ontos verlag - Verlag für Philosophie und Mathematik

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?

About the Author

Manuel Bremer is professor of philosophy at the University of Düsseldorf (Germany). His areas of specialization are philosophical logic and the philosophy of language. His publications with Ontos include Philosophische Semantik and Information and Information Flow.

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Review published by "Notre Dame Philosophical Review"

ISBN: 978-3-86838-071-2 125 pp Hardcover €69.00

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