Some Remarks on Zawadowski’s Theory of Preordered Quantifiers

Abstract

According to Barwise and Cooper [1], the words ‘all’ and ‘some’ are only two of many quantifier words and phrases in natural language, including ‘one’, ‘most’, ‘at least seven’, ‘the’, ‘both’, etc. Quantifier words (determiners, specifiers; hereafter, just ‘quantifiers’) occur naturally in quantifier phrases in which the quantifier is combined with a restrictive description, as in ‘ all electrons’, ‘many intelligent logicians’, ‘most students of Polish’, etc. Barwise and Cooper provide a compositional formal semantics for these generalized quantifiers. As the extension of the quantifier phrase ‘most students of Polish’, in a model with domain D and in which S is the set of all students of Polish, they give the family F of all and only those subsets D* ⊆ D that could truly be said to contain most of the elements of S. The claim that most students of Polish are male would then be true in the model iff M ∈ F, where M is the set of males.