Abstract
A simple inductive argument shows natural languages to have infinitly many sentences, but workers in the field have uncovered clear evidence of a diverse group of ‘exceptional’ languages from Proto-Uralic to Dyirbal and most recently, Pirahã, that appear to lack recursive devices entirely. We argue that in an information-theoretic setting non-recursive natural languages appear neither exceptional nor functionally inferior to the recursive majority.
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Notes
According to some, “in human language communications, the probability of an utterance varies from situation to situation, moment to moment: if an elephant appears on the university campus, this affects the probability of ‘elephant’-utterances, threatening the empirical basis of (3)” This view rests on a confusion between the probability value and the method of sampling: clearly average human height is not at all affected by the fact whether we use the basketball team or the kindergarten as our sample, it’s just that neither sample is very representative.
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Acknowledgments
We thank Geoff Pullum, Christina Behme, and the anonymous referees for detailed comments on earlier versions. Work supported by OTKA Grants #82333 and 77476 and by the European Union and the European Social Fund through project FuturICT.hu (Grant Number TAMOP-4.2.2.C-11/1/KONV-2012-0013).
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For Marcus Kracht on his 50th birthday.
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Kornai, A. Resolving the Infinitude Controversy. J of Log Lang and Inf 23, 481–492 (2014). https://doi.org/10.1007/s10849-014-9203-2
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DOI: https://doi.org/10.1007/s10849-014-9203-2