This article argues that the thesis of composition as identity (CAI) is incoherent because its proponents assume the existence of composite objects (i.e., objects with proper parts) to propose the thesis to cast light on their nature. To do so, the article proves that CAI is logically equivalent to the (part-whole) triviality thesis, the thesis that everything is a part of itself but of nothing else. In proving this, the article distinguishes three formulations of CAI resulting from different analyses of the composition relation, and proves that all three formulations of the thesis are logically equivalent to the triviality thesis. It also argues that CAI is logically equivalent to the triviality thesis on any adequate analysis of composition.