Old and new approaches to the Sorites paradox

The Sorites paradox is the name of a class of paradoxes that arise when vague predicates are considered. Vague predicates lack sharp boundaries in extension and is therefore not clear exactly when such predicates apply. Several approaches to this class of paradoxes have been made since its first formulation by Eubulides of Miletus in the IV century BCE. In this paper I survey some of these approaches and point out some of the criticism that these approaches have received. A new approach that uses tools from nonstandard analysis to model the paradox is proposed.