Merge Does Not Trigger a n + 1 Recursive Function: A Reply to Mendivil-Giró (2025)

Abstract

This article examines the claim that the recursive operation Merge underlies the generative structure of the natural number system. I argue that this claim rests on a conflation between recursion as a property of syntactic representation and recursion as a property of numerical computation. In syntax, repeated applications of Merge yield hierarchically structured expressions; in arithmetic, the successor function yields successive values. These are not the same kind of operation. Focusing on recent proposals by Mendívil-Giró (2025) and Watanabe (2017), I show that Merge, whether external or internal, does not by itself derive numerical succession, but only structured symbolic objects whose interpretation must be independently determined. I further argue that the principal assumptions needed to sustain a Merge-based theory of natural number (innate numerical generativity, hierarchical structure in the count list, and a primitive lexical item corresponding to 1) lack independent empirical support. I conclude that number generativity is better understood as an emergent property of compositional symbolic structure than as the direct output of a successor-like operation implemented by narrow syntax.