ABSTRACT
In Chapter 3 predicates were introduced, but these were assumed to take individuals as
their arguments (typically represented by proper names). In the previous chapter, in the
course of discussing quantifiers, we looked at predicates whose arguments involved what
are called ‘common nouns’ (such as ‘student’ or ‘cricketer’). These can also be predicates
(‘John is a student’)—but in these examples they showed up together with a quantifier (as
in ‘all students’), with another expression as the main predicate. They still denote a set
(this time the restriction set for the quantifier). This chapter is going to extend some of
these notions. First, it will look at ways of extending the predicate-argument notation so
that its arguments can include these quantified expressions as well as individuals. (In fact
we will look at two subtly different ways of doing this.)
Have another look at the Venn diagrams for the basic quantifiers all, some and none.
