What different relativist claims about a given domain are to be distinguished? Which of them is best placed to account for intuitive facts about disagreement in that domain? In a recent paper in this journal, ‘Indexical Relativism versus Genuine Relativism’ (2004), Max Kölbel distinguishes two forms of relativism, andargues that one of them, indexical relativism, faces problems in accounting for disagreement. In the first part of this discussion I present my own taxonomy of relativist positions in a given domain, which (...) is based on David Lewis’s 1980 essay, and I compare it with Kölbel’s and other recent suggestions. In the second part, I argue that the presuppositional defence of indexical relativism against related objections that I have elaborated elsewhere is also effective against Kölbel’s recent charges. (shrink)