Full Idea
If anyone does think of something a greater than which cannot be thought, then he thinks of something which cannot be thought of as nonexistent, ...for then it could be thought of as having a beginning and an end. And this is impossible.
Gist of Idea
Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end
Source
Anselm (Proslogion [1090], Reply 3)
Book Reference
'The Existence of God', ed/tr. Hick,John [Macmillan 1964], p.28
A Reaction
A nice idea, but it has a flip side. If the atheist denies God's existence, then it follows that (because no beginning is possible for such a being) the existence of God is impossible. Anselm adds that contingent existents have parts (unlike God).