Your objection to the notion of positive and negative properties is the first that stood out to me after reading the Wikipedia summary. If I'm understanding things correctly, Godel's proof seems committed to some objective notion of goodness--I'm not sure how such a thing could exist without some higher power, which makes the proof somewhat circular in my mind.

I could be missing something here as I only took my first philosophy class this semester and I'm not taking ethics until next, but is that basically what you're getting at?