By Ferdinand von Mengden
The booklet embeds an research of the previous English numeral process and its particularities right into a broader, cross-linguistic dialogue and offers a theoretical framework for the overall examine of numeral structures. a unique viewpoint at the morphosyntactic behaviour of numerals permits the writer to check and refine a few lengthy status tenets within the learn of numerals.
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Additional info for Cardinal Numerals: Old English from a Cross-linguistic Perspective
3. Let us for the moment accept that variants such as ten and -teen and -ty all represent the same entities of the systems. 9 The Chinese expression lìhng is often mentioned in this context as an exception to this universal. e. as ‘(1 × 100) + 0 + 7’. It is not used, however, to express bases or their multiples, as in ‘10’ or ‘100’; cf. MATTHEWS/YIP (1994: 385). These are all represented by simple expressions. Therefore, Chinese does not deviate in this respect from what can be observed cross-linguistically.
WIESE acknowledges this restriction by saying that natural numbers must only be potentially infinite (2003: 58, n. 5 and 77). With this modification, the property ‘infinity’ (or rather: potential infinity) does apply to any kind of system used in number assignment. This aspect is, however, not ultimately relevant in our context. On the contrary: it is impossible for linguistic numeral systems to achieve infinity simply because no language can possibly have an infinite set of expressions or infinitely complex numeral formations.
A set of five apples shares one common property with a set of five books, namely the property of containing five elements. This particular type of property of a set – the number of elements contained in a set – is called its ‘cardinality’. Now, if we compare two sets of the same cardinality, it may perhaps suffice to say that a given set A (say, a set of five apples) has the same number of elements as a certain set B (say, a set of five books). However, if we would like to refer to this property, for instance when buying apples or books in a shop, we need to specify or label these properties, or, to put it more simply, we need to give a name to each cardinality.
Cardinal Numerals: Old English from a Cross-linguistic Perspective by Ferdinand von Mengden