There’s no problem here: a circle in 1-D consists of the two points equidistant from the center point. I’m not sure about 0-D: the empty set? Better ask a mathematician.
This makes me wonder, tho: If the proof in question requires God’s existence in all possible worlds, what about the world that consists of only a single point. Nothing else. Does God exist in this world? If so, then God can be nothing more than an abstract point.
Not much of a God, IMO.
My point is that, since we all agree that the nature of “God” is not determined by this proof, beyond the definition, it really shouldn’t be called a proof of God’s existence. Let’s call it “Glumpf”.
“Hey, I’ve just proved that Glumpf exists!”
“Huh? What’s Glumpf?”
“I don’t know, but I’m sure it exists!”
Your circle cannot be differentiated from a line segment, and in zero dimensions does not exist at all.
You’re assigning a nonpositive attribute to God, and thereby contradicting the definition. Nothing about the ontological proof addresses any spatial size or spatial properties of any kind.
Not much of an analysis, either.
Um, that IS what it’s called.
The metaphysical nature is not determined, but the ontological nature is. He is perfect. He is necessary. He exists in all possible worlds, including the one in which you taunt Him.
That is a woefully inaccurate rendering of the argument. The definition is wrong. The assumption is random. And the conclusion is a non sequitur. Heck, Tisthammer’s proof isn’t even a syllogism.
Libertarian, would you please tell those of us who fail to reach your lofty level of logical discourse, in plain English without using a lot of X squiggle arrow P stuff, what is an accurate rendering of the argument?
You have it exactly backward Lib. The concept of circle includes all perfect circles. There is no way to draw a circle greater than the concept of circles. If you want to deny this, you are the one who has to show how a circle can be constructed that is greater than the concept of circles. Of course, this is impossible. But I won’t deny you the pleasure of trying.
In the same way, it is impossible for an actual god to exist in reality which is greater than the god which exists in your mind. Your concept of god is greater than any real god could be. Therefore it is NOT at all true to say:
This assumes that necessary existence is the most perfect existence, but that is simply not true. Existing only as a concept is the most perfect existence. Therefore the first postulate is false. If you wish to deny this, feel free to present anything which is greater than its concept. Again, this is impossible, but since you liked the proof it may be right up your alley.
How did I know that the name “Godel” would show up sooner or later?
Of course I am. Any vision of a undetectable entities (like God or my little men directing everything and communicating by mental telepath) that cannot be sensed in any way and is a product solely of mental activity is an hallucination.
So, to get back to the original question about substance in logical arguments about God, since the logic is entirely about hallucinationis it is without substance.
I’ll sign off now. The discussion about the first two sentences of you proof is getting tiresome, and the rest of the symbology in the proof has no reason to exisit.
OK, I’ll refrain from assigning nonpositive aspects to Glumpf. Please tell me, in the possible world that consists in a single point, and nothing else, what sort of a Glumpf can exist?
**
I don’t think I was taunting, just questioning.
Mapache
Yes, providing, of course, that you understand that such a rendering will not be precisely accurate anymore than a metaphorical rendering of quantum mechanics would be. Okay? The steps are as follows:
Definition: God is a being of maximal perfection in every possible world.
Given:
If He does exist, then He exists necessarily.
God’s existence is possible.
Derived:
If God exists necessarily, then He exists.
Suppose for the sake of argument that if God exists necessarily, then it is possible that He doesn’t exist. (This is the Law of the Excluded Middle.)
If it is possible that God does not exist, then it is necessarily true that He cannot exist in every possible world, since He is a being of maximal perfection. (This is the application of Becker’s Postulate.)
Therefore, if God exists necessarily, then it is necessarily true that He cannot exist in every possible world. (This is the Transitive Law.)
If God cannot exist in every possible world, then God necessarily does not exist. (This is an inference from modus tollens.)
Therefore, if God exists necessarily, then God necessarily does not exist. (Transitive Law)
If it must be true that God exists necessarily, then it cannot be true that God necessarily does not exist; therefore, God necessarily exists. (This is a disjunctive syllogism)
Therefore, since God exists necessarily, God exists. (This is a modus ponens) QED
These ten steps are in lay person’s language and correspond to the ten steps in Tisthammer’s proof.
Friend
A Glumpf who knows everything there is to know about the point and has all possible power over it.
Fair enough. I apologize.
David
Well, we’re big boys here, so if you take your ball and go home, we have balls of our own.
You know, those kinds of random assertions — you’re wrong, nyah nyah! — are entirely worthless. What I find tiresome are desparate presumptions that symbols you don’t understand mean nothing.
This is just… bizarre! You make an unsupported assertion and then ask me to prove it for you. There are possibly worlds in which circles don’t exist, some of which I’ve pointed out to you as your definition of a circle has morphed. If you claim that a circle exists in a one-dimensional universe, then the burden to describe that circle is not on me, but you.
Random. What about worlds where there are no brains to form conceptions?
Actually, Lib, I kind of want you to attempt what Mapache wants.
The statement of the entire proof in standard English would help me a lot to follow it in a logical, and mathematical sense, as well. I found in calculus that it helped me to read problems aloud in English, including phrases that grouped parenthetical operations. The sentences are long, but entirely grammatical if you do it right.
I lack the vocabulary to do it myself, but would be happy to attempt it with a brief dictionary of symbols, and English equivalents.
Not to mention how terribly erudite it makes you sound when you quote the notation during an ordinary argument, as support. 
Tris
It’s just above, Tris, about four posts above yours. Enjoy.
Thanks, Lib.
I don’t know how I missed it.
So far, after three reads I am about where I was.
It doesn’t prove to me that God exists, but it proves to me that there is no logical flaw inherent in such a belief. Nothing to use to pound on an atheist’s head, but a nice thing to have when one is pounding on mine.
You take what you can get, I suppose. 
Tris
Yeah. I would show you the proof that I exist if such a proof were possible. But unfortunately, it isn’t.
Triskadecamus:
It’s not line-by-line, but I can reduce the proof to its essentials.
First, a few preliminaries. There are possible worlds like our own. They don’t have to actually exist, they may be merely abstract things that are useful to talk about. The exactly nature of possible worlds is a philosophical question, and doesn’t affect the proof (it may have some bearing on how palatable you find the assumptions).
There is a relation on possible worlds. The meaning of the relation is not crucial to the proof, either. Informally, it specifies which worlds are like others. A world B is like a world A if things that are true in B are relevant to world A. A proposition is necessary in a world if it is true in every world like that world. A proposition is possible in a world if it is true in some world like that world.
Assume: It is necessary that if God exists he necessarily exists. Specifically, in every world like our own, if God exists in that world, then he exists in every world like that world.
Assume: God is possible. Specifically, God exists in some world like our own.
Assume: Accessibility is symmetric. Specifically, if world A is like world B, then world B is like world A.
Proposition: God exists in our world.
Proof: Identify the world like our own where God exists. Since God exists in that world and it’s like our own, God must exist in every world like that world. Our world must be included in the set of worlds like that world, because that world is like our world.
So, if a philosopher exists in any world, and the accessibility among that world, and any other world is not symmetric, it is possible that God might exist, or might not exist, in that philosopher’s world.
Right?
Tris
Well, Lib, I’m pleased you haven’t gotten annoyed, though given the subject matter, it would seem an odd reaction. I must admit, though, it would be entertaining to have Collounsbury participating in this thread:
[Collounsbury]
Oppy, eh? Listen logic-boy, I’ve had beers with God and your ontological ramblings are ridiculous. Before you make stupid generalizations about the deific “street,” you ought to look at some unbiased sources for a change. Perfection, indeed!
[/Collousnbury]
I haven’t the time these days that following all aspects of this argument would require. I did want to make a couple of comments here, though.
The Perfect Circle
This is a non-issue. I can quite easily construct a definition of an “Equaladron” that would resolve to a point in zero dimensions, a line segement in 1 dimension, a circle in two dimensions, etc… One can argue, I suppose, that there exists a “possible” world that does not contain even a single point. Given the definition of a point, we really would be dancing on the head of a pin at that point, you should pardon the expression. I also don’t think this really gets us anywhere because I could respond by saying that there then also exists a possible world made up entirely of the null set. In other words, there is a possible world with nothing in it. I need even not be that radical, what about a world with no beings in it of any description?
Onotological Proofs Can Say Nothing About the Nature of God
I simply don’t get this. The entire concept of an ontological proof is made possible by a definition of the nature of God. The proof and the assumptions required to make it work, put definite restrictions on what attributes God can have. Ontological proofs say, in essence, “God has some set of attributes, X. These attributes imply God exists because . . . In order to make this proof work, God cannot be a (toaster oven, island, cheese burger, etc.) nor can God have certain attributes that would either conflict with the definition or render it meaningless.” You can even go on and argue (as I believe Lib had done) that God must have every attribute that is necessary to meet the definition and no attribute that is not necessary to meet the definition. This is saying volumes about the nature of God. Whether what it is saying is valid is another question.
**Perhaps we will just have to agree to disagree. However, my being does exist in all possible worlds, if “god” does. You keep saying that it doesn’t work with the second axiom, but I still don’t understand why. Your insistence that only that which is perfect as possible necessarily exists strikes me as non-axiomatic and, indeed, wrong. From a mathematical perspective rather than an ontological one, I can easily posit worlds where my definition of a being exists and yours does not. (This is the orthogonality problem again which I doubt now that we’ll ever get to.)
BTW isn’t your definition of “God” in the “translation” of the proof you provided a bit too expansive? God is a being of maxim possible perfection. God doesn’t exist in “all possible worlds” by definition. That’s really the first axiom.
**Well, I’ve been waiting for Plato to rear his ugly head. This isn’t really the problem. The problem is that we can’t agree on what attributes the perfect toaster oven would have so it isn’t a meaningful definition. If there were an archetypal ideal of “toaster oven” that could reflect itself in all possible worlds, then a toaster oven could be as perfect as possible in all possible worlds. “God” works in the proof because we are positing an archetypal ideal for “God.” In principle, I see no reason why anything that can be defined similarly can’t be proved to exist using this proof. You’ll recall that Tisthammer expressed a similar concern. All I’ve done is formulate a definition that avoids his objections.
Oh, and Collounsbury, sorry about that, I couldn’t resist. 
Thank you, Lib. Finally we have something concrete to argue about.
The point that I have been trying to make is this:
You, and Tisthammer, and Anselm all define God as “a Being of maximal perfection in every possible world.”
You make no attempt to demonstrate that God actually corresponds, in any way, to your definition.
So: I define God as “A figment of theistic imagination.”
By definition, figments of imagination do not exist.
So God does not exist.
Why is your definition valid and mine not?
Mapache
One key point is that this particular proof doesn’t actually prove all the much.
**
Calling this being “God” is just a convenient shorthand. (In fact, this being as defined in this proof probably doesn’t correspond to any religion’s definition of “God.”) Your “figment of the imagination” definition, on the other hand, won’t work in this proof because this definition can’t satisfy the “if God exists, God necessarily exists” axiom. Under your definition, God doesn’t exist.
In other words, we can use your definition. But all it proves is that, “That being which is just a figment of my imaginition does not exist in all possible worlds.” This is trivial since you are starting from the premise that this being does not exist in this world.