Universal #1205

Legacy number: 1205

 Number  1201
 Original  Determiner universal:
Every natural language contains basic expressions (called determiners) whose semantic function is to assign to common count noun denotations (i.e., sets) A a quantifier that lives on A.
 Standardized  Determiner universal:
Every natural language contains basic expressions (called determiners) whose semantic function is to assign to common count noun denotations (i.e., sets) A a quantifier that lives on A.
 Keywords  quantification, determiner, quantifier, count noun
 Domain  syntax, semantics
 Type  unconditional
 Status  achronic
 Quality  absolute
 Basis  unspecified
 Source  Barwise & Cooper 1981: 179, U3

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Discussion
Counterexamples
All the following lack determiner quantification: Straits (Salish), Asurini (Tupi), Mohawk (Iroquoian), Lakhota (Siouan), Navajo (Athabaskan), Warlpiri (Pama-Nyungan), Gun-djeyhmi (Gunwingguan, Australian). Warlpiri and Gun-djeyhmi, for example, make use of verbal affixes to express various kinds of quantificational meaning. And Asurini quantifiers such as all, many, two do not form a syntactic constituent with the noun, because they do not belong to the category of determiners. They are instead members of other categories such as adverb, verb and noun. See discussion in Bach et al. (1995).
Notes
For technical reasons, the following logical relations are abbreviated as follows: A is a subset of E = A $ E ; X is a member of set Q = X % Q; the union of the sets X and A = X § A. In a model M = <E,|| ||>, a quantifier Q lives on a set A$E if Q is a set of subsets of E with the property that, for any X$E, X%Q iff (X § A)% Q.English examples which illustrate this notion are the following equivalences: Many men run <-> Many men are men who run; Few women sneeze <-> Few women are women who sneeze; John loves Mary <-> John is John and loves Mary.
Comment
Frans Plank · 3 Aug 2006
For technical reasons, the following logical relations are abbreviated as follows:
<table class = "texttable">
<tr>
<td> </td>
<td>A is a subset of E </td>
<td> =</td>
<td>A $ E ;</td>
</tr>
<tr>
<td> </td>
<td>X is a member of set Q </td>
<td> = </td>
<td>X % Q;</td>
</tr>
<tr>
<td> </td>
<td>the union of the sets X and A </td>
<td> =</td>
<td>X § A.</td>
</tr>
</table> In a model M = <E,|| ||>, a quantifier Q lives on a set A$E if Q is a set of subsets of E with the property that, for any X$E, X%Q iff (X § A)% Q.

English examples which illustrate this notion are the following equivalences:

<table class = "texttable">
<tr>
<td> </td>
<td>Many men run</td>
<td> ↔ </td>
<td>Many men are men who run; </td>
</tr>
<tr>
<td> </td>
<td>Few women sneeze</td>
<td> ↔ </td>
<td>Few women are women who sneeze;</td>
</tr>
<tr>
<td> </td>
<td>John loves Mary</td>
<td> ↔ </td>
<td>John is John and loves Mary. </td>
</tr>
</table>