Universality in Set Theories. A Study in Formal Ontology

• Tác giả: Manuel Bremer
• Ngôn ngữ: eng
• ISBN-13: 978-3110326109
• Ký hiệu phân loại: 111 Ontology
• Thông tin xuất bản: De Gruyter, 2010
• Mô tả vật lý: 1 electronic resource (125 p.)
• Bộ sưu tập: Tài liệu truy cập mở
• ID: 205350

Tóm tắt

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?