Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method

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.

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List of contents

Preface.- Chapter 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.

Summary

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.

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Additional text

“Cellucci puts logic back in its place, after it was turned upside down by the drifts of AP (analytical philosophy), which pushed the search for certainty and foundations too far.” (Emiliano Ippoliti, Epistemologia, Vol. 38 (2), July-December, 2015)
“Well documented, closely argued, and informed by truly inspired, and truly incompatible, interpretations of the Western tradition of logic, mathematics, and metaphysics.” (Emily R. Grosholz, Philosophia Mathematica, Vol. 23 (1), February, 2015)
“This textbook traces the history of Logic ranging from epistemology to induction and deduction. … I can recommend it to the philosophical audience for which it is addressed.” (Joseph Grenier, Amazon.com, March, 2014)
“Rethinking Logic is a valuable and remarkable book, especially because it does not resemble to any of the books dealing with logic which normally can be found on the market. … It is … a global and wide philosophical reflection on what logic and knowledge are, which argues for a theoretically purposeful view, with which one may obviously disagree, but with which it is certainly interesting confronting.” (Fabio Sterpetti, Philosophical Inquiries, Vol. 2 (2), 2014)

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"Cellucci puts logic back in its place, after it was turned upside down by the drifts of AP (analytical philosophy), which pushed the search for certainty and foundations too far." (Emiliano Ippoliti, Epistemologia, Vol. 38 (2), July-December, 2015)
"Well documented, closely argued, and informed by truly inspired, and truly incompatible, interpretations of the Western tradition of logic, mathematics, and metaphysics." (Emily R. Grosholz, Philosophia Mathematica, Vol. 23 (1), February, 2015)
"This textbook traces the history of Logic ranging from epistemology to induction and deduction. ... I can recommend it to the philosophical audience for which it is addressed." (Joseph Grenier, Amazon.com, March, 2014)
"Rethinking Logic is a valuable and remarkable book, especially because it does not resemble to any of the books dealing with logic which normally can be found on the market. ... It is ... a global and wide philosophical reflection on what logic and knowledge are, which argues for a theoretically purposeful view, with which one may obviously disagree, but with which it is certainly interesting confronting." (Fabio Sterpetti, Philosophical Inquiries, Vol. 2 (2), 2014)

Product details

• Authors: Carlo Cellucci
• Publisher: Springer Netherlands
• Languages: English
• Product format: Hardback
• Released: 01.02.2014
• EAN: 9789400760905
• ISBN: 978-94-0-076090-5
• No. of pages: 389
• Dimensions: 168 mm x 241 mm x 28 mm
• Weight: 767 g
• Illustrations: XV, 389 p. 35 illus.
• Series: Logic, Argumentation & Reasoning; Logic, Argumentation & Reasoning
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; B, Logic, Philosophy, History of Philosophy, Religion and Philosophy, Mathematical theory of computation, History of philosophy, philosophical traditions, Mathematical logic, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages