Prehistory of Mathematical Structuralism
Herausgeber: Reck, Erich H; Schiemer, Georg
Prehistory of Mathematical Structuralism
Herausgeber: Reck, Erich H; Schiemer, Georg
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This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.…mehr
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This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
Produktdetails
- Produktdetails
- Verlag: Oxford University Press, USA
- Seitenzahl: 468
- Erscheinungstermin: 1. Juni 2020
- Englisch
- Abmessung: 239mm x 163mm x 39mm
- Gewicht: 778g
- ISBN-13: 9780190641221
- ISBN-10: 0190641223
- Artikelnr.: 57827317
- Verlag: Oxford University Press, USA
- Seitenzahl: 468
- Erscheinungstermin: 1. Juni 2020
- Englisch
- Abmessung: 239mm x 163mm x 39mm
- Gewicht: 778g
- ISBN-13: 9780190641221
- ISBN-10: 0190641223
- Artikelnr.: 57827317
Erich H. Reck is Professor of Philosophy at the University of California at Riverside. He is the author of a number of articles in the philosophy of mathematics, the history and philosophy of logic, and the history of 19th/20th-century philosophy. In addition, he is the editor, or co-editor, of several related collections of essays: From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy (OUP, 2002); Frege's Lectures on Logic: Carnap's Student Notes, 1910-1914 (Open Court, 2004); Gottlob Frege: Critical Assessments of Leading Philosophers, Vols. I-IV (Routledge, 2005); The Historical Turn in Analytic Philosophy (Palgrave Macmillan, 2013); and Logic, Philosophy of Mathematics, and their History: Essays in Honor of W.W. Tait (College Publications, 2018). Currently he is working on a book on the mathematician and philosopher of mathematics Richard Dedekind. Georg Schiemer is Assistant Professor at the Department of Philosophy at the University of Vienna as well as external fellow at the Munich Center for Mathematical Philosophy at LMU Munich. He is currently principal investigator of the project "The Roots of Mathematical Structuralism" funded by an ERC Starting Grant. His research focuses on the history and philosophy of mathematics and early analytic philosophy. He is also interested in the history and philosophy of logic and formal philosophy of science.
* 1. Erich Reck and Georg Schiemer: The Prehistory of Mathematical
Structuralism: Introduction and Overview
* Part I: Mathematical Developments
* 2. Paola Cantù: Grassmann's Concept Structuralism
* 3. José Ferreirós and Erich Reck: Dedekind's Mathematical
Structuralism: From Galois Theory to Numbers, Sets, and Functions
* 4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
* 5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and
Methodological Structuralism
* 6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and
Formal
* 7. Audrey Yap: Noether as Mathematical Structuralist
* 8. Gerhard Heinzmann and Jean Petitot: The Functional Role of
Structures in Bourbaki
* 9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica
through Göttingen to the Working Theory of Structures
* Part II: Logical and Philosophical Reflections
* 10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning:
Structuralist Elements in the Work of Charles Sanders Peirce
* 11. Janet Folina: Poincaré and the Pre-History of Mathematical
Structuralism
* 12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be
Intrinsically Something': Bertrand Russell and Mathematical
Structuralism
* 13. Erich Reck: Cassirer's Reception of Dedekind and the
Structuralist Transformation of Mathematics
* 14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical
Structuralism, and Proof Theory
* 15. Georg Schiemer: Carnap's Structuralist Thesis
* 16. Sean Morris: Explication as Elimination: W.V. Quine and
Mathematical Structuralism
Structuralism: Introduction and Overview
* Part I: Mathematical Developments
* 2. Paola Cantù: Grassmann's Concept Structuralism
* 3. José Ferreirós and Erich Reck: Dedekind's Mathematical
Structuralism: From Galois Theory to Numbers, Sets, and Functions
* 4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
* 5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and
Methodological Structuralism
* 6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and
Formal
* 7. Audrey Yap: Noether as Mathematical Structuralist
* 8. Gerhard Heinzmann and Jean Petitot: The Functional Role of
Structures in Bourbaki
* 9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica
through Göttingen to the Working Theory of Structures
* Part II: Logical and Philosophical Reflections
* 10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning:
Structuralist Elements in the Work of Charles Sanders Peirce
* 11. Janet Folina: Poincaré and the Pre-History of Mathematical
Structuralism
* 12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be
Intrinsically Something': Bertrand Russell and Mathematical
Structuralism
* 13. Erich Reck: Cassirer's Reception of Dedekind and the
Structuralist Transformation of Mathematics
* 14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical
Structuralism, and Proof Theory
* 15. Georg Schiemer: Carnap's Structuralist Thesis
* 16. Sean Morris: Explication as Elimination: W.V. Quine and
Mathematical Structuralism
* 1. Erich Reck and Georg Schiemer: The Prehistory of Mathematical
Structuralism: Introduction and Overview
* Part I: Mathematical Developments
* 2. Paola Cantù: Grassmann's Concept Structuralism
* 3. José Ferreirós and Erich Reck: Dedekind's Mathematical
Structuralism: From Galois Theory to Numbers, Sets, and Functions
* 4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
* 5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and
Methodological Structuralism
* 6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and
Formal
* 7. Audrey Yap: Noether as Mathematical Structuralist
* 8. Gerhard Heinzmann and Jean Petitot: The Functional Role of
Structures in Bourbaki
* 9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica
through Göttingen to the Working Theory of Structures
* Part II: Logical and Philosophical Reflections
* 10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning:
Structuralist Elements in the Work of Charles Sanders Peirce
* 11. Janet Folina: Poincaré and the Pre-History of Mathematical
Structuralism
* 12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be
Intrinsically Something': Bertrand Russell and Mathematical
Structuralism
* 13. Erich Reck: Cassirer's Reception of Dedekind and the
Structuralist Transformation of Mathematics
* 14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical
Structuralism, and Proof Theory
* 15. Georg Schiemer: Carnap's Structuralist Thesis
* 16. Sean Morris: Explication as Elimination: W.V. Quine and
Mathematical Structuralism
Structuralism: Introduction and Overview
* Part I: Mathematical Developments
* 2. Paola Cantù: Grassmann's Concept Structuralism
* 3. José Ferreirós and Erich Reck: Dedekind's Mathematical
Structuralism: From Galois Theory to Numbers, Sets, and Functions
* 4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism
* 5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and
Methodological Structuralism
* 6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and
Formal
* 7. Audrey Yap: Noether as Mathematical Structuralist
* 8. Gerhard Heinzmann and Jean Petitot: The Functional Role of
Structures in Bourbaki
* 9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica
through Göttingen to the Working Theory of Structures
* Part II: Logical and Philosophical Reflections
* 10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning:
Structuralist Elements in the Work of Charles Sanders Peirce
* 11. Janet Folina: Poincaré and the Pre-History of Mathematical
Structuralism
* 12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be
Intrinsically Something': Bertrand Russell and Mathematical
Structuralism
* 13. Erich Reck: Cassirer's Reception of Dedekind and the
Structuralist Transformation of Mathematics
* 14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical
Structuralism, and Proof Theory
* 15. Georg Schiemer: Carnap's Structuralist Thesis
* 16. Sean Morris: Explication as Elimination: W.V. Quine and
Mathematical Structuralism