Science and Semantics: A Note on Rough Sets and Vagueness

Abstract

In the chapter we present rough set theory against the background of recent philosophical discussions about vagueness and empirical sciences. Weiner, in her article about this topic, discusses the supervaluationist semantics of vague predicates and its criticism offered by Fodor and Lepore. She argues that neither the former nor latter approach is consistent with the scientific methodology of dealing with vague concepts such as “obese”. In actual fact, it is Frege’s philosophical approach that concepts must have sharp boundaries, which is the closest to scientific practice. In this context, rough set theory can be viewed as a modified supervaluationist semantics. To be more precise, rough sets provide a modal version of this semantics, where the super-truth is replaced by a local one. However, there are flies in the ointment: firstly, rough set theory is philosophically weaker than supervaluationism (in consequence, more vulnerable to the criticism of Fodor and Lepore); secondly, Weiner’s arguments concerning scientific methods apply to rough sets as well. Yet there is also good news: this philosophical weakness stays actually in full accordance with scientific practice. Thus, rough set theory may be seen as a supervaluationism shifted toward the scientific methodology. In the chapter we shall make a further step into this direction and also present how rough set theory would be like when made fully consistent with the scientific approach to vague predicates. In other words, we also offer a Fregean rough set methodology.