数学的実践の歴史と哲学ハンドブック（全４巻）
Handbook of the History and Philosophy of Mathematical Practice
Editors: Bharath Sriraman, Professor of Mathematics, University of Montana (USA)
Editorial Advisory Board: Andrew Aberdein, Florida Institute of Technology, USA, Jody Azzouni,
Tufts University, USA, Otávio Bueno, University of Miami, USA, William Byers, Concordia University, Canada, Carlo Cellucci, Sapienza University of Rome, Italy, Chandler Davis, University of Toronto, Canada (1926-2022), Paul Ernest, University of Exeter, UK, Michele Friend,George Washington University, USA, Reuben Hersh, University of New Mexico, USA (1927-2020), Kyeong-Hwa Lee, Seoul National University, South Korea, Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023), Athanase Papadopoulos, University of Strasbourg, France, Ulf Persson, Chalmers University of Technology, Sweden, John Stillwell, University of San Francisco, USA & David Tall, University of Warwick, UK
2024:05 4 vols. 3,260 p. ISBN 978-3-031-40845-8 EUR 1299.99
(Springer) -DE-
概要
数学における直観とは、抽象とは、証明とは、何でしょうか。数学の人類文化への貢献を語るうえで、哲学的視座は欠かせません。本書は数学の歴史と哲学の関係を実践を通して解き明かすレファレンスです。同じくSpringerから2021年に刊行の好評レファレンス『芸術と科学の数学ハンドブック（全３巻）』（ISBN: 9783319570716）に引き続き、モンタナ大学のBharath Sriramanが編集主幹を務めています。
全4巻の本書は、古代から現代までの数学的実践の歴史を通して、数学の哲学がたどってきた道とその意味を探究します。各章では、今日の数学の哲学を特徴づける起源や議論、方法論、新しい視点を示します。数学、歴史学、哲学などの分野の境界を越えて数学の歴史・哲学的研究に貢献してきた多数の学者たちが、哲学の発展と対比させながら、さまざまな時代の多様な数学的実践を詳述します。
数学的な実践が多様化していく中で、すでに知られたこととこれまで扱われていないことを総合し、数学の哲学が向かっていく方向を指し示す必携レファレンスとして、本書をおすすめいたします。
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収録内容
Volume 1
Section I From Origins to the Natural Historians/Philosophers
Bharath Sriraman
- Introduction to the Handbook of the History and Philosophy of Mathematical Practice
Bharath Sriraman
- The History and Philosophy of Mathematical Practice: From Origins to Natural Historians/Philosophers – A Conversation
Bharath Sriraman and Reuben Hersh
- Yuri Ivanovich Manin (1937–2023): Mathematics, Philosophy, and Poetry
Athanase Papadopoulos
- The Nature of Mathematical Objects
Carlo Cellucci
- The Ghost and the Spirit of Pythagoras
Arkady Plotnitsky
- The Metaphysics of Platonism
Ulf Persson
- Mathematical Practices Can Be Metaphysically Laden
Colin Jakob Rittberg
- Definitions (and Concepts) in Mathematical Practice
J. W. Coumans
- Mathematics and the Method of Abstraction
Kit Fine
- Leibniz on Number Systems
Lloyd Strickland
- Fermat and Descartes in Light of Premodern Algebra and Viète
Jeffrey A. Oaks
- Descartes’ Transformation of Greek Notion of Proportionality
Piotr Błaszczyk
- Leonhard Euler Between Mathematics and Natural Philosophy: An Introduction to Natural Science Anleitung zur Naturlehre
Danilo Capecchi
- Algebraic Versus Geometric Thought and Expression in the Early Calculus
Viktor Blåsjö
- Evolution of Leibniz’s Thought in the Matter of Fictions and Infinitesimals
Monica Ugaglia and Mikhail Katz
- René Thom: From Mathematics to Philosophy
Athanase Papadopoulos
- Heuristics and Mathematical Practice
Otávio Bueno
- Finding a Fit Among Philosophical Finitisms
Eamon Darnell and Aaron Thomas-Bolduc
Section II Mathematician’s Reflections on Practice and Working Philosophy of Mathematics
Athanase Papadopoulos
- Introduction to Mathematicians’ Reflections on Practice and Working Philosophy of Mathematics
Athanase Papadopoulos
- The Anthyphairetic Interpretation of Knowledge as Recollection in Plato’s Meno 80d-86e and 97a-98b
Stelios Negrepontis
- The Mystery of Plato’s Receptacle in the Timaeus Resolved
Stelios Negrepontis and Demetra Kalisperi
- The Indivisible Line Coincides with the Platonic Intelligible Being
Stelios Negrepontis
- Brouwer’s Intuitionism
Victor Pambuccian
- Mathematical Practice as Philosophy, with Galois, Riemann, and Grothendieck
Arkady Plotnitsky
- “That Which a Minority Construct”: Abelian Mathematics in Abel, Galois, Noether, and Grothendieck
Arkady Plotnitsky
- Pavel Florensky and His World
Athanase Papadopoulos
- The Practice of Mathematics in a Totalitarian Society
B. Sossinsky
- Philosophy Behind Mathematics
Ken’ichi Ohshika （学習院大学 大鹿健一教授）
- Some Disillusioned Thoughts About School and Teaching
Valentin Poénaru
Volume 2
Section III Influences in Twentieth- and Twenty-First-Century Mathematical Practice
Bharath Sriraman and Kyeonghwa Lee
- Influences in Twentieth- and Twenty-First-Century Mathematical Practice
Bharath Sriraman and Kyeonghwa Lee
- The Pell Equation in the Pythagoreans, Theaetetus, and Hindu Mathematics
Stelios Negrepontis, Vassiliki Farmaki, and Marina Brokou
- Ancient Indian Mathematics: Sulbasutras – A Mathematical Review
G. Dani
- An Ethnoarithmetic Excursion into the Javanese Calendar
Natanael Karjanto and François Beauducel
- Historiography of Mathematics from the Mathematician’s Point of View
Viktor Blåsjö
- A Tale of Three Cities: Thebes, Babylon, and Alexandria
Maurice Burke
- Sir Isaac Newton and Opticks
Jonah Britton and Bharath Sriraman
- Olry Terquem’s Forgotten Problem and an EnumerativeCombinatorial Perspective on the Euclidean Algorithm
Robert G. Donnelly, Molly W. Dunkum, and Rachel McCoy
- The Ethics of Mathematical Practice
Paul Ernest
- Grothendieck: A Short Guide to His Mathematical and Philosophical Work (1949–1991)
Fernando Zalamea
- An Uncertain Travel
Elijah Liflyand
- The Unreasonable Effectiveness of Mathematics to Generate New Spatial Imaginaries
Nathalie Sinclair
- High Mathematics Meets High Finance
Tom P. Davis
Section IV Practical, Historical, and Philosophical Instances of Probability
Egan J. Chernoff
- Introduction to Practical, Historical, and Philosophical Instances of Probability
Egan J. Chernoff
- How Markov’s Little Idea Transformed Statistics
Jeffrey S. Rosenthal
- The Use and Abuse of Probability in Evolutionary Biology
Jason Rosenhouse
- Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-as-Model
Christian Hennig
Section V Constructing the Reals: Paradoxes and Foundations
Paul M. Livingston and Bharath Sriraman
- Introduction to the History and Philosophy of Mathematical Practice in Constructing the Reals
Paul M. Livingston
- The Continuum and the Evolution of the Concept of Real Number
John L. Bell
- On Bolzano and Greek Concepts of Continuity
Piotr Błaszczyk and Marlena Fila
- Bolzano’s Theory of meßbare Zahlen: Insights and Uncertainties Regarding the Number Continuum
Elías Fuentes Guillén
- Abel’s Approach to Elliptic Integrals
John K. Dagsvik
- The Absolute Arithmetic Continuum and Its Geometric Counterpart
Philip Ehrlich
Volume 3
Section VI Practices in Euclidean and Non-Euclidean Geometry
Bharath Sriraman
- Euclidean and Non-Euclidean Geometry in the History and Philosophy of Mathematical Practice
Bharath Sriraman
- Cultures of Mathematical Practice in Alexandria in Egypt: Claudius Ptolemy and His Commentators (Second–Fourth Century CE)
Alberto Bardi
- Menelaus’ Spherics in Greek and Arabic Mathematics
Athanase Papadopoulos
- Copernicus and Axiomatics
Alberto Bardi
- Visual Representations of Euclidean Geometry: Diagrammatic Reasoning in Oliver Byrne’s Work
Andrea Pedeferri
- From Friezes to Quasicrystals: A History of Symmetry Groups
Franka Miriam Brückler and Vladimir Stilinović
- The Notion of Space in Grothendieck
John Alexander Cruz Morales
- Geometry in the Twentieth Century: A Return to Euclid – The Work of Herbert Busemann
Athanase Papadopoulos
Section VII Logic
Bharath Sriraman
- Logic in the History and Philosophy of Mathematical Practice
Valentina Harizanov
- Model Theory of Nonstandard Structures with Applications
Roman Kossak
- Computability Theory
Valentina Harizanov, Keshav Srinivasan, and Dario Verta
- Reverse Mathematics
John Stillwell
- Countable Nonstandard Models: Following Skolem’s Approach
Rumen D. Dimitrov and Valentina Harizanov
- Fermat’s Last Theorem
Colin McLarty
Section VIII Proof
Bart Van Kerkhove and Joachim Frans
- Proof in the History and Philosophy of Mathematical Practice: An Introduction
Joachim Frans and Bart Van Kerkhove
- Diagrammatic Proofs in Mathematics: (Almost) 20 Years of Research
Valeria Giardino
- The Social Epistemology of Mathematical Proof
Line Edslev Andersen
- The Values of Mathematical Proofs
Rebecca Lea Morris
- Formal Proofs in Mathematical Practice
Danielle Macbeth
- The Dark Side of the History of Proof
Karine Chemla
Section IX Ontology
Bharath Sriraman and Michael N. Fried
- Ontology in the History and Philosophy of Mathematical Practice: An Introduction
Michael N. Fried
- The Algorithmic-Device View of Informal Rigorous Mathematical Proof
Jody Azzouni
- Counterpossibles in Mathematical Practice: The Case of Spoof Perfect Numbers
Alan Baker
- What Mathematicians Do: Mathematics as Process and Creative Rationality
William Byers
- Platonism, De Re, and (Philosophy of) Mathematical Practice
Marco Panza
Section X Pluralism
Michele Friend
- One Mathematic(S) or Many? Foundations of Mathematics in Twentieth-Century Mathematical Practice
Andrei Rodin
- Multiverse and the Society
Mirna Džamonja
- Implicitly Defining Mathematical Terms
Demetra Christopoulou
- Non-deductive Justification in Mathematics
C. Paseau
Volume 4
Section XI “Experimental” Mathematics
Jessica Carter
- Experimental Mathematics in Mathematical Practice
Jessica Carter
- The Role of Experiments in Experimental Mathematics
Henrik Kragh Sørensen
- Revisiting “The New 4CT Problem”
Mark McEvoy
- Proofs, Arbitrary Exemplifications, and Inductive Generalizations in Euler’s Mathematical Practice
Giovanni Ferraro
- Mathematical Experiments on Paper and Computer
Dirk Schlimm and Juan Fernández González
- Thought Experiments in Mathematics: From Fiction to Facts
Irina Starikova
- The Intimate Interplay Between Experimentation and Deduction: Some Classroom Implications
Michael de Villiers and Hans Niels Jahnke
Section XII Views from Other Domains
Andrew Aberdein
- Introduction to Views from Other Domains
Andrew Aberdein
- Inverting Hierarchies: The Sociology of Mathematical Practice
Michael J. Barany and Milena I. Kremakova
- Practice Makes Perfectoid
Michael J. Barany
- Mathematics Education Research on Mathematical Practice
Keith Weber and Matthew Inglis
- Argumentation in Mathematical Practice
Andrew Aberdein and Zoe Ashton
- Rhetorical Approaches to the Study of Mathematical Practice
Mitchell Reyes
- Bayesian Perspectives on Mathematical Practice
James Franklin
- Polymath as an Epistemic Community
Patrick Allo, Jean Paul Van Bendegem, and Bart Van Kerkhove
- Is Mathematics Connected to Religion?
Stanisław Krajewski
Section XIII New Perspectives
Valeria Giardino
- New Perspectives: An Introduction
Valeria Giardino
- What Are Mathematical Practices? The Web-of-Practices Approach
José Ferreirós
- Experiments in Mathematics: Fact, Fiction, or the Future?
Jean Paul Van Bendegem
- The Social Constitution of Mathematical Knowledge: Objectivity, Semantics, and Axiomatics
Paola Cantù
- The Epistemological Subject(s) of Mathematics
Silvia De Toffoli
- Agency in Mathematical Practice
Yacin Hamami
- The Language of Proofs: A Philosophical Corpus Linguistics Study of Instructions and Imperatives in Mathematical Texts
Fenner Stanley Tanswell and Matthew Inglis
Section XIV Semiology of Mathematical Practice
Juan Luis Gastaldi
- Introduction to the Semiology of Mathematical Practice
Juan Luis Gastaldi
- Signs as a Theme in the Philosophy of Mathematical Practice
David Waszek
- Structural Semiotics as an Ontology of Mathematics
Roi Wagner
- Shaping, Revisited
Reviel Netz
- Mathematical Practices and Written Evidence: General Reflections Based on a Historian’s Experience
Karine Chemla
- What Happens, from a Historical Point of View, When We Read a Mathematical Text?
Lucien Vinciguerra
- Symbolic Algebra as a Semiotic System
Ladislav Kvasz
- Reading Mathematical Texts with Structuralist Semiotics
Anna Kiel Steensen
- The Design of Mathematical Language
Jeremy Avigad
- How to Do Maths with Words: Neural Machine Learning Applications to Mathematics and Their Philosophical Significance
Juan Luis Gastaldi
Index
（学術洋書部）
