Granular partitions and vagueness

  • Authors:

  • Thomas Bittner;Barry Smith

  • Affiliations:

  • Northwestern University;State University of New York at Buffalo

  • Venue:
  • Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
  • Year:
  • 2001

  • A Taxonomy of Granular Partitions

    COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science

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Abstract

There are some who defend a view of vagueness according to whichthere are intrinsically vague objects or attributes in reality.Here, in contrast, we defend a view of vagueness as a semanticproperty of names and predicates. All entities are crisp, on thisview, but there are, for each vague name, multiple portions ofreality that are equally good candidates for being its referent,and, for each vague predicate, multiple classes of objects that areequally good candidates for being its extension. We provide a newformulation of these ideas in terms of a theory of granularpartitions. We show that this theory provides a generalframework within which we can understand the relation between vagueterms and concepts on the one hand and correlated portions ofreality on the other. We also sketch how it might be possible toformulate within this framework a theory of vagueness whichdispenses with the notion of truth-value gaps and other artifactsof more familiar approaches.