About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-100190641223

ISBN-139780190641221

eBay Product ID (ePID)9038251811

Product Key Features

Number of Pages472 Pages

LanguageEnglish

Publication NamePrehistory of Mathematical Structuralism

Publication Year2020

SubjectGeneral, Logic

TypeTextbook

Subject AreaMathematics, Philosophy

AuthorGeorg Schiemer

SeriesLogic and Computation in Philosophy Ser.

FormatHardcover

Dimensions

Item Height1.3 in

Item Weight27.5 Oz

Item Length6.3 in

Item Width9.4 in

Additional Product Features

Intended AudienceScholarly & Professional

Dewey Edition23

TitleLeadingThe

Reviews"The strategy of presenting both aspects of structuralism (mathematical and philosophical) in the same volume successfully shows the deep connections between these forms of thought...Recommended. Lower- and upper-division undergraduates. Graduate students and faculty." -- M. Clay, University of Arkansas, CHOICE "an excellent coherent well thought out collection." -- Mark Zelcer, Metascience, "The strategy of presenting both aspects of structuralism (mathematical and philosophical) in the same volume successfully shows the deep connections between these forms of thought...Recommended. Lower- and upper-division undergraduates. Graduate students and faculty." -- M. Clay, University of Arkansas, CHOICE"an excellent coherent well thought out collection." -- Mark Zelcer, Metascience

IllustratedYes

Dewey Decimal510.1

Table Of Content1. Erich Reck & Georg Schiemer: The Prehistory of Mathematical Structuralism: Introduction and OverviewPart I: Mathematical Developments2. Paola Cantù: Grassmann's Concept Structuralism3. José Ferreirós & Erich Reck: Dedekind's Mathematical Structuralism: From Galois Theory to Numbers, Sets, and Functions4. Dirk Schlimm: Pasch's Empiricism as Methodological Structuralism5. Georg Schiemer: Transfer Principles, Klein's Erlangen Program, and Methodological Structuralism6. Wilfried Sieg: The Ways of Hilbert's Axiomatics: Structural and Formal7. Audrey Yap: Noether as Mathematical Structuralist8. Gerhard Heinzmann & Jean Petitot: The Functional Role of Structures in Bourbaki9. Colin McLarty: Saunders Mac Lane: From Principia Mathematica through Göttingen to the Working Theory of StructuresPart II: Logical and Philosophical Reflections10. Jessica Carter: Logic of Relations and Diagrammatic Reasoning: Structuralist Elements in the Work of Charles Sanders Peirce11. Janet Folina: Poincaré and the Pre-History of Mathematical Structuralism12. Jeremy Heis: 'If Numbers Are To Be Anything At All, They Must Be Intrinsically Something': Bertrand Russell and Mathematical Structuralism13. Erich Reck: Cassirer's Reception of Dedekind and the Structuralist Transformation of Mathematics14. Wilfried Sieg: Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory15. Georg Schiemer: Carnap's Structuralist Thesis16. Sean Morris: Explication as Elimination: W.V. Quine and Mathematical Structuralism

SynopsisThis is an open access title available under the terms of a CC BY-NC-ND 4.0 licence. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries.This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy., Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries. This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy., 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., Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries.This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked "pre-history" of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy., This is an open access title available under the terms of a CC BY-NC-ND 4.0 licence. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. Recently, debates about mathematical structuralism have picked up steam again within the philosophy of mathematics, probing ontological and epistemological issues in novel ways. These debates build on discussions of structuralism which began in the 1960s in the work of philosophers such as Paul Benacerraf and Hilary Putnam; going further than these previous thinkers, however, these new debates also recognize that the motivation for structuralist views should be tied to methodological developments within mathematics. In fact, practically all relevant ideas and methods have roots in the structuralist transformation that modern mathematics underwent in the 19th and early 20th centuries. This edited volume of new essays by top scholars in the philosophy of mathematics explores this previously overlooked 'pre-history' of mathematical structuralism. The contributors explore this historical background along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics, such as Dedekind, Hilbert, and Bourbaki, who are responsible for the introduction of new number systems, algebras, and geometries that transformed the landscape of mathematics. Second, they reexamine a range of philosophical reflections by mathematically inclined philosophers, like Russell, Cassirer, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism. Overall, the essays in this volume show not only that the pre-history of mathematical structuralism is much richer than commonly appreciated, but also that it is crucial to take into account this broader intellectual history for enriching current debates in the philosophy of mathematics. The insights included in this volume will interest scholars and students in the philosophy of mathematics, the philosophy of science, and the history of philosophy.

LC Classification NumberQA8.4