On recursion

Abstract

It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However, the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauseretal's. (2002) articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language—the faculty of language in the narrow sense (FLN)—is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded—existent or non-existent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension); definition by induction (i.e., rules strongly generative of structure); and mathematical induction (i.e., rules for the principled—and potentially unbounded—expansion of strongly generated structure). By these necessary and sufficient criteria, the grammars of all natural languages are recursive.

Gramática E Lógica

“…Entre eles, em janeiro é publicado, numa plataforma eletrônica destinada à apresentação do resultado de pesquisas e debate dessas apresentações chamada Frontiers in Psychology, um texto chamado "On recursion", escrito por Jeffrey Watumull, Marc Hauser, Ian Roberts e Norbert Hornstein (Watumull et al, 2014). Em abril, David Lobina publica um texto chamado "Probing Recursion" no periódico Cognitive Processing (Lobina, 2014a) e, em maio, dois outros textos: um chamado "What linguists are talking about when talking about..." (Lobina, 2014b), no periódico Language Sciences, e outro chamado "When linguists talk mathematica llogic" (Lobina, 2014c), na plataforma Frontiers in Psychology.…”

“…Vou começar pela crítica que Lobina (2014c) faz da noção de recursividade proposta em (Watumull et al, 2014) Gödel apenas diz que dada uma lista de funções, qualquer uma delas será dita recursiva se (i) for definida por indução de outras funções anteriores, OU (ii) for substituída por alguma delas, OU (iii) for a função constante, OU (iv) for a função sucessor. Em outras palavras, Watumull et al entendem como ligada por conjunção a lista disjuntiva de propriedades apresentada por Gödel.…”

Leaving the myth behind: A reply to

“…Ever since, an acrimonious debate has raged about who misunderstands what recursion is (e.g. Nevins et al, 2009a,b;Everett, 2009;Evans and Levinson, 2009;Levinson, 2013;Legate et al, 2014;Watumull et al, 2014). Unfortunately, the by now voluminous literature about recursion has contributed little to a better understanding of the core issues.…”

It is an organ, it is new, but it is not a new organ. Conceptualizing language from a homological perspective

“…On the other hand, a quick look at the vocalizations of monkeys and apes indicates that, while there may be some hints of semantics in them, this does not come together with the ability to combine them into complex vocalizations to produce new expressions. This evidence is customarily interpreted in the sense that what both birds and primates are lacking is a CS implementing a basic combinatory computational operation (typically referred to as merge) that is supposed to account for the full power of human language syntax and that makes it a unique character in the natural world (Berwick et al, 2012(Berwick et al, , 2013Bolhuis et al, 2014;Watumull et al, 2014).…”