# Quantifier (in predicate logic)

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In predicate logic, the logical constant indicating whether a statement is universal or particular is calles quantifier. The universal quantifier All indicates that all entities in the universe have a given property while the existential quantifier ThereIs indicates that at least one entity has the property:

```(i)  a  All(x) [ P(x) ]
"Every x has property P"
b  ThereIs(y) [ Q(y) ]
"At least one y has property Q"
```

The term quantifier can either be used for the symbols All and ThereIs themselves or for the combination with the variable they bind: All(x) and ThereIs(y). A more complex use of quantifiers is shown in (ii):

```(ii) All(x) [ P(x) -> ThereIs(y) [ Q(y) & R(x,y) ]
```

which might be the translation of a sentence like Every teenage girl adores a rock star.

### References

• Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.