Universality in Set Theories: A Study in Formal Ontology

Manuel Bremer

Open Access Published by De Gruyter 2010

Universality in Set Theories

A Study in Formal Ontology

Manuel Bremer

Volume 36 in the series Philosophische Analyse / Philosophical Analysis

https://doi.org/10.1515/9783110326109

Overview
Contents

About this book

The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

Topics

Frontmatter Publicly Available Download PDF	i
Content Publicly Available Download PDF	5
INTRODUCTION Publicly Available Download PDF	7
I. Iteration, Foundation, and Reflection Publicly Available Download PDF	13
II. Limitations of Size Publicly Available Download PDF	31
III. Virtual Sets and Constructivism Publicly Available Download PDF	43
IV. Consistent Set Theories with a Universal Set Publicly Available Download PDF	49
V. Paraconsistent Set Theories with a Universal Set Publicly Available Download PDF	57
VI Broader Ontological Reflections Publicly Available Download PDF	97
Abbreviations and Notation Publicly Available Download PDF	119
REFERENCES Publicly Available Download PDF	120

(Deutsch)

Language: English
Publisher: De Gruyter
Pages
- Main content: 125
Keywords: Ontologie; Philosophie; Sprachphilosophie

eBook

Published: May 2, 2013
ISBN: 9783110326109

Hardcover

Published: February 22, 2010
ISBN: 9783110325263