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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"?
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The argument begs the assumption. It's a rather old trick, and what worries is that some really believe it holds some water. –  DonAntonio Jun 3 '13 at 0:10
This is St. Anselm's ontological argument from the 11th century. –  Zen Jun 3 '13 at 0:13
en.wikipedia.org/wiki/Ontological_argument Also I could really go for a perfect ham sandwich right now (which by the same argument also exists). –  Rahul Jun 3 '13 at 0:14
@Rahul: One can easily prove that the perfect sandwich is not edible (since being indestructible, for example by digestion system, is an imperfection). Therefore if it exists, the perfect sandwich cannot be eaten. Therefore it isn't so perfect after all... –  Asaf Karagila Jun 3 '13 at 0:18
@RahulNarain: Or perhaps, God contains all of its limit points, and every point is a limit point. :P –  Prism Jun 3 '13 at 0:21
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closed as not a real question by Andres Caicedo, Austin Mohr, Rahul, srijan, Amzoti Jun 3 '13 at 0:32


3 Answers

up vote 10 down vote accepted

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..?

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So you are implying that there is no way to make the notion "perfect" mathematically precise? –  mezhang Jun 3 '13 at 0:18
No, but any mathematical precision will depend on the interpretation of whoever wrote it/reads it. So in order to argue mathematically we have to suspend our definition of perfect and accept an alternative concept. So God is t perfect, but something else. The main point though is that existence is not a property. –  Asaf Karagila Jun 3 '13 at 0:21
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"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!

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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 to all hell, I only ask if/when you do can you leave a comment as to why? Thanks!

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