Proof and Other Dilemmas

Mathematics and Philosophy

AvBonnie Gold,Roger A. Simons

Inbunden, Engelska, 2008

Del i serien Spectrum

754 kr

Slutsåld

Beskrivning

During the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.

Produktinformation

Utgivningsdatum:2008-12-30
Mått:152 x 229 x undefined mm
Vikt:825 g
Format:Inbunden
Språk:Engelska
Serie:Spectrum
Antal sidor:346
Förlag:Mathematical Association of America
ISBN:9780883855676

Utforska kategorier

Matematikens filosofi inom Naturvetenskap och teknik

Mer om författaren

Bonnie Gold is a Professor in the Mathematics Department at Monmouth University, New Jersey. Roger Simons is a Professor in the Department of Mathematics and Computer Science at Rhode Island College.

Innehållsförteckning

Acknowledgments; Introduction; Part I. Proof and How it is Changing: 1. Proof: its nature and significance Michael Detlefsen; 2. Implications of experimental mathematics for the philosophy of mathematics Jonathan Borwein; 3. On the roles of proof in mathematics Joseph Auslander; Part II. Social Constructivist Views of Mathematics: 4. When is a problem solved? Philip J. Davis; 5. Mathematical practice as a scientific problem Reuben Hersh; 6. Mathematical domains: social constructs? Julian Cole; Part III. The Nature of Mathematical Objects and Mathematical Knowledge: 7. The existence of mathematical objects Charles Chihara; 8. Mathematical objects Stewart Shapiro; 9. Mathematical Platonism Mark Balaguer; 10. The nature of mathematical objects Øystein Linnebo; 11. When is one thing equal to some other thing? Barry Mazur; Part IV. The Nature of Mathematics and its Applications: 12. Extreme science: mathematics as the science of relations as such R. S. D. Thomas; 13. What is mathematics? A pedagogical answer to a philosophical question Guershon Harel; 14. What will count as mathematics in 2100? Keith Devlin; 15. Mathematics applied: the case of addition Mark Steiner; 16. Probability - a philosophical overview Alan Hájek; Glossary of common philosophical terms; About the editors.