Properties of lower numerals and their explanation: A reply to Paweł Rutkowski (original) (raw)

A Minimalist Account of Numerals

Dilbilim Araştırmaları, 2022

Numerals participate in the expression of a wide range of operations, including mass, volume, degree, ordering, counting, and arithmetic calculations. This raises the questions of what they denote semantically and how they are derived morpho-syntactically. Although a number of theories have been advanced regarding their semantics, studies on the syntactic side are rather scarce. Further, the syntactic accounts of numerals date back to GB period, calling for a reinterpretation of their conclusions under Minimalist considerations. This study attempts to develop a syntactic account of numerals under Minimalist desiderata. It is proposed that numerals are number-denoting type n objects, derived from two primitives: saturated DIGITs of type n, and unsaturated BASEs of type <n,n>, instrumental in the derivation of simplex and complex numerals, respectively. This view is demonstrated to account for a wide range of distributional and interpretive possibilities of numerals as well as provide principled reasons for why some plausible forms are consistently unattested across languages.

Licensing Polish Higher Numerals: an Account of the Accusative Hypothesis

This paper addresses the issue of the Accusative Hypothesis, which is a descriptive fact about Polish numeral expressions with higher numerals according to which they are intrinsically accusative. The hypothesis has been a debatable issue for almost the past two centuries, and remains so till today. I will argue in its favour and attempt to provide an answer as to the source of the accusative case borne by the numerals.

Cross-linguistic representations of numerals and number marking

Semantics and Linguistic Theory, 2015

Inspired by Partee (2010), this paper defends a broad thesis that all modifiers, including numeral modifiers, are restrictive in the sense that they can only restrict the denotation of the NP or VP they modify. However, the paper concentrates more narrowly on numeral modification, demonstrating that the evidence that motivated Ionin & Matushansky (2006) to assign non-restrictive, privative interpretations to numerals – assigning them functions that map singular sets to sets containing groups – is in fact consistent with restrictive modification. Ionin & Matushansky (2006)’s argument for this type of interpretation is partly based on the distribution of Turkish numerals which exclusively combine with singular bare nouns. Section 2 demonstrates that Turkish singular bare nouns are not semantically singular, but rather are unspecified for number. Western Armenian has similar characteristics. Building on some of the observations in section 2, section 3 demonstrates that restrictive modi...

Comparative Analysis of the Numeral Systems of Ígálà, Yoruba, German and English

This study undertakes a comparative analysis of the numeral systems of Igala, Yoruba, English and German. An essential part of data collation for the study comprises compilation of comparative wordlists of Ígálà, Yoruba, German and English numeral systems in addition to the writer's personal observation and knowledge of the systems. The investigation reveals that the complexity of deriving especially non-basic numerals in the languages involves three predominant arithmetic processes of addition, subtraction (Yoruba in particular) and multiplication in addition to certain grammatical processes, especially vowel elision, clipping, compounding and so on. In addition, the summary of the quasi constraints or derivational patterns for the languages reveals that whereas German and English maintain very similar patterns because of their very close affinity as sisters from the same parent, it is not so with Ígálà and Yoruba even though both belong to the same language family. Incorporating insights from optimality theory, the paper argues that even though numeracy and the constraints that ensure well-formedness of numerals are somewhat universal, parametric variations abound. The actual patterning of the sequences of the derivational processes in individual languages may be very similar but definitely not the same, no matter how closely related the languages concerned may be. If not, they would cease to represent core grammars of different languages.