  In the modern predicate calculus, the symbols ‘\(\forall\)’ (‘every’) and ‘\(\exists\)’ (‘some’) are called the ‘universal’ and ‘existential’ quantifier, respectively, and the variable ‘\(x\)’ in the sentence ‘\(\forall xMx\)’ is called a ‘quantified variable’, or ‘variable bound by the quantifier’. We will follow this practice of calling statements involving one of these quantifier phrases ‘quantified statements’. As one can see from the table above, Frege didn’t use an existential quantifier. He was aware that a statement of the form ‘\(\exists x\phi \)’ could always be defined as ‘\(\neg \forall x \neg \phi\)’, where \(\phi\) is any formula.