ABSTRACT. In The Logical Basis of Metaphysics, Dummett argues at length that Geach has been wrong in taking the sense of a predicate to be a function that sends the sense of a proper name to that of a sentence, and claims that it should instead be a means to determine the referent of the predicate, as is suggested by Frege’s sense-determines-reference (SDR) principle. This disagreement between Dummett and Geach calls for a serious investigation into two of Frege’s sense-related principles, namely the Compositionality thesis and the SDR thesis. By making precise both theses in terms of supervenience, we pin down a preferable sense of compositionality for senses, and resolve the debate in question.