UID:
almahu_9949473982702882
Umfang:
1 online resource (125 p.)
ISBN:
9783110326109
,
9783110636949
Serie:
Philosophische Analyse / Philosophical Analysis , 36
Inhalt:
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?
Anmerkung:
Frontmatter --
,
Content --
,
INTRODUCTION --
,
I. Iteration, Foundation, and Reflection --
,
II. Limitations of Size --
,
III. Virtual Sets and Constructivism --
,
IV. Consistent Set Theories with a Universal Set --
,
V. Paraconsistent Set Theories with a Universal Set --
,
VI Broader Ontological Reflections --
,
Abbreviations and Notation --
,
REFERENCES
,
Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DGBA Philosophy 2000 - 2014, De Gruyter, 9783110636949
In:
eBook Package De Gruyter Ontos 2002-2012, De Gruyter, 9783110331226
In:
eBook Paket De Gruyter Ontos 2002-2012, De Gruyter, 9783110331219
Weitere Ausg.:
ISBN 9783110325263
Sprache:
Englisch
Schlagwort(e):
Electronic books
DOI:
10.1515/9783110326109
URL:
Volltext
(kostenfrei)
URL:
Volltext
(Open Access)
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