The Linguistic Theory of Numerals

Merrifield, William R.; Hurford, James R.

doi:10.2307/413066

Cited by 39 publications

(10 citation statements)

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“…We use the grammar proposed by Hurford (1975, 2007) for natural language numerals generation to generate numerals of artificial languages. Hurford (1975, 2007) in his seminal work proposes that number‐denoting morphemes across languages are of the syntactic category Digits (

D

) or Multipliers (

M

).…”

Section: Methodsmentioning

confidence: 99%

“…As, to our knowledge, the extent to which division can be used productively in numeral systems is not well understood (cf. Hurford, 1975Hurford, , 2007, we assume for simplicity that division is not available, and exclude Danish from the corpus of natural languages. 5 We postulate covert morphemes only when this is necessary to account for the semantics of numerals; for instance, to account that the meaning of the Fulfulde numeral jowe go'o (6) is computed from the meaning of jowe (5) and go'o (1) (cf.…”

Section: Notesmentioning

confidence: 99%

“…Table 2), we need to assume that these are combined by an addition operator, which is introduced by a covert morpheme. 6 Hurford (1975) further assumes that the generation of syntactic structures by (4) may for certain numerals-for example, English -teen numerals-be followed by a linearization operation "switch" which inverses the linear order of two sister nodes. As this linearization operation does not affect the number of morphemes in a numeral, we will disregard it for the purpose of our analysis.…”

Section: Notesmentioning

confidence: 99%

“…One language in WALS corpus, Ainu, has numerals which cannot be derived by this grammar. Hurford (1975) is aware of this and discusses the case of Ainu at length; he considers different extensions of the grammar in (4) to accommodate Ainu but provides arguments against each of them, thus leaving the problem of Ainu unresolved. Because we will rely on the grammar in (4) to generate artificial languages and to estimate the Pareto frontier (cf.…”

Section: Notesmentioning

confidence: 99%

“…Morphosyntactically complex numerals for numbers 1-99 across languages reveal that addition, multiplication, and subtraction are productively involved in their construction 4 (cf. Hurford, 1975Hurford, , 2007. Both number-denoting morphemes and morphemes denoting arithmetic operators can in principle be phonetically overt or covert: in practice, number-denoting morhemes are very rarely covert, while morphemes denoting arithmetic operators often are.…”

mentioning

confidence: 99%

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Recursive Numeral Systems Optimize the Trade‐off Between Lexicon Size and Average Morphosyntactic Complexity

Denić,

Szymanik

2024

Cognitive Science

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Human languages vary in terms of which meanings they lexicalize, but this variation is constrained. It has been argued that languages are under two competing pressures: the pressure to be simple (e.g., to have a small lexicon) and to allow for informative (i.e., precise) communication, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures. However, in certain semantic domains, languages can reach very high levels of informativeness even if they lexicalize very few meanings in that domain. This is due to productive morphosyntax and compositional semantics, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey very many natural number meanings using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages need to solve a different kind of trade‐off problem: the trade‐off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances). To support this claim, we will present a case study of 128 natural languages' numeral systems, and show computationally that they achieve a near‐optimal trade‐off between lexicon size and average morphosyntactic complexity of numerals. This study in conjunction with previous work on communicative efficiency suggests that languages' lexicons are shaped by a trade‐off between not two but three pressures: be simple, be informative, and minimize average morphosyntactic complexity of utterances.

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