Sorites paradox and vague geographies

The sorites paradox is ranked among the top five paradoxes of philosophy (Sainsbury, Paradoxes, 2nd ed., Cambridge University Press, Cambridge, 1995). It is simply stated as 'what is a heap'. Deriving from the paradox is a definition of vagueness, which is contrary to the Boolean concept of the world implicit in much geographical teaching and thought, and the representation of geographical information in modem geographical information system. The argument of Sorites Paradox is suggested as a test of whether a concept is vague. If that concept is sorites susceptible, then it should be modelled as a vague concept, otherwise a Boolean model may be appropriate. The recognition of whether or not a particular concept is sorites susceptible does not have to influence the methods of analysis. It should merely inform the interpretation, and the investigator and reader should be aware that the outcome of the analysis is only one of a set of possible outcomes, which depends on how the vague concept is crispened. Furthermore, it is argued here that very many geographical phenomena (relations, objects and processes) can be shown to be sorites susceptible, and so vague, both generically and genetically. Vagueness can be addressed by multi-valued logic and applications of fuzzy set theory (the most common method of implementing multi-valued logic) to geography are reviewed. A formal recognition of vagueness in geographical phenomena is long overdue, and should be welcome in geographical analysis and, certainly, in geographical information systems. (C) 2000 Elsevier Science B.V. All rights reserved.