Amartya Sen has argued that poverty is a vague concept. This paper develops a methodology for applying a framework which uses a ‘supervaluationist’ account of vagueness in the context of poverty. Within this framework people or households are termed ‘core poor’ if there is no ambiguity about whether or not they are poor. The framework is applied using data from a survey on the ‘Essentials of Life’ conducted in three locations in South Africa in 2001. The methodology relates the data to the framework using an insight of Max Black’s. While the application of the methodology is, in its very nature, somewhat arbitrary, we illustrate how it can lead to an estimate of core poverty which differs from standard measures of the ‘ultra-poor’ and ‘most deprived’. Finally, the possibility that respondents may have adapted to their living conditions is investigated. A first look at the data does not provide conclusive evidence of such
adaptation.