Preyer / Peter Philosophy of Mathematics

Set Theory, Measuring Theories, and Nominalism
1. Auflage 2013
ISBN: 978-3-11-032368-9
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 184 Seiten

Reihe: ISSN

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.

Autoren/Hrsg.

Preyer, Gerhard

Peter, Georg

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

1;Contents;5
2;Preface;7
3;Part I: Set Theory, Inconsistency, and Measuring Theories;9
3.1;Representationalism and Set-Theoretic Paradox;11
3.2;Who’s Afraid of Inconsistent Mathematics?;28
3.3;Logical and Semantic Puritiy;40
3.4;On Using Measuring Numbers according to Measuring Theories;53
4;Part II The Challenge of Nominalism;71
4.1;The Compulsion to Believe: Logical Inference and Normativity;73
4.2;Nominalism and Mathematical Intuition;93
4.3;Jobless Objects: Mathematical Posits in Crisis;112
4.4;Is Indispensability Still a Problem for Fictionalism?;132
5;Part III: Historical Background;145
5.1;Mill, Frege and the Unity of Mathematics;147
5.2;Descartes on Mathematical Essences;164
6;Editors and Contributors;183