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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| Natura: | Online |
| Lingua: | inglese |
| Pubblicazione: |
De Gruyter
2021
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| Soggetti: | |
| Accesso online: | 18078 |
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| _version_ | 1869524831751372800 |
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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? |
| format | Online |
| id | doab-20.500.12854ir-61623 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | De Gruyter |
| publisherStr | De Gruyter |
| record_format | ojs |
| 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 |