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This is a follow-up to Could Anselm's argument also "prove" that a perfectly evil god must exist?, and also to Why is existence not a true predicate with respect to Anselm's argument?, especially Einer's answer.

I will try to paraphrase Anselm's argument to make its problematic aspects better visible, and examine possible ambiguity and flaws in it. My actual question then will be if that line of reasoning is related to Kant's criticism of ontological arguments.

Anselm's original argument (mildly paraphrased)

  • I imagine the greatest thing I can imagine.

  • I can imagine it existing, or not-existing.

  • If it existed it would be greater than if it existed not.

  • So imagening it as not-existing means I'm not actually imagening the greatest thing, and is a contradiction.

  • So if I imagine the greatest thing, I also have to assume it exists.

Anselms's argument (heavily) paraphrased

  • I create a mental model of god (:= "the greatest thing"). Let's call it "ModelGod_One".

  • I can create a mental model of the universe (:= "all that exists"), and make "ModelGod_One" a part of that (:= existing). Let's call that model "UniversePlus".

  • I can also create a mental model of the universe, and leave "ModelGod_One" completely out of it (:= not existing). Let's call that model "UniverseMinus".

Assumption A: By being part of "UniversePlus", "ModelGod_One" becomes the mental model of something greater (in itself!). Let's call that "ModelGod_Two".

Conclusion A: Therefore we have a contradiction, as argued before. It becomes logically inconsistent to keep on using the model "ModelGod_One", we have from now on always to use "ModelGod_Two", which is a part of "UniversePlus".

Assumption B: If we assumed "UniversePlus" to be the correct description of reality, "ModelGod_One" would become the mental model of something greater. Let's call that "ModelGod_Three".

Conclusion B: Because of that, we HAVE to assume that the model "UniversePlus" is the correct description of reality, and it is logically inconsistent to keep on assuming "UniverseMinus" could be the correct description of reality.

Criticism

It seems to me that Anselm's argument is ambiguous whether he argues for "Conclusion A" or "Conclusion B". But both are unsatisfying as genuine proofs of god's existence.

"Conclusion A" says nothing about if the model with god should be considered more than pure speculation, and if it might claim any truth.

"Conclusion B" does that. But the logical step from "Assumption B" to "Conclusion B" seems hardly convincing. Given "Assumption B", we might conclude that "ModelGod_One" is no longer allowed, and we have to use "ModelGod_Three" instead; but that contains no claim about the possible truth of "UniverseMinus", which is totally independent of either "ModelGod_One", "ModelGod_Two" or "ModelGod_Three", and cannot be excluded just because one of the model gods must be excluded.

One might propose another conclusion, that "UniverseMinus" logically implies "ModelGod_One". But that would be a contradiction, since "UniverseMinus" was explicitly defined as not containing "ModelGod_One".

Another argument might be that "UniverseMinus" is by logic implicitly forced to contain another model of "the greatest thing", which is not identical to god (let's call that "ModelGod_Zero"). So what? Among the things "UniverseMinus" contains maybe must be a thing that is greater than all other things in it, but no assumption forces us to conclude that it must be the greatest thing we can imagine. So the use of "ModelGod_Zero", i.e. the "non-existing-god", remains allowed.

Question

My actual question is this:

Has my paraphrasing somehow distorted Anselm's argument?

Is my criticism of the paraphrased conclusions in some way faulty?

And if not, is that criticism similar to what Kant meant when he criticised ontological arguments by saying that “existence” is not a predicate? (Disclaimer: I know very little about Kant's philosophy, so that half-guessed similarity might be totally absent. But Why is existence not a true predicate with respect to Anselm's argument? seems to make it plausible.)

  • You are correct that Anselm's argument does not prove God's existence for many reason's, including Kantian "existence is not a predicate". See Plantinga's reconstruction of the argument and how it relates to Kant's objection under: Is there a suppressed premise in Anselm's Ontological Argument? philosophy.stackexchange.com/questions/24484/… – Conifold Sep 3 '16 at 21:02
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Has my paraphrasing somehow distorted Anselm's argument?

I'm afraid it might have. Your "assumption A" seems incoherent.

Assumption A: By being part of "UniversePlus", "ModelGod_One" becomes the mental model of something greater (in itself!). Let's call that "ModelGod_Two".

How can an element change it itself, just by being, or nor being, a part of some set? This borders on self contradiction. You are here on the verge of a set-theorical paradox, perhaps something similar to Russell's paradox...

So it seems that rephrasing Anselm's argument in term of "universes" adds to the argument more (and unnecessary) problems than it had to begin with.

Is my criticism of the paraphrased conclusions in some way faulty?

It might be. For example:

"Conclusion A" says nothing about if the model with god should be considered more than pure speculation...

How is this relevant?

...and if it might claim any truth.

Where does this come from?

but that contains no claim about the possible truth of "UniverseMinus", which is totally independent of either "ModelGod_One", "ModelGod_Two" or "ModelGod_Three".

Totally independent? It's just the opposite. UniverseMinus was explicitly defined in terms of ModelGod_One. How can they be independent?

And if not, is that criticism similar to what Kant meant when he criticised ontological arguments by saying that “existence” is not a predicate?

No, it doesn't seem similar. Kant's criticism would have been analogous to a criticism of your "assumption A". But your own criticisms were directed elsewhere.

  • How can an element change it itself, just by being, or nor being, a part of some set? Is this only directed at Assumption A, or also B? You seem to imply that Anselm's original does not have this problem. – elias_d Sep 5 '16 at 6:01
  • rephrasing Anselm's argument in term of "universes" adds to the argument more (and unnecessary) problems than it had to begin with. Could you elaborate how? At least in the first three points before Assumption A I tried to replace with words of equal meaning in a straightforward way. Is the problem you see already in that part, or do you think neither Assumption A or B captures Anselm's logic? – elias_d Sep 5 '16 at 6:08
  • UniverseMinus was explicitly defined in terms of ModelGod_One. How can they be independent? In that aspect, sure, but I argue the conclusion only forces a choice between the "ModelGod" versions if you already start with one of them, and I can't see how that makes a claim about UniverseMinus. – elias_d Sep 5 '16 at 6:12
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    @elias_d Anselm's proof relies on the assumption that existence is a property intrinsic to the existing thing. The assumption might be false (as Kant argued), but it is not prima facie absurd. But when you replace existence with set membership, the assumption (your assumption A) does become prima facie absurd. No one would think of set membership as an intrinsic property of an element in the set. This is the sense in which I thought that your version distorted Anselm's argument. – Ram Tobolski Sep 5 '16 at 17:56

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