Introducing the Subject-Predicate Formal Language: Can Names and Quantifiers Share the Same Logical Category?

Abstract

There is a well known discrepancy between the grammatical and the logical treatment of expressions such as something, everything, somebody, everybody, some pig, every pig. Grammarians traditionally consider such expressions together with names (singular name expressions) as belonging to the category of noun phrases. The reason for this is simple: both quantifier expressions and names can be used as subjects in sentences. Logicians, particularly those dealing with the classical logic (predicate calculus), treat quantifier expressions (in short: quantifiers) as operators, i.e. as expressions of a different category from the name category. The distinction seems clear: names are categorematic, whereas operators are syncategorematic.