Philosophy of mathematics Books

Book SynopsisHenri Poincaré (1854-1912) was a French mathematician, theoretical physicist, and a philosopher of science.David J. Stump is Professor of Philosophy at the University of San Francisco, USA.Melanie Frappier is Associate Professor of Humanities at the University of King's College, Canada.Andrea Smith has a Ph.D. in Romance Languages from UCLA, USA.Trade ReviewFrappier et al. have done an excellent job of bringing back—so to speak—Poincaré’s masterpiece of philosophical and scientific thought. * Metascience *I heartily applaud David Stump, Melanie Frappier and Andrea Smith for this splendid new edition of Poincaré's Science and Hypothesis. By bringing language and terminology up-to-date and providing new insights they have ensured that the book can once again reach the wide audience originally reached by Poincaré. At the same time, they give us a fascinating glimpse into the state of philosophy on the eve of the 20th-century revolutions in mathematical and scientific thought. -- John Stillwell, Professor of Mathematics, University of San Francisco, USAPoincaré’s essays on science and mathematics retain their importance after over a century because he stood back from the day-to-day tasks to reflect on what it is to do research, the kinds of questions that can be asked, and the kind of answers one might get. This new translation displays the lucidity of his thought, and David Stump’s Foreword brings out the depths that lie beneath Poincaré’s urbane style. There is new material here, too, and altogether this book is a fresh presentation of Poincaré as an intellectual companion for the twenty-first century. -- Jeremy Gray, Emeritus Professor, The Open University, UKThis updated and corrected translation of Science and Hypothesis is an essential addition to both personal and institutional libraries. Scholars who prefer to read Poincaré in English, as well as general readers of philosophy of science, will appreciate this version, which was produced by a team of three translators/editors. In addition to corrections, the volume includes an additional chapter 14: a paper written in 1906 and added to French editions of 1917, but not included in any prior English translations. Happy reading! -- Janet Folina, Professor of Philosophy, Macalester College, USAThis book is a must-read in the foundations of mathematics and physics. For the beginner, the accurate translation of Poincaré’s masterpiece is an excellent introduction to the subject, full of verve and good humor. For the expert, the brilliant foreword gives a lucid account of the major interpretations of Poincaré’s work. -- Gerhard Heinzmann, President of the International Academy of Philosophy of Science (AIPS), Bruxelles, Université de Lorraine/CNRS, FranceThis is the edition of Poincaré’s Science and Hypothesis English-speaking scholars will henceforth want to use in their teaching and research. The translators have made it more readable without sacrificing accuracy, and their helpful notes, references, and explanations reflect the most recent scholarship on this important philosopher and mathematician. -- Warren Schmaus, Professor of Philosophy, Illinois Institute of Technology, USAIt was certainly about time a new translation of Poincaré’s great classic came out. The translators have done a thorough job comparing first and subsequent editions and updating the language. This volume is to become the definitive English edition of Science and Hypothesis. -- María de Paz, Department of Philosophy, Universidad de Sevilla, SpainPoincare’s Science and Hypothesis offers one of the deepest and yet most accessible investigations into the nature of science, constituting one of the most significant works in philosophy of science of the 20th century. This excellent new translation and introduction to Poincare’s philosophy offers an invaluable resource for anyone interested in the scientific method and the nature of scientific knowledge. -- Milena Ivanova, University of Cambridge, UKTable of Contents1. Introduction by David J. Stump Origin of the parts of the book Author’s Preface Part I: Number and Magnitude 2. On the Nature of Mathematical Reasoning 3. Mathematical Magnitude and Experiment Part II: Space 4. Non-Euclidean Geometries 5. Space and Geometry 6. Experiment and Geometry Part III: Force 7. Classical Mechanics 8. Relative and Absolute Motion 9. Energy and Thermo-Dynamics Part IV: Nature 10. Hypotheses in Physics 11. The Theories of Modern Physics 12. The Calculus of Probabilities 13. Optics and Electricity 14. XIII Electro-Dynamics 15. The End of Matter Index

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Book SynopsisSofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in becoming arguably the first woman to have a professional university career in the way we understand it today.Trade ReviewFrom the book reviews:“For those who have already read one or two of the numerous biographies, Audin’s portrayal can serve as a valuable addition and a stimulus to rethink opinions already formed. Moreover, for scholars conducting research on Kovalevskaya, the multifaceted potpourri presented in this book will raise a lot of interesting questions and perspectives from which to approach their subject in a different way.” (Eva Kaufholz-Soldat, Historia Mathematica, Vol. 40 (4), 2013)“The book under review is devoted to Sofia Kovalevskaya. She was the first woman with a university professional activity. This book gives a particular vision of her. … The book provides a picture of Sofia Kovalevskaya that stresses the unity of different aspects of her personality. It has been published in a very nice way, it contains a lot of illustrations and photos. It will be an interesting source of information about Kovalevskaya, even more interesting because it contains the author’s personal view of her.” (Roman Murawski, Zentralblatt MATH, Vol. 1234, 2012)Table of ContentsSofya’s chronology.- Sofya’s names.- Stories.- The thesis of Sofya, the Cauchy–Kovalevskaya theorem.- The Solid.- A letter to Mittag-Leffler.- Stockholm.- A letter to Vollmar.- The Bordin prize and Sofya’s reputation.- The women of Men of mathematics.- I remember Sofya, by George, Gösta, Julia and all the rest.- I too remember Sofya.- Bibliography.

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Trade ReviewThis is a reader-friendly, broad collection of original works on the philosophy of mathematics, ranging from Pythagoras to other contemporary authors. The subjects are organized chronologically, rather than thematically. Each chapter starts with a valuable introductory overview; this puts the original works of the chapter into context, suggests aspects of information to explore, and offers recommendations for further reading. Part 1 (“Ancients”—Pythagoras, Plato and Aristotle) and part 2 (“Moderns”—Descartes, Leibniz, Locke, Kant, etc.) are primarily meant for undergraduate and beginning graduate students. The later parts of the work will be of interest to advanced graduate students and researchers. These include part 3 (“Nineteenth and Early Twentieth Centuries”) and part 4 (“Contemporary Views”), which comprise more than two-thirds of the volume. Particularly refreshing is the fact that the book explores classic authors like Cantor and Gödel. However, the book also surveys the contemporary school of “experimental mathematics” and the ideas of its proponents—Doron Zeilberger (Rutgers Univ.) and Jonathan Borwein (The Univ. of Newcastle, Australia). This branch of mathematics did not exist as recently as 25 years ago. As a result, it is a milestone for experimental mathematics to be discussed in this volume. * CHOICE *[This book] brings together an impressive collection of primary sources from ancient and modern philosophy of mathematics ... It is aimed primarily at undergraduates and early graduate students, however it can serve as an invaluable sourcebook for working researchers as well. * Zentralblatt MATH *This rich historical collection is an invaluable resource. The greats are represented from Pythagorus to Putnam. Classic issues and even current ones, such as fictionalism and naturalism, are included. Plato famously insisted that no one gets into his academy who is ignorant of geometry. Today we should insist that no one gets out of the academy who is ignorant of the philosophy of mathematics. This book will greatly help in that regard. -- James Robert Brown, Professor of Philosophy, University of Toronto, Canada and author of 'Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures'A highly-accessible introduction to the philosophy of mathematics. This well-curated reader includes engaging introductory essays for each chapter that will help students tackle some challenging material. It is a welcome addition to the pedagogical literature. -- Lisa Warenski * Dr. Lisa Warenski, The City College of New York, USA *This is a unique anthology of texts in the philosophy of mathematics, thematically grouped, with informative introductory overviews. * Mathematical Reviews *Table of ContentsHow to use this book Introduction: Terminology and Axioms Part I: Ancients and Medievals Introductory overview I.1. Pythagoreans I.2. Parmenides and Zeno’s Paradoxes I.3. Plato I.4. Aristotle Part II: Moderns Introductory overview II.1. The Rationalists II.2. The Empiricists II.3. Kant Part III: 19th and Early 20th Centuries Introductory overview III.1. Mill III.2. Cantor III.3. Logicism III.4. Formalism III.5. Intuitionism III.6. Conventionalism III.7. Wittgenstein III.8. Gödel’s Theorem III.9. Gödel’s Platonism Part IV: Contemporary Views Introductory overview IV.1. The Problem IV.2. The Indispensability Argument IV.3. Benacerraf’s Number Puzzle and Structuralism IV.4. Modalism IV.5. Fictionalism. IV.6. Apriorism IV.7. Naturalism. IV.8. Plenitudinous Platonism V.9. Challenges to Mathematical Apriorism Bibliography Index

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Book SynopsisSimon B. Duffy is a Senior Lecturer in Philosophy at Yale-NUS College, Singapore, and Honorary Research Associate in the Department of Philosophy at the University of Sydney, Australia. He is the author of The Logic of Expression: Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze (2006).Table of ContentsAcknowledgements \ List of Abbreviations \ Introduction \ 1. Leibniz and the Concept of the Infinitesimal \ 2. Maimon’s Critique of Kant’s Approach to Mathematics \ 3. Bergson and Riemann on Qualitative Multiplicity \ 4. Lautman’s Concept of the Mathematical Real \ 5. Badiou and Contemporary Mathematics \ Conclusion \ Notes \ Bibliography \ Index

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Book SynopsisMathematics often gets a bad press. Describing someone as ''calculating'' or ''rational'' is hardly as flattering as being labelled ''artistic'' or ''creative'' and mathematicians in movies or novels are often portrayed as social misfits who rarely get the guy or girl. No wonder some folks say ''oh I don''t care for mathematics, I was never any good at it'' with a wistful sense of pride.Yet professional mathematicians talk of the subject differently. They look for elegant solutions to problems, revel in playing around with mathematical ideas and talk of the creative nature of mathematics. As the Russian mathematician Sophia Kovalevskaya said It is impossible to be a mathematician without being a poet in soul.By looking at some of the history of mathematics, psychological studies into how we come to know mathematics and key ideas in mathematics itself, this book will, if not make you fall in love with mathematics, then at least come to understand its nature a l

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Book SynopsisBasic Mathematics is aimed primarily at management students preparing to write the GMAT test which requires a strong foundation in fundamentals of mathematics.Table of ContentsChapter 1: Basic arithmetic; Chapter 2: Fundamental algebra; Chapter 4: Basic statistics; Appendix A: Pre-revision test; Appendix B: Post-revision test; Appendix C: Solutions to exercises; Appendix D: Solutions to pre-revision test; Appendix E: Solutions

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Book SynopsisTest Prep Books'' GED Math Study Guide 2023-2024: 3 Practice Exams and GED Test Prep Book [6th Edition]Taking the GED Math test? Want to get a good score?Written by Test Prep Books, this comprehensive study guide includes: Quick Overview Test-Taking Strategies Introduction Math Reference Sheet Mathematical Reasoning Practice Questions Detailed Answer Explanations Disclaimer: GED is a registered trademark of the American Council on Education (ACE) and administered exclusively by GED Testing Service LLC under license. This material is not endorsed or approved by ACE or GED Testing Service.Studying is hard. We know. We want to help. You can ace your test.Each part of the test has a full review. This study guide covers everything likely to be on the test.Lots of GED Math practice test questions are included. Miss one and want to know why? There are detailed answer explanations to help you avoid missing the same question a second time.Are you a bad test taker?Use your time wisely with the latest test-taking strategies. Don''t settle for just learning what is on the test. Learn how to be successful with that knowledge.Test Prep Books has drilled down the top test-taking tips. This will help you save time and avoid making common mistakes on test day.Get your GED Math study guide. It includes review material, practice test questions, and test-taking strategies.It has everything you need for success.

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Book SynopsisA Mathematician''s Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.?A Mathematician''s Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.

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Book SynopsisChapter 1. Autobiography (Penelope Maddy).- Part 1: Philosophy of set theory and mathematics.- Chapter 2. Generically invariant set-theory (John Steel).- Chapter 3. Response to John Steel (Penelope Maddy).- Chapter 4. Intrinsic and extrinsic evidence in set theory (Donald A. Martin).- Chapter 5. Response to Tony Martin (Penelope Maddy).- Chapter 6. Maddy on classes (Øystein Linnebo).- Chapter 7. Response to Øystein Linnebo (Penelope Maddy).- Chapter 8. A general framework for a second philosophy analysis of set-theoretic methodology (Carolin Antos and Deborah Kant).- Chapter 9. Response to Carolin Antos & Deborah Kant (Penelope Maddy).- Chapter 10. Maddy's notion of Maximize' and strong theories of sets (Jeffrey Schatz).- Chapter 11. Exploring the generous arena (John T. Baldwin).- Chapter 12. Response to John Baldwin (Penelope Maddy).- Part 2: Realism, anti-realism and thin realism.- Chapter 13. Second philosophy and realism (Patricia Blanchette).- Chapter 14. Response to Patricia Blanchette (Penelope Maddy).- Chapter 15. Meditations on second philosophy: Anti-nominalist reflections on Maddy's semi-nominalism (John P. Burgess).- Chapter 16. Response to John P. Burgess (Penelope Maddy).- Chapter 17. Enhanced If-thenism, fictionalism, and realist anti-platonism (Mary Leng).- Chapter 18. Response to Mary Leng (Penelope Maddy).- Chapter 19. Logical realism A tale of two theories (Gila Sher).- Chapter 20. Response to Gila Sher (Penelope Maddy).- Chapter 21. Trumping naturalism revisited (A. C. Paseau).- Chapter 22. Response to Alex Paseau (Penelope Maddy).- Part 3: History of philosophy.- Chapter 23. What do philosophers do? Maddy, Moore (and Wittgenstein) II (Annalisa Coliva).- Chapter 24. Response to Annalisa Coliva (Penelope Maddy).- Chapter 25. A carnapian solution to the puzzle of extrinsic justifications (Zeynep Soysal).- Chapter 26. Response to Zeynep Soysal (Penelope Maddy).- Chapter 27. Wittgenstein's wayward student: The unauthorized autobiography (Curtis Franks).- Chapter 28. Response to Curtis Franks (Penelope Maddy).- Part 4: Mathematical practice.- Chapter 29. Realizing infinity (Maryanthe Malliaris and Assaf Peretz).- Chapter 30. Second philosophy and the depth metaphor (Juliette Kennedy).- Chapter 31. Response to Juliette Kennedy (Penelope Maddy).- Chapter 32. The flight from application (Mark Wilson).- Chapter 33. Response to Mark Wilson (Penelope Maddy).- Part 5: Conversations on Set Theory.- Chapter 34. A conversation between Penelope Maddy and Menachem Magidor (Jeffrey Schatz).- Chapter 35. Interview with David Asperó (Corey Switzer).- Chapter 36. A conversation with Hugh Woodin (Juliette Kennedy and Beau Madison Mount).- Chapter 37. On multiversism (Penelope Maddy).

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Book Synopsis1. Introduction (Mattia Petrolo and Giorgio Venturi).- Part I. Methodological Considerations. 2. Paradoxes: between revision and accommodation (Jonas R. Becker Arenhart and Ederson Safra Melo).- 3. Reference Fixing and the Paradoxes (Mario Gómez-Torrente).- 4. Transcending the Theory of Types (Simone Picenni and Thomas Schindler).- Part II. Semantic Approaches to Paradoxes. 5. Paradoxes, Contradictions and Circularity (Eduardo Barrio, Bruno Da Ré and Miguel Álvarez Lisboa).- 6. Impossible Truths: a non-dialetheist paraconsistent approach to paradoxes (Guilherme Cardoso).- 7. Paradoxes, Hypodoxes, and More (Camila Gallovich and Lucas Rosenblatt).- Part III. Syntactic Approaches to Paradoxes. 8. Substructural Solutions to the Semantic Paradoxes: a Dialetheic Perspective (Graham Priest).- 9. A substructural solution to the Lottery and Preface Paradoxes (Pilar Terrés Villalonga).- Part IV. Paradoxes of Epistemology and Vagueness. 10. Tolerance and degrees of truth (Pablo Cobreros, Paul Égré, David Ripley, Robert van Rooij).- 11. Self-Referential Gettier Sentences (Volker Halbach and Leon Horsten).- 12. Solovay's Theorem and The Unexpected Examination (Graham Leach-Krouse).- 13. Verdict Exclusion, Higher-Order Vagueness, Cross-Order Vagueness and Borderlineness: Reflections on Footnote 41 of CrispinWright's On Being in a Quandary' (Elia Zardini).

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Book Synopsis1 Introduction.- 2 Methodological shortcoming in the philosophy of arithmetic.- 3. A methodological alternative.- 4 Quantical cognition.- 5 Numerical cognition.- 6 The historical origins of number concepts.- 7 The reification of number concepts.- 8 Back to the philosophy of arithmetic.- 9 Concluding remarks.- Glossary.

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Book Synopsis1 Introduction.- Part I: The Indispensability of Mathematics.- 2 The enhanced indispensability argument.- 3 Objections.- 4 Circularity and interpretability.- 5 Conclusion of Part I.- 6 Counterfactual explanation and mathematics.- 7 A number-theoretic counterpossible.- 8 De Re knowledge of numbers.- 9 Conclusion of Part II.- 10 Epilogue.- Bibliography.

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Book SynopsisDie Mathematik im mittelalterlichen Islam hatte großen Einfluss auf die allgemeine Entwicklung des Faches. Der Autor beschreibt diese Periode der Geschichte der Mathematik und bezieht sich dabei auf die arabischsprachigen Quellen. Zu den behandelten Themen gehören Dezimalrechnen, Geometrie, ebene und sphärische Trigonometrie, Algebra sowie die Approximation von Wurzeln von Gleichungen. Das Buch wendet sich an Mathematikhistoriker und -studenten, aber auch an alle Interessierten mit Mathematikkenntnissen der weiterführenden Schule.Trade ReviewAus den Rezensionen:“... hat neuere Entwicklungen der Forschung aufgenommen und bekannte Fehler der englischsprachigen Version beseitigt. Der Verlag hat – der Zeit und den modernen Druckmedien angemessen – nun farbige Abbildungen zugelassen und das tut dem Erscheinungsbild des Buches natürlich sehr gut. ... Die Einbeziehung von Beschreibungen dieser historisch-kulturellen Entwicklungen macht einen der Reize dieses Buches aus. Ein weiterer großer Pluspunkt ist die Konzentration auf die Quellen. ... ist hervorragend lesbar ... die Übersetzerin Petra Schmidl in Zussamenarbeit mit Heinz Klaus Strick hervorragend gearbeitet haben ...“ (in: Mathematische Semesterberichte, September/2011)Aus den Rezensionen zur englischen Ausgabe "Episodes in the Mathematics of Medieval Islam":"This is a most scholarly book. The presentation is in the style of a textbook; each of the six chapters being followed by a set of exercises and a bibliography. … There is a good table of contents and a comprehensive index. … This is an excellent book full of information and thought-provoking ideas. It is worthy of careful study which will lead to a greater understanding of what the Islamic world has contributed to mathematics." (D.Stander, The Mathematical Gazette, Vol. 89 (515), 2005)"Written in 1986 and inspired by Asger Aaboe’s classic Episodes in the Early History of Mathematics, this book contains a wealth of classroom-ready examples of much of the mathematics one finds in high school and early college … . Springer has taken the right step by issuing a paperback edition to get the book into the hands of a more general readership. … The re-issue of this gem is significant and welcomed. It will enrich your classes and deepen your perspective on mathematics and culture." (Glen van Brummelen, The MAA Mathematical Sciences Digital Library, January, 2004)

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Book SynopsisTable of ContentsInhaltsübersicht: Abhandlungen zur Zahlentheorie und Algebra.- Abhandlungen zur Funktionentheorie.- Abhandlungen zur Mengenlehre.- Abhandlungen zur Geschichte der Mathematik und zur Philosophie des Unendlichen.- Anhang: Aus dem Briefwechsel zwischen Cantor und Dedekind.- Das Leben Georg Cantors.- Bibliographie weiterer Arbeiten von Georg Cantor.

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Book SynopsisKindheit und erste Schuljahre.- Jugendzeit und Abitur.- Erstes Semester in Jena.- Drei weitere Semester in Jena.- Studium in Göttingen, Dissertation und Habilitation.- Begriffsschrift.- Selbstbehauptung in Jena.- Der Streit um die Zahlen. Die Hochzeit.- Die ersten Ehejahre. Die Grundgesetze der Arithmetik-Teil 1.- Philosophische Auseinandersetzungen und Briefwechsel. Cantors Mengenlehre und erste Antino-mien.- Die Grundgesetze der Arithmetik-Teil 2. Russells Hinweis und seine Folgen.- Vormundschaft und Abschied von Jena. Ruhestand in Bad Kleinen.- Kriegsfolgen und letzte Gedanken.- Freges Logik und die Informatik.- Die moderne Frege-Tradition.- Nachrufe.- Quellenangaben.- Personenverzeichnis.

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Book SynopsisThis elementary introduction was developed from lectures by the authors on business mathematics and the lecture "Analysis and Linear Algebra" for Bachelor's degree programmesTable of Contents1. elementary basics.- 2. functions.- 3. differential calculus.- 4. integral calculus.- 5. linear algebra.- 6. functions with several variables.- 7. financial mathematics.

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