ENGLISH

Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics

By Ernest Davis , Philip J. Davis (eds.)

Book information

Publisher
Springer
Year
2015
ISBN
3319214721, 978-3-319-21472-6, 978-3-319-21473-3
Language
english
Format
PDF
Filesize
4 MB (4270932 bytes)
Edition
1st ed.
Pages
379\374
Library
kolxoz
Time added
2017-10-15 16:00:00
Mathematics -- Philosophy;Mathematics;Mathematics

Description

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume: Jeremy Avigad Jody Azzouni David H. Bailey David Berlinski Jonathan M. Borwein Ernest Davis Philip J. Davis Donald Gillies Jeremy Gray Jesper Lützen Ursula Martin Kay O’Halloran Alison Pease Steven Piantadosi Lance Rips Micah T. Ross Nathalie Sinclair John Stillwell Hellen Verran Front Matter....Pages i-vi Introduction....Pages 1-7 Hardy, Littlewood and polymath ....Pages 9-23 Experimental computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics....Pages 25-67 Mathematical products....Pages 69-74 How should robots think about space?....Pages 75-99 Mathematics and its applications....Pages 101-131 Nominalism, the nonexistence of mathematical objects....Pages 133-145 An Aristotelian approach to mathematical ontology....Pages 147-176 Let G be a group....Pages 177-192 From the continuum to large cardinals....Pages 193-211 Mathematics at infinity....Pages 213-234 Mathematics and language....Pages 235-255 The linguistic status of mathematics....Pages 257-285 Mathematics as multimodal semiosis....Pages 287-303 Problems in philosophy of mathematics: A view from cognitive science....Pages 305-320 Beliefs about the nature of numbers....Pages 321-345 What kind of thing might number become?....Pages 347-363 Enumerated entities in public policy and governance....Pages 365-379

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