Abstract: This chapter introduces the satisfaction relation, which relates an open sentence to objects associated with its argument places, to deal with quantifiers. The truth of closed sentences is then defined in terms of the notion of satisfaction. Recursive satisfaction clauses are introduced for classical unrestricted quantifiers (‘everything’ and ‘something’). It is argued that restricted quantifiers (such as ‘Most philosophers’ and ‘Some politicians’) should not be analyzed in terms of unrestricted quantifiers, and then recursive satisfaction clauses are introduced for restricted quantifiers.

Keywords: restricted quantifiers, satisfaction relation, open sentence, closed sentence,