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Universality in Set Theories: A Study in Formal Ontology by Manuel Bremer

Universality in Set Theories: A Study in Formal Ontology

by Manuel Bremer
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Book cover type: Hardcover
  • ISBN13: 9783110325263
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: de Gruyter
  • Publisher Imprint: de Gruyter
  • Publication Date:
  • Pages: 125
  • Original Price: GBP 92.0
  • Language: English
  • Edition: N/A
  • Item Weight: 404 grams
  • BISAC Subject(s): Minority Studies

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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