Series Statement: Logic, Epistemology, and the Unity of Science 30
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg.
    RVK:
    Keywords: Philosophy (General) ; Logic ; Computer science ; Logic, Symbolic and mathematical ; Philosophy ; Philosophy (General) ; Logic ; Computer science ; Logic, Symbolic and mathematical
    Abstract: Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
    Description / Table of Contents: IntroductionPart I. What are Mathematical Arguments? -- Chapter 1. Non-Deductive Logic in Mathematics: The Probability of Conjectures; James Franklin -- Chapter 2. Arguments, Proofs, and Dialogues; Erik C. W. Krabbe -- Chapter 3. Argumentation in Mathematics; Jesús Alcolea Banegas -- Chapter 4. Arguing Around Mathematical Proofs; Michel Dufour -- Part II. Argumentation as a Methodology for Studying Mathematical Practice -- Chapter 5. An Argumentative Approach to Ideal Elements in Mathematics; Paola Cantù -- Chapter 6. How Persuaded Are You? A Typology of Responses; Matthew Inglis and Juan Pablo Mejía-Ramos -- Chapter 7. Revealing Structures of Argumentations in Classroom Proving Processes; Christine Knipping and David Reid -- Chapter 8. Checking Proofs; Jesse Alama and Reinhard Kahle -- Part III. Mathematics as a Testbed for Argumentation Theory -- Chapter 9. Dividing by Zero-and Other Mathematical Fallacies; Lawrence H. Powers -- Chapter 10. Strategic Maneuvering in Mathematical Proofs; Erik C. W. Krabbe -- Chapter. 11 Analogical Arguments in Mathematics; Paul Bartha -- Chapter 12. What Philosophy of Mathematical Practice Can Teach Argumentation Theory about Diagrams and Pictures; Brendan Larvor -- Part IV. An Argumentational Turn in the Philosophy of Mathematics -- Chapter 13. Mathematics as the Art of Abstraction; Richard L. Epstein -- Chapter 14. Towards a Theory of Mathematical Argument; Ian J. Dove -- Chapter 15. Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics; Alison Pease, Alan Smaill, Simon Colton and John Lee -- Chapter 16. Mathematical Arguments and Distributed Knowledge; Patrick Allo, Jean Paul Van Bendegem and Bart Van Kerkhove -- Chapter 17. The Parallel Structure of Mathematical Reasoning; Andrew Aberdein -- Index.
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  • 7
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789401700832
    Language: English
    Pages: Online-Ressource (X, 251 p) , digital
    Edition: Springer eBook Collection. Humanities, Social Sciences and Law
    Series Statement: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science 310
    Parallel Title: Erscheint auch als
    Parallel Title: Erscheint auch als
    Parallel Title: Erscheint auch als
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    Keywords: Science Philosophy ; Logic, Symbolic and mathematical ; Philosophy and science. ; Mathematics ; Logic ; Mathematical logic. ; Science—Philosophy. ; Arithmetik ; Logischer Schluss
    Abstract: Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene
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