Universal #1209

Legacy number: 1209

 Number  1205
 Original  Persistent determiner constraint:
Every persistent determiner of human language is monotone ¡ncreasing and weak.
 Standardized  Persistent determiner constraint:
Every persistent determiner of human language is monotone ¡ncreasing and weak.
 Keywords  quantification, monotonicity, persistence, determiner
 Domain  syntax, semantics
 Type  unconditional
 Status  achronic
 Quality  absolute
 Basis  unspecified
 Source  Barwise & Cooper 1981: 193, U8

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Discussion
Counterexamples
Notes
1. 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. 2. A determiner D is ‘persistent’ if for all M = <E,|| ||> and all A $ B $ E, if X % ||D|| (A) then X % ||D|| (B). On the other hand, D is anti-persistent if A $ B $ E and X $ ||D|| (B) implies X $ ||D|| (A).)English examples for persistent determiners are ‘some’, ‘at least n’, ‘infinitely many’, ‘uncountably many’ etc., for anti-persistent determiners ‘every’, ‘no’, ‘at most n’, ‘finitely many’ etc.
Comment
Frans Plank · 3 Aug 2006
1. 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>
</table>

2. A determiner D is 'PERSISTENT' if for all M = <E,|| ||> and all A $ B $ E, if X % ||D|| (A) then X % ||D|| (B). On the other hand, D is anti-persistent if A $ B $ E and X $ ||D|| (B) implies X $ ||D|| (A).)
English examples for persistent determiners are 'some', 'at least n', 'infinitely many', 'uncountably many' etc., for anti-persistent determiners 'every', 'no', 'at most n', 'finitely many' etc.