TITLE: Existence and uniqueness of God
QUESTION [7 upvotes]: Over lunch, my math professor teasingly gave this argument

God by definition is perfect. Non-existence would be an imperfection, therefore God exists. Non-uniqueness would be an imperfection, therefore God is unique.

I have thought about it, please critique from mathematical/logical point of view on

Why does/doesn't this argument fall through? Does it violate any logical deduction rules?  
Can this statement be altered in a way that it belongs to ZF + something? What about any axiomatic system?  
Is it positive to make mathematically precise the notion of "perfect"?

REPLY [2 votes]: Let's define the following:

'Derp' is defined as something that is perfect whereas perfect is defined as something that is unique, exists, is green and has 3 horns

Clearly a derp exists, there's only 1 derp and it's green with 3 horns.
We can define things that logically will always be true but that doesn't make it in reality a universal truth. A less silly example is the following:

'Set' is a well defined collection of objects

Non-existence of a set would imply that we can't find a well defined collection of objects (whatever that means), so a set exists. However in reality I've never held a 'set'. I've never watched a 'set'.
In other words I can define anything I want but this does not really translate into anything useful (as in the derp example) or anything that's presented in reality (the derp or set example)
I am prepared to be downvoted, I only ask if/when you do can you leave a comment as to why? Thanks!