Abstract: This paper takes issue with the widely held view that semantic properties supervene on some class of non-semantic properties. The focus here is on singular thoughts and utterances of sentences involving proper names, such as ‘Socrates’, or demonstratives, such as ‘that’. First, it is argued that the popular thesis that names and demonstratives (and their mental analogues) are object-involving rigid designators entails haecceitism—that qualitatively indistinguishable possible worlds can differ in non-qualitative respects. Second, it is argued that if haecceitism is true, the semantic supervenience thesis is either false or trivial. The upshot is that if one accepts the view that names and demonstratives are object-involving rigid designators, semantic properties do not non-trivially supervene on any class of non-semantic properties.