| The distinction here can be seen as a distinction of scope for the existential quantifier. |
| The claim, of course, was that referential uses of a description are a function of pragmatics, not quantifier scope. |
| These axiom schemata are also used in the predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus. |
| A different approach would be to take the existential quantifier as a substitutional quantifier where the substitution class consists of sentences. |
| Of course, more complex formulas than these can easily be constructed, using more than one quantifier and symbols for negation, conjunction, disjunction, and so forth. |
| In each case, the proposition expressed is argued to be that which would be expressed if the indefinite determiner were replaced by the existential quantifier. |
