# logic – Is the universal quantifier redundant?

Whenever we use the string

$$(forall x)P(x)$$

We are using a meta variable, in this case $$x$$, which stands for any object in the reference set.

However, the semantics of the symbol $$forall$$ indicate that we are refering to all objects that satisfy certain condition $$P(x)$$.

So, the semantics of “for all the objects over which the metavariable varies, $$P(x)$$” but we know, a priori, that the meta variable already refers to all the objects in the reference set.

This looks redundant to me.

So, is the universal quantifier redundant?