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  • Dordrecht : Springer  (10)
  • Mathematics  (10)
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  • 1
    ISBN: 9789400723214 , 1283944987 , 9781283944984
    Language: English
    Pages: Online-Ressource (X, 250 p, online resource)
    Series Statement: Mathematics Education in the Digital Era 1
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Martinovic, Dragana Visual Mathematics and Cyberlearning
    RVK:
    Keywords: Visualization ; Computer software ; Mathematics ; Education ; Education ; Visualization ; Computer software ; Mathematics ; Education Philosophy
    Abstract: The first volume in this new Springer series explores innovative ways of learning and doing mathematics to make it more appealing to the Net Generation. This generation consists of visual learners who thrive when surrounded with new technologies and whose diverse needs can be met by a variety of cyber tools. In their search for novel ways of studying, such as collaboration with peers and multitasking by using multimedia, the Internet, and other Information and Communication Technologies, they learn mathematics by playing games online, watching and sharing presentations on YouTube, exploring and creating Java applets of mathematics simulations and exchanging thoughts over the instant chat tools. This volume presents mathematics teaching and learning in a way that resonates with these new learners: as a contemporary subject that is engaging, exciting and enlightening. It offers educators insight into how they can make meaningful use of the dynamic, interactive, collaborative, and visual nature of new learning environments while having a deeper understanding of their potential advantages and limitations. This volume:- Bridges the gap between Net Generation learners and mathematics education- Presents conceptual frameworks for research in this area- Explores research data that shed a light on innovative theories and practices in the field of visual mathematics and cyberlearning.
    Description / Table of Contents: Visual Mathematics and Cyberlearning; Introduction; Mathematics Education in the Digital Era (MEDEra) Series; Visual Mathematics and Cyberlearning - The First Book in the MEDEra Series; Contents; Patterns of Collaboration: Towards Learning Mathematics in the Era of the Semantic Web; Introduction; Cyberlearning: From Web 1.0 to Web 2.0; Patterns of Collaboration: The Case of the MiGen and Metafora Projects; Collaboration in Exploratory Learning Environments; The MiGen System and the Metafora Platform; Collaboration Within the MiGen System and the Metafora Platform
    Description / Table of Contents: Student Collaboration and the TeacherCyberlearning: From Web 2.0 to Web 3.0; The Likely Impact of Web 3.0 on Systems Such as MiGen and Metafora; Conclusion; References; Collaborative Mathematics Learning in Online Environments; Introduction; Collaborative Online Learning of Research-Level Mathematics; Why Talk About the Research Level?; Overview of Online Collaboration at the Research Level; The Polymath Projects; The MathOverflow Website; Collaborative Online Learning: Undergraduate and School-Age Mathematics; Mathematics - Stack Exchange
    Description / Table of Contents: An Excerpt of an Exchange on Mathematics - Stack ExchangeA Global Learning Project; Virtual Math Teams; Analysis and Contextualization; Computer Supported Collaborative Learning; The Computer Moderated Communication Model; Networked Learning, and Collaboration Versus Cooperation; Self-Regulated Learning; Discussion; References; The Integration of Mathematics Discourse, Graphical Reasoning and Symbolic Expression by a Virtual Math Team; Mathematical Practices; Data Collection and Methodology; Setting Up the Mathematical Analysis; Excerpt 1: Constitution of a New Math Task
    Description / Table of Contents: Excerpt 2: Co-construction of a Method for Counting SticksExcerpt 3: Collective Noticing of a Pattern of Growth; Excerpt 4: Resolution of Referential Ambiguity via Visual Proof; Concluding the Mathematical Analysis; Excerpt 5: Re-initiating the Discussion of the Algebraic Formula; Excerpt 6: Co-reflection on What the Team has Achieved So Far; Excerpt 7: Overcoming the Problem of Overlapping Sticks; Excerpt 8: Derivation of the Formula for the Number of Sticks; Discussion; Visibility of the Production Process; Persistent Presence of Contributions
    Description / Table of Contents: Methods for Referencing Relevant Artifacts in the Shared Visual FieldCoordination of Whiteboard Visualizations and Chat Narratives; Past and Future Relevancies Implied by Shared Mathematical Artifacts; Conclusion; References; Investigating the Mathematical Discourse of Young Learners Involved in Multi-Modal Mathematical Investigations: The Case of Haptic Technologies; Background and Rationale; Dynamic Geometry; Haptic Technology; Merging Fields; Theoretical Perspectives; Multi-modal Environment Design; Technical Specifications; Design of Mathematical Activities; Classification of Solids
    Description / Table of Contents: Planar Intersections
    Description / Table of Contents: 1. Keith Jones, Eirini Geraniou, & Thanassis Tiropanis: Patterns of collaboration: Towards learning mathematics in the era of the semantic web -- 2. Gorjan Alagic & Mara Alagic: Collaborative mathematics learning in online environments -- 3. Murat Perit Cakir & Gerry Stahl: The integration of mathematics discourse, Graphical reasoning and symbolic expression by a Virtual Math Team -- 4. Beste Güçler, Stephen Hegedus, Ryan Robidoux, & Nicholas Jackiw: Investigating the Mathematical Discourse of Young Learners Involved in Multi-Modal Mathematical Investigations: The Case of Haptic Technologies -- 5. Dragan Trninic & Dor Abrahamson: Embodied interaction as designed mediations of conceptual performance -- 6. Luis Radford: Sensuous Cognition -- 7. George Gadanidis & Immaculate Namukasa: New media and online mathematics learning for teachers -- 8. Ann LeSage: Web-based video clips: A supplemental resource for supporting pre-service elementary mathematics teachers -- 9. Dragana Martinovic, Viktor Freiman, & Zekeriya Karadag: Visual mathematics and cyberlearning in view of Affordance and Activity Theories. .
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  • 2
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789400760912
    Language: English
    Pages: Online-Ressource (XV, 389 p. 35 illus, online resource)
    Series Statement: Logic, Argumentation & Reasoning, Interdisciplinary Perspectives from the Humanities and Social Sciences 1
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Druckausg. Cellucci, Carlo, 1940 - Rethinking logic
    RVK:
    Keywords: Philosophy (General) ; Logic ; Computer science ; Philosophy ; Philosophy (General) ; Logic ; Computer science ; Computer science ; Logic ; Philosophy ; Philosophy (General) ; Logik ; Interdisziplinäre Forschung
    Abstract: 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
    Description / Table of Contents: PrefaceChapter 1. Introduction -- Part I. Ancient Perspectives -- Chapter 2. The Origin of Logic -- Chapter 3. Ancient Logic and Science -- Chapter 4. The Analytic Method -- Chapter 5. The Analytic-Synthetic Method -- Chapter 6. Aristotle's Logic: The Deductivist View -- Chapter 7. Aristotle's Logic: The Heuristic View -- Part II. Modern Perspectives -- Chapter 8. The Method of Modern Science -- Chapter 9. The Quest for a Logic of Discovery -- Chapter 10. Frege's Approach to Logic -- Chapter 11. Gentzen's Approach to Logic -- Chapter 12. The Limitations of Mathematical Logic -- Chapter 13. Logic, Method, and the Psychology of Discovery -- Part III: An Alternative Perspective -- Chapter 14. Reason and Knowledge -- Chapter 15. Reason, Knowledge and Emotion -- Chapter 16. Logic, Evolution, Language and Reason -- Chapter 17. Logic, Method and Knowledge -- Chapter 18. Classifying and Justifying Inference Rules -- Chapter 19. Philosophy and Knowledge -- Part IV: Rules of Discovery -- Chapter 20. Induction and Analogy -- Chapter 21. Other Rules of Discovery -- Chapter 22. Conclusion -- References -- Name Index -- Subject Index.
    Note: Includes bibliographies and index
    URL: Cover
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  • 3
    ISBN: 9789400757219
    Language: English
    Pages: Online-Ressource (XV, 258 p. 135 illus, digital)
    Series Statement: Archimedes, New Studies in the History and Philosophy of Science and Technology 31
    Series Statement: SpringerLink
    Series Statement: Bücher
    Parallel Title: Buchausg. u.d.T. Meskens, Ad, 1962 - Practical mathematics in a commercial metropolis
    RVK:
    Keywords: Science History ; Architecture ; Science, general ; Science History ; Architecture ; Coignet, Michel, 1549-1623 ; Heyns, Peeter, 1537-1598 ; Mathematics ; Belgium ; Antwerp ; History ; 16th century ; Angewandte Mathematik ; Geschichte
    Abstract: Describes the development and the ultimate demise of the practice of mathematics in sixteenth century Antwerp. Against the background of the violent history of the Religious Wars the story of the practice of mathematics in Antwerp is told through the lives of two protagonists Michiel Coignet and Peeter Heyns. The book touches on all aspects of practical mathematics from teaching and instrument making to the practice of building fortifications of the practice of navigation.?
    Abstract: This volumedescribes the development and the ultimate demise of the practice of mathematics in sixteenth century Antwerp. Against the background of the violent history of the Religious Wars the story of the practice of mathematics in Antwerp is told through the lives of two protagonists Michiel Coignet and Peeter Heyns. The book touches on all aspects of practical mathematics from teaching and instrument making to the practice of building fortifications of the practice of navigation.​
    Description / Table of Contents: 1 Preface -- 2 Introduction -- 3 The Family Coignet -- 4 Peeter Heyns and the Nymphs of the Laurel Tree -- 5 The Arithmetic Teacher and his School -- 6 The Antwerp arithmetic books -- 7 Winegauging -- 8 Instrumentmakers -- 9 The Art of Navigation -- 10 Mapping the World -- 11 Looking towards the Stars -- 12 Ballistics and fortifications -- 13 Conclusion -- Appendices -- Index.​.
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  • 4
    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
    RVK:
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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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  • 5
    ISBN: 9789400714335
    Language: English
    Pages: 1 Online-Ressource (xix, 1187 Seiten)
    Series Statement: Springer reference
    DDC: 302.12
    RVK:
    RVK:
    Keywords: Decision making ; Economic theory ; Game theory ; Industrial safety ; Operations research ; Philosophy ; Philosophy and science ; Quality control ; Reliability ; Philosophy of Science. ; Economic Theory/Quantitative Economics/Mathematical Methods. ; Game Theory, Economics, Social and Behav. Sciences. ; Operations Research/Decision Theory. ; Philosophy of Technology. ; Quality Control, Reliability, Safety and Risk.
    Note: Enthält die Bände 1 und 2 der Printausgabe. , Literaturangaben
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  • 6
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9789400700079 , 9400700075 , 9789400700086 , 9400700083 , 9781282995833
    Language: English
    Pages: 1 Online-Ressource (xiii, 155 p.)
    Series Statement: Synthese library v. 350
    DDC: 519.2
    RVK:
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    Keywords: Probabilities ; Mathematical statistics ; Logic, Symbolic and mathematical ; Statistik ; Wahrscheinlichkeitsverteilung ; Mathematische Logik ; Mathematische Logik ; Statistik ; Wahrscheinlichkeitsverteilung
    Note: Includes bibliographical references (p. 141-151) and index
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  • 7
    ISBN: 9780387096094 , 0387096094
    Language: English
    Pages: XI, 268 S. , graph. Darst. , a
    Series Statement: Statistics for social and behavioral sciences
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    Keywords: Schätztheorie ; Modellierung ; Qualitative Methode ; Zeitreihenanalyse ; Kausalanalyse ; Statistische Methode ; Social sciences Mathematical models ; Social sciences Statistical methods ; Social sciences Research ; Marginalanalyse ; Schätztheorie ; Sozialwissenschaften ; Verhaltenswissenschaften ; Statistik ; Social sciences Mathematical models ; Social sciences Statistical methods ; Social sciences Research ; Marginalanalyse ; Schätztheorie
    Note: Literaturverz. S. 247 - 257
    URL: Cover
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  • 8
    Online Resource
    Online Resource
    Dordrecht : Springer
    ISBN: 9781402055874
    Language: English
    Pages: Online-Ressource , v.: digital
    Edition: Online-Ausg. Springer eBook Collection. Humanities, Social Science and Law Electronic reproduction; Available via World Wide Web
    RVK:
    Keywords: Science Logic, Symbolic and mathematical ; Computer science ; Artificial intelligence ; Geometry ; Topology ; Philosophy (General) ; Logic, Symbolic and mathematical ; Raum ; Mathematische Logik
    Abstract: Johan Benthem
    Abstract: A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, descr
    Description / Table of Contents: CONTENTS; Preface; Contributing Authors; Second Readers xxi; Chpater 1 What is Spatial Logic?; Chapter 2 First-Order Mereotopology; Chapter 3 Axioms, Algebras and Topology; Chpater 4 Qualitative Spatial Reasoning Using Constraint Calculi; Chapter 5 Modal Logics of Space; Chapter 6 Topology and Epistemic Logic; Chapter 7 Logical Theories for Fragments of Elementary Geometry; Chapter 8 Locales and Toposes as Spaces; Chapter 9 Spatial Logic + Temporal Logic = ?; Chapter 10 Dynamic Topological Logic; Chapter 11 Logic of Space-Time and Relativity Theory; Chapter 12 Discrete Spatial Models
    Description / Table of Contents: Chapter 13 Real Algebraic Geometry and Constriaint DatabasesChapter 14 Mathematical Morphology; Chapter 15 Spatial Resoning and Ontology: Parts, Wholes, and Locations; Index
    Note: Includes bibliographical references and index , Electronic reproduction; Available via World Wide Web
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  • 9
    ISBN: 1402042728 , 9781402042720 , 1402042736
    Language: English
    Pages: XIV, 462 S , graph. Darst.
    Series Statement: NATO science series 216
    Series Statement: Sub-series 2, Mathematics, physics and chemistry
    Parallel Title: Online-Ausg. Biran, Paul Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology
    DDC: 510
    RVK:
    Keywords: Morse theory Congresses ; Symplectic and contact topology Congresses ; Konferenzschrift ; Nichtlineare Analysis ; Symplektische Geometrie ; Morse-Theorie
    URL: Cover
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  • 10
    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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