All or nothing: No half-Merge and the evolution of syntax

In their Essay on the evolution of human language, Martins and Boeckx seek to refute what they call the "half-Merge fallacy" - the conclusion that the most elementary computational operation for human language syntax, binary set formation, or "Merge," evolved in a single step. We show that their argument collapses. It is based on a serious misunderstanding of binary set formation as well as formal language theory. Furthermore, their specific evolutionary scenario counterproposal for a "two-step" evolution of Merge does not work. Although we agree with their Essay on several points, including that there must have been many steps in the evolution of human language and the importance of understanding how language and language syntax are implemented in the brain, we disagree that there is any justification, empirical or conceptual, for the decomposition of binary set formation into separate steps.