Erkki Luuk

The redundancy of recursion and infinity for natural language

An influential line of thought claims that natural language and arithmetic processing require recursion, a putative hallmark of human cognitive processing (Chomsky in Evolution of human language: biolinguistic perspectives. Cambridge University Press, Cambridge, pp 45–61, 2010; Fitch et al. in Cognition 97(2):179–210, 2005; Hauser et al. in Science 298(5598):1569–1579, 2002). First, we question the need for recursion in human cognitive processing by arguing that a generally simpler and less resource demanding process—iteration—is sufficient to account for human natural language and arithmetic performance. We argue that the only motivation for recursion, the infinity in natural language and arithmetic competence, is equally approachable by iteration and recursion. Second, we submit that the infinity in natural language and arithmetic competence reduces to imagining infinite embedding or concatenation, which is completely independent from the ability to implement infinite processing, and thus, independent from both recursion and iteration. Furthermore, we claim that a property of natural language is physically uncountable finity and not discrete infinity.

The evolution of syntax: Signs, concatenation and embedding

The paper argues that the structure, derivation and evolution of syntax is given by the sequence (elements, concatenation, embedding). We discuss the implications of this sequence for language and the numeral system in general and on the evolution of language in particular. A four-stage model of the evolution of syntax, broadly compatible with several earlier scenarios, is proposed. The four stages are (1) signs, (2) increased number of signs, (3) commutative concatenation, and (4) noncommutative concatenation. We support the model by showing that its stages can be adaptive per se, which could explain why they evolved. We also identify two preconditions for maintaining the stages: stage (2) depends on the ability to conceptualize asymmetric relations between concepts and the adaptiveness of stage (3) depends on cultural constraints on linguistic interpretation.

The emergence of compound signals

The paper argues that the structure, derivation and evolution of syntax is given by the sequence (elements, concatenation, embedding). A four-stage model of the evolution of syntax is proposed. The four stages are (1) signs, (2) increased number of signs, (3) commutative concatenation, and (4) noncommutative concatenation. We support the model by showing that its stages can be adaptive per se, which could explain why they evolved. We also identify two preconditions for maintaining the stages: stage (2) depends on the ability to conceptualize asymmetric relations between concepts and the adaptiveness of stage (3) depends on cultural constraints on linguistic interpretation.