Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism

Published by De Gruyter 2008

Philosophy of Mathematics

Set Theory, Measuring Theories, and Nominalism

Edited by: Gerhard Preyer and Georg Peter

Volume 13 in the series Logos

https://doi.org/10.1515/9783110323689

Overview
Contents

About this book

One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	v
Preface Requires Authentication Unlicensed Licensed Download PDF	7
Part I: Set Theory, Inconsistency, and Measuring Theories
Representationalism and Set-Theoretic Paradox Douglas Patterson Requires Authentication Unlicensed Licensed Download PDF	11
Who’s Afraid of Inconsistent Mathematics? Mark Colyvan Requires Authentication Unlicensed Licensed Download PDF	28
Logical and Semantic Puritiy Andrew Arana Requires Authentication Unlicensed Licensed Download PDF	40
On Using Measuring Numbers according to Measuring Theories Wilhelm K. Essler Requires Authentication Unlicensed Licensed Download PDF	53
Part II The Challenge of Nominalism
The Compulsion to Believe: Logical Inference and Normativity Jody Azzouni Requires Authentication Unlicensed Licensed Download PDF	73
Nominalism and Mathematical Intuition Otávio Bueno Requires Authentication Unlicensed Licensed Download PDF	93
Jobless Objects: Mathematical Posits in Crisis Yvonne Raley Requires Authentication Unlicensed Licensed Download PDF	112
Is Indispensability Still a Problem for Fictionalism? Susan Vineberg Requires Authentication Unlicensed Licensed Download PDF	132
Part III: Historical Background
Mill, Frege and the Unity of Mathematics Madeline Muntersbjorn Requires Authentication Unlicensed Licensed Download PDF	147
Descartes on Mathematical Essences Raffaella De Rosa and Otávio Bueno Requires Authentication Unlicensed Licensed Download PDF	164
Editors and Contributors Requires Authentication Unlicensed Licensed Download PDF	183

(Deutsch)

Language: English
Publisher: De Gruyter
Pages
- Main content: 184
Keywords: Philosophie; Philosophie der Mathematik; mathematische Logik

eBook

Published: May 2, 2013
ISBN: 9783110323689

Hardcover

Published: August 20, 2008
ISBN: 9783110323092