The syllogism idea appeals to me also. But I don't believe that is what people mean, because often, I can complete a syllogism in the abstract (at least believe that I have) and still leave people wondering.
Sometimes, I just give another example that adds nothing to the syllogism (in terms of proof of existence) and that is all that was needed.
Sometimes, I can complete a syllogism and give example after example, and nothing satisfies.
I don't often use that phrase, and can't remember the last time I used it, to see what would have satisfied me.
Perhaps a more pointed questions is:
"When is a thought finished for you?"