Granular partitions and vagueness

ABSTRACT

There are some who defend a view of vagueness according to which there are intrinsically vague objects or attributes in reality. Here, in contrast, we defend a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts on the one hand and correlated portions of reality on the other. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches.

REFERENCES

• 1: Thomas Bittner, On Ontology and Epistemology of Rough Location, Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science, p.433-448, August 25-29, 1999
• 2: Thomas Bittner , Barry Smith, A Taxonomy of Granular Partitions, Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science, p.28-43, September 19-23, 2001
• 3: Fine, K., Vagueness, Truth and Logic, Synthese, 30 (1975), pp. 265-300.
• 4: Fisher, P., Boolean and Fuzzy Regions, in P. Burrough and A. U. Frank, eds., Geographic Objects with Indeterminate Boundaries, 1996.
• 5: Fraassen, B. C. v., Singular Terms, Truth-Value Gaps, and Free Logic, Journal of Philosophy, 63 (1966), pp. 481-495.
• 6: Hyde, D., Sorites Paradox, Stanford Encyclopedia of Philosophy, 1996.
• 7: Moffitt, F. H. and Bouchard, H., Surveying, Harper and Row Publishers, New York, 1987.
• 8: Smith, B., On Drawing Lines on a Map, in A. U. Frank and W. Kuhn, ed., Conference on Spatial Information Theory, COSIT Semmering, Austria, 1995.
• 9: Smith, B., Fiat Objects, Topoi, 20 (2001).
• 10: Smith, B. and Brogaard, B., A Unified Theory of Truth and Reference, Logique et Analyse, 200 1.
• 11: Tye, M., Vague Objects, Mind (1990).
• 12: Varzi, A., Vagueness in Geography, Philosophy and Geography, 4 (2001), pp. 49-65.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.4 Knowledge Representation Formalisms and Methods

Additional Classification:
  F. Theory of Computation
  F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
      F.4.0 General

  I. Computing Methodologies
  I.m MISCELLANEOUS

General Terms:
Human Factors, Theory

Keywords:
granular partitions, ontology, semantics, vagueness