Existence (n.) has its purpose fulfilled by the man who is happy, as Dostoevsky said.
Existence (n.) is for physics to say, not logic, and whether there are infinitely many things experience cannot decide.
Existence (n.) has, in mathematics, no concept independent of the concept of an existence proof.
Existence (n.) of books and armchairs is not a lesson children receive — they learn to fetch books and sit in armchairs, and a question about unicorns is possible only because as a rule no such question arises.
Existence (n.) in mathematics is simply defined when a proof is required to contain a construction; it is not like proving a man is in the room by looking.