Boston Studies in the Philosophy and History of Science

Objectivity, Realism, and Proof

FilMat Studies in the Philosophy of Mathematics

Editors: Boccuni, Francesca, Sereni, Andrea (Eds.)

  • Contains cutting-edge research from renowned philosophers and younger scholars
  • Shows the lively and multifarious character of the current debate
  • Presents new contributions in several areas of the philosophy of mathematics and logic
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eBook 83,29 €
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  • ISBN 978-3-319-31644-4
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  • Immediate eBook download after purchase
Hardcover 103,99 €
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  • ISBN 978-3-319-31642-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge.

The essays collected here  explore  the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe.  They consider fundamental philosophical notions such as set, cardinal number, truth, ground,  finiteness and infinity, examining  how their informal conceptions can best be captured in formal theories.

The philosophy of mathematics is an extremely lively  field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns.

Promoted by the Italian Network for the Philosophy of Mathematics – FilMat



About the authors

Andrea Sereni is Associate Professor in Epistemology and Philosophy of Mathematics at the Institute of Advanced Studies (IUSS) in Pavia. He was a Lecturer at Vita-Salute San Raffaele University, Milan, Italy, where he still teaches. He obtained his PhD at Bologna University and was a visiting scholar at the Arche Centre (St.Andrews, Scotland), MCMP Munich, and University of Oslo. His teaching, research and publications cover issues in the philosophy of mathematics, epistemology, and the philosophy of language. He is co-author, with M. Panza, of Plato’s Problem, An Introduction to Mathematical Platonism (Palgrave, 2013) and co-editor (with F. Pataut and D. Molinini) of Synthese special issue Indispensability and Explanation. He is member of COGITO, CRESA and NeTS research centres, and coordinator of the promoting committee of the Italian Network for the Philosophy of Mathematics (FilMat). Francesca Boccuni is a Lecturer in Logic and Philosophy of Logic and Science at Vita-Salute San Raffaele University, Milan, Italy. She was a visiting scholar at the University of Oxford, Institute Jean Nicod – CNRS (Paris), Ohio State University, University of Bristol, University of London, and University of Oslo. Her research interests and main publications (Studia Logica, Erkenntnis) concern the abstractionist programme in the philosophy of mathematics and Frege's Logicism, second-order logic and plural logic, and the issue of reference in mathematics. She is member of COGITO and CRESA research centres, and a member of the promoting committee of the Italian Network for the Philosophy of Mathematics (FilMat).

Table of contents (17 chapters)

  • Mathematics in Philosophy, Philosophy in Mathematics: Three Case Studies

    Shapiro, Stewart

    Pages 1-9

    Preview Buy Chapter 30,19 €
  • Semantic Nominalism: How I Learned to Stop Worrying and Love Universals

    Antonelli, G. Aldo

    Pages 13-32

    Preview Buy Chapter 30,19 €
  • Discussion Note On: “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals” by G. Aldo Antonelli

    May, Robert C. (et al.)

    Pages 33-41

    Preview Buy Chapter 30,19 €
  • Semantic Assumptions in the Philosophy of Mathematics

    Knowles, Robert

    Pages 43-65

    Preview Buy Chapter 30,19 €
  • The Modal Status of Contextually A Priori Arithmetical Truths

    Pantsar, Markus

    Pages 67-79

    Preview Buy Chapter 30,19 €

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-319-31644-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-31642-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Objectivity, Realism, and Proof
Book Subtitle
FilMat Studies in the Philosophy of Mathematics
Editors
  • Francesca Boccuni
  • Andrea Sereni
Series Title
Boston Studies in the Philosophy and History of Science
Series Volume
318
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-31644-4
DOI
10.1007/978-3-319-31644-4
Hardcover ISBN
978-3-319-31642-0
Series ISSN
0068-0346
Edition Number
1
Number of Pages
XL, 344
Number of Illustrations and Tables
22 b/w illustrations
Topics