Dual quantifier universal: If a natural language has a basic determiner for each of D and d then these are semantically equivalent to ‘some’ and ‘every’.
Standardized
Dual quantifier universal: IF there is a basic determiner for each of D and d, THEN these are semantically equivalent to ‘some’ and ‘every’.
1. Barwise & Cooper propose this rather for consideration than as a strict universal, discussing also the counterexample ‘the one’ and conclude: “U10 would predict that no human language would have basic determiners for each element of such pairs. The proposed universal also predicts that of the sentences below, only (i) and (ii) could be paraphrased as ‘D men left’ for some basic determiner D. i) It is not true that some man didn’t leave. (I.e. every man left.); ii) It is not true that every man didn’t leave. (I.e. some man left.); iii) It is not true that the most men didn’t leave. iv) It is not true that two men didn’t leave. v) Not many men didn’t leave.”2. Note also # 1210.
1. Barwise & Cooper propose this rather for consideration than as a strict universal, discussing also the counterexample ‘the one’ and conclude: “U10 would predict that no human language would have basic determiners for each element of such pairs. The proposed universal also predicts that of the sentences below, only (i) and (ii) could be paraphrased as ‘D men left’ for some basic determiner D. i) It is not true that some man didn’t leave. (I.e. every man left.); ii) It is not true that every man didn’t leave. (I.e. some man left.); iii) It is not true that the most men didn’t leave. iv) It is not true that two men didn’t leave. v) Not many men didn’t leave.”2. Note also # 1210.