Significant advances have been made in artificial systems by using biological systems as a guide. However, there is often little interaction between computational models for emergent communication and biological models of the emergence of language. Many researchers in language origins and emergent communication take compositionality as their primary target for explaining how simple communication systems can become more like natural language. However, there is reason to think that compositionality is the wrong target on the biological side, and so too the wrong target on the machine-learning side. As such, the purpose of this paper is to explore this claim. This has theoretical implications for language origins research more generally, but the focus here will be the implications for research on emergent communication in computer science and machine learning---specifically regarding the types of programmes that might be expected to work and those which will not. I further suggest an alternative approach for future research which focuses on reflexivity, rather than compositionality, as a target for explaining how simple communication systems may become more like natural language. I end by providing some reference to the language origins literature that may be of some use to researchers in machine learning.