This paper examines Jaegwon Kim's Supervenience Argument (SA) against nonreductive physicalism, concentrating on Kim's response to two of the most important objections against the SA: First, the Overdetermination Argument, according to which Kim has no convincing argument against the possibility that mental causation might be a case of genuine or systematic overdetermination; second, the Generalization Argument, according to which the SA would entail that causation at any level gives way to causation at the next lower level, thereby leading to an (...) untenable all-encompassing epiphenomenalism. It is argued that as of yet, Kim has failed to develop a coherent overall position, since various moves he makes in response to these criticisms are strangely at odds with other parts of his philosophical position. (shrink)