I remember making this argument :D Haha, I was quickly downvoted.
Anyhow, "vaguely specified goals" actually turns out to be a property of you, not the AI.
If an agent has formally definable goals, then of course they are precisely specified. Vagueness can only be a property of matching actual goals to higher level descriptions.
Related post: Muehlhauser-Wang Dialogue.
Motivation Management in AGI Systems, a paper to be published at AGI-12.
From the discussion section: