We introduce the distinctive, self-referential, logic of self-reproduction originally formulated by John von Neumann and present some initial results from a novel implementation of this abstract architecture, embedded within the Avida world. These show that, with this particular implementation, in this particular world, the von Neumann architecture proves to be evolutionarily unstable and degenerates, surprisingly easily, to a primitive, non-self-referential, “copying” or “template replication”, mode of reproduction. We briefly discuss some implications, and sketch prospects for further investigation.