© 2016

Objectivity, Realism, and Proof

FilMat Studies in the Philosophy of Mathematics

  • Francesca Boccuni
  • Andrea Sereni

Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 318)

Table of contents

  1. Front Matter
    Pages i-xl
  2. The Ways of Mathematical Objectivity: Semantics and Knowledge

  3. Realism in a World of Sets: from Classes to the Hyperuniverse

    1. Front Matter
      Pages 101-101
    2. Brice Halimi
      Pages 123-142
    3. Gianluigi Oliveri
      Pages 143-164
    4. Sy-David Friedman, Claudio Ternullo
      Pages 165-188
    5. Giorgio Venturi
      Pages 211-241
  4. The Logic Behind Mathematics: Proof, Truth, and Formal Analysis

    1. Front Matter
      Pages 243-243
    2. Mario Piazza, Gabriele Pulcini
      Pages 245-263
    3. Massimiliano Carrara, Matteo Plebani, Enrico Martino
      Pages 311-318

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


Formal Analysis Formal Theories Foundations of Mathematics Informal Notions Ontology in Mathematics Philosophy of Mathematics and Logic

Editors and affiliations

  • Francesca Boccuni
    • 1
  • Andrea Sereni
    • 2
  1. 1.San Raffaele UniversityMilanItaly
  2. 2.Institute of Advanced StudiesPaviaItaly

About the editors

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).

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 Abbreviated Title Boston Stud. Philosophy
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Religion and Philosophy Philosophy and Religion (R0)
  • Hardcover ISBN 978-3-319-31642-0
  • Softcover ISBN 978-3-319-81085-0
  • eBook ISBN 978-3-319-31644-4
  • Series ISSN 0068-0346
  • Series E-ISSN 2214-7942
  • Edition Number 1
  • Number of Pages XL, 344
  • Number of Illustrations 22 b/w illustrations, 0 illustrations in colour
  • Topics Philosophy of Science
    Mathematical Logic and Foundations
  • Buy this book on publisher's site