This dissertation presents an objection to Wittgenstein's concept of family resemblances, three possible solutions to the objection, evaluations of the solutions, and a sketch of Wittgenstein's approach to the objection. My thesis is that none of the three proposed solutions is satisfactory, but that Wittgenstein can deal with the objection. ;Chapter I presents the Problem of the Under-Determination of Extension, the claim that family resemblances are not enough to explain the extension of a concept, since resemblances may be postulated between (...) cases falling under different concepts. ;Chapters II and III discuss three solutions proposed by commentators on family resemblances. The Basic Predicates Solution claims that points of family resemblance are sufficient conditions, and is incorrect since Wittgenstein denies that one can infer the applicability of a concept based on the presence of a resemblance to an instance of the concept. The Simple Properties Solution claims that only some concepts are family resemblance concepts, and depend upon concepts which are not family resemblance concepts, and is incorrect, since Wittgenstein does not require that family resemblance concepts be reducible to non-family resemblance concepts. The Bi-Directional Determination of Concepts Solution is the claim that a concept is determined by an interaction between facts about cases subsumed under it, and needs and purposes of language-users. This solution is non-Wittgensteinian by ignoring the ramifications of his concepts of grammar and language-games. ;Chapter IV argues that Wittgenstein deals with the original objection by developing new models for understanding language, involving the concepts of grammar and language-games. (shrink)