Manuel Bremer

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?

Conceptual atomism claims that most concepts cannot be decomposed into features, so that the conjunction of the features is equivalent to the concept in question. Conceptual atomism of this type is incompatible with many other semantic approaches. One of these approaches is justificationist semantics. This book assumes conceptual atomism. Justificationist semantics in its pure form, therefore, has to be wrong. Nevertheless, its epistemological approach to questions of evaluations and semantic rules could still stand. The main question is how conceptual atomism can be combined with some justificationist ideas. This new synthesis centres on the representational theory of mind and ‘internalist’ semantics, but ties these to ideas which stress the epistemic commitments that accompany successful assertions.

This series provides a forum for cutting-edge studies in logic and the modern philosophy of language as well as for publications in the field of analytical metaphysics.

This book is conceived as an introductory text into the theory of syntactic and semantic information, and information flow. Syntactic information theory is concerned with the information contained in the very fact that some signal has a non-random structure. Semantic information theory is concerned with the meaning or information content of messages and the like. The theory of information flow is concerned with deriving some piece of information from another. The main part will take us to situation semantics as a foundation of modern approaches in information theory. We give a brief overview of the background theory and then explain the concepts of information, information architecture and information flow from that perspective.