Universality in Set Theories. A Study in Formal Ontology

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 t...

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Autore principale: Bremer, Manuel
Natura: Online
Lingua:inglese
Pubblicazione: De Gruyter 2021
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Accesso online:18078
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author Bremer, Manuel
author_browse Bremer, Manuel
author_facet Bremer, Manuel
author_sort Bremer, Manuel
collection Directory of Open Access Books
description 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?
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spelling doab-20.500.12854ir-616232024-04-05T17:30:20Z Universality in Set Theories. A Study in Formal Ontology Bremer, Manuel B1-5802 thema EDItEUR::Q Philosophy and Religion::QD Philosophy 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? 2021-02-12T07:01:50Z 2021-02-12T07:01:50Z 2016-01-15 13:16:19 2010 book 18078 2198-2074 9783110326109 https://directory.doabooks.org/handle/20.500.12854/61623 eng Philosophische Analyse / Philosophical Analysis image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://doi.org/10.1515/9783110326109 De Gruyter 10.1515/9783110326109 10.1515/9783110326109 af2fbfcc-ee87-43d8-a035-afb9d7eef6a5 9783110326109 125 open access
spellingShingle B1-5802
thema EDItEUR::Q Philosophy and Religion::QD Philosophy
Bremer, Manuel
Universality in Set Theories. A Study in Formal Ontology
title Universality in Set Theories. A Study in Formal Ontology
title_full Universality in Set Theories. A Study in Formal Ontology
title_fullStr Universality in Set Theories. A Study in Formal Ontology
title_full_unstemmed Universality in Set Theories. A Study in Formal Ontology
title_short Universality in Set Theories. A Study in Formal Ontology
title_sort universality in set theories a study in formal ontology
topic B1-5802
thema EDItEUR::Q Philosophy and Religion::QD Philosophy
topic_facet B1-5802
thema EDItEUR::Q Philosophy and Religion::QD Philosophy
url 18078
work_keys_str_mv AT bremermanuel universalityinsettheoriesastudyinformalontology