In formal logic, what is the converse of 'all'?

*Note: because within predicate logic with quantifiers, the term "converse" is very ambiguous, I will assume, unless told otherwise by Trogdor, that what seems to be meant is "negation".

The negation of "$\forall n, P(n)$" is "$\exists n$ such that $\lnot P(n).$"

In other words, the negation of your statement is "There exist(s) $n$ such that it is not the case that $P(n)$ holds" or "The statement is not true for one or more values of n."