Infinite generation of language unreachable from a stepwise approach

Abstract

Language is commonly thought of as a culturally evolved system of communication rather than a computational system for generating linguistic objects that express thought. Furthermore, language is commonly argued to have gradually evolved from finite proto-language which eventually developed into infinite language of modern humans. Both ideas are typically integrated in accounts that attempt to explain gradual evolution of more complex language from the increasingly strong pressures of communicative needs. Recently some arguments have been presented that the probability of the emergence of infinitely productive languages is increased by communicative pressures. These arguments fail. The question whether decidable languages evolve into infinite language is vacuous since infinite generation is the null hypothesis for a generative procedure. The argument that increasing cardinality leads to infinite language is incoherent since it essentially conflates concepts of performance with notions of competence. Recursive characterization of infinite language is perfectly consistent with finite output. Further, the discussion completely ignores a basic insight that language is not about decidability of weakly generated strings but rather about properties of strongly generated structures. Finally, the plausibility proof that infinite productivity evolves from finite language is false because it confuses (infinite) cardinal numbers with (natural) ordinal numbers. Infinite generation cannot be reached with a stepwise approach.