Existence and uniqueness of God

Question

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

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

Answer 1

Existence is not a predicate. You may want to read Gödel's onthological proof, which you can find on Wikipedia.

Equally good is the claim that uniqueness is imperfection, since something which is perfect cannot be scarce and unique. Therefore God is inconsistent..?

Answer 2

"Non-existence would be an imperfection, therefore God exists." What this statement actually says it that "If God exists, then he would be perfect, and therefore it isn't possible that he doesn't exist, since non-existence is an imperfection."

Well, if God exists, then it is pretty clear that He exists, and this proposed argument is not so useful. But if God doesn't exist, then the argument certainly doesn't prove that He does exist!

Answer 3

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!