The redundancy of recursion and infinity for natural language and arithmetic processing
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1
University of Düsseldorf, Germany
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2
University of Tartu, Estonia
An influential line of thought claims that natural language and arithmetic processing require recursion, a putative hallmark of human cognitive processing (Chomsky, 2010; Fitch et al., 2005; Hauser et al., 2002). We have analyzed the plausibility of this claim (Luuk & Luuk, 2011), and conclude with the following points. First, both recursion and iteration allow for finite definitions of infinite sets. Moreover, iterative solutions are frequently less resource demanding than recursive ones. Second, contrary to Chomsky et al. (Chomsky, 1995; Hauser et al., 2002), we argue that a property of natural language is not discrete infinity but physically uncountable finity. Third, we reject the received opinion, articulated by Chomsky and colleagues, that neurally implemented recursion is necessary to explain natural language and arithmetic competence and performance. The only motivation for neurally implemented recursion is infinity in natural language and arithmetic competence (e.g. the knowledge that one can add 1 to n, append a natural language expression to text or embed clauses indefinitely). We claim that infinity in natural language and arithmetic competence reduces to imagining infinite embedding or concatenation, which is completely independent from an algorithmic capacity for infinite processing, and hence, completely independent from neurally implemented recursion or iteration. As the only purported motivators for recursion in human cognitive processing are natural language and arithmetic, the need for recursion in human cognitive processing is effectively downplayed. In sum, we submit that there is no infinity in natural language and arithmetic processing, but even if there were, iteration would be sufficient for generating it.
Keywords:
Arithmetic processing,
Language
Conference:
XI International Conference on Cognitive Neuroscience (ICON XI), Palma, Mallorca, Spain, 25 Sep - 29 Sep, 2011.
Presentation Type:
Poster Presentation
Topic:
Poster Sessions: Neural Bases of Language
Citation:
Luuk
E and
Luuk
H
(2011). The redundancy of recursion and infinity for natural language and arithmetic processing.
Conference Abstract:
XI International Conference on Cognitive Neuroscience (ICON XI).
doi: 10.3389/conf.fnhum.2011.207.00299
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Received:
22 Nov 2011;
Published Online:
28 Nov 2011.
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Correspondence:
Dr. Erkki Luuk, University of Düsseldorf, Düsseldorf, Germany, erkkil@gmail.com