Scope

Scope is a notion used by logicians and linguists in describing artificial and natural languages. It is best introduced in terms of the languages of formal logic. Consider a particular occurrence of an operator in a sentence – say, that of ‘→’ in (1) below, or that of the universal quantifier ‘∀’ in (2) below.

Speaking intuitively, the scope of the operator is that part of the sentence which it governs. The scope of ‘→’ in (1) is the whole sentence; this renders the whole sentence a conditional. The scope of ‘&’, on the other hand, is just ‘(B & C)’. In (2), the scope of the quantifier ‘∀’ is the whole sentence, which allows it to bind every occurrence of x. The scope of ‘∃’ is only ‘∃yAxy’. Since ‘Bxy’ is outside its scope, the ‘y’ in ‘Bxy’ is left unbound.