Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Boston Studies in the Philosophy and History of Science (BSPS, volume 318)
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Table of contents (17 chapters)
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The Ways of Mathematical Objectivity: Semantics and Knowledge
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Realism in a World of Sets: from Classes to the Hyperuniverse
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The Logic Behind Mathematics: Proof, Truth, and Formal Analysis
Keywords
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
Editors and Affiliations
About the editors
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
DOI: https://doi.org/10.1007/978-3-319-31644-4
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-31642-0Published: 12 July 2016
Softcover ISBN: 978-3-319-81085-0Published: 30 May 2018
eBook ISBN: 978-3-319-31644-4Published: 05 July 2016
Series ISSN: 0068-0346
Series E-ISSN: 2214-7942
Edition Number: 1
Number of Pages: XL, 344
Number of Illustrations: 22 b/w illustrations
Topics: Philosophy of Science, Logic, Epistemology, Mathematical Logic and Foundations