Full Idea
Since one wants to say that real numbers exist and yet one cannot name each of them, it is not unreasonable to relinquish the connection between naming an object and making an existence claim about it.
Gist of Idea
If we had to name objects to make existence claims, we couldn't discuss all the real numbers
Source
Willard Quine (works [1961]), quoted by Alex Orenstein - W.V. Quine Ch.2
Book Reference
Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.27
A Reaction
One could say that same about people, such as 'the most recent citizen of Brazil'. Some sort of successful reference seems to be needed, such as 'the next prime beyond the biggest so far found'. Depends what your predicate is going to be.