In this article, we evaluate the Compositionality Argument for structured propositions. This argument hinges on two seemingly innocuous and widely accepted premises: the Principle of Semantic Compositionality and Propositionalism (the thesis that sentential semantic values are propositions). We show that the Compositionality Argument presupposes that compositionality involves a form of building, and that this metaphysically robust account of compositionality is subject to counter-example: there are compositional representational systems that this principle cannot accommodate. If this is correct, one of the most important arguments for structured propositions is undermined.