Revisiting the Ontological Argument

[judechild]

In the past I've said that the Ontological Argument for God's existence is fundamentally flawed, but now I'm not so sure. It is easy to misunderstand the argument because it is pure logic, and if it is misunderstood then it seems nothing more than a word game, but if properly understood it is formidable. I'm sorry for this very long thread, but I'm floating a couple of thought-balloons here, without knowing exactly how they will turn out.

I'll try to explain it easily. Here is the skeleton of the proof:

1) The idea of God as a maximally-great-Being is possible.

2) A maximally-great-Being is a necessary being

3) A necessary being exists in all possible-worlds

4) The extent world (this world) is a possible-world

5) Therefore, God is either necessary or impossible

6) The existence of God is not impossible (see premise 1)

7) Therefore, God in some possible world.

8) A necessary being exists in all possible worlds.

9) (re-stated) The exent world is a possible world

10) Therefore, God exists in the extent world.

There are a number of terms that must be defined for this to make sense:

Possible-world: this just means "a way that the world could have turned out." It does not mean that these hypothetical worlds exist, only that they are possibilities which are not excluded by logical-inconsistencies.

Extent world: The really-existing world (id est, this world).

Necessary thing/being: Something that is described as necessary is something which must exist in all possible worlds. An example is mathematical facts such as 3 + 2 = 5. There can be no possible world where adding 3 of one thing to 2 of the same gives you anything but 5 of that thing.

Impossible: Something which is logically-contradictory (e.g. Judechild draws square-circles in his free time). Things that are impossible cannot exist in any possible world.

Maximally-great being: A being which possesses all things that it is better to have than not to have, and possesses them to the maximal extent.

Here, then, is a little narration that I've developing to explain it:

Imagine you are in a round, vaulted room with thousands of shuttered windows. In the middle of the room is a pedestal with the words "Each opens onto a possible-world" written on it. Curious, you unlatch one of the windows, and remove the shutter. You see in this world that air particles reflect red light, and so the sky is red. You try another; in this world, the Earth is much more massive - but still supports life - and so the animals all have thicker bones to deal with the increased gravity. You look into a third and find unicorns, knights, and people who can tap into some metaphysical force which they can use for medicinal or aggressive purposes. You continue to try several other windows.

But no matter how many possible worlds you look on to, you realize that there are some properties which are common to all possible-worlds. In one of the worlds, you see a woman trading at a market. She is holding two apples and she asks the merchant for three more. He gives these to her, and you count that she now has five apples. In another world, you see the same scene, even though the surroundings are very different, and the "apples" are blue and flat; still, when the woman asks for three apples to add to her two, you count five apples. The same happens in a third world, only this time the fruit is much smaller and perfectly round. You also notice that time progresses: past, present, future, in relation to the material of the world. Finally, you notice that in many cases there are people standing and there are people sitting, but in no world can one of these people both sit and stand at the same time, and in the same respect. From these considerations, you come to distinguish between the possible, and the necessary; the possible is any way that the world could be and as such is not common to every possible-world, but the necessary, you reason, is common to all possible worlds and any world that does not have one of these necessary principles is not possible - but impossible.

As you back away from the windows which look out on possible-worlds, you notice a second inscription on the pedestal in the center of the vaulted room. You pick out the words "Is God possible?" As you ponder this, a woman approaches who introduces herself as the curator. She asks you what your answer to the question is. You don't feel the need to dispute the claim at the moment, and so you say "yes." The Curator says, "then God exists - hypothetically, mind you - in at least one of these possible-worlds?" Remembering that even things which do not exist in the extent world - such as unicorns and wizards - exist in at least one of the possible-worlds, you agree that it is hypothetically true. "Now, if something exists in one possible world, and it is necessary, what do we know?" You respond that it would follow that a necessary thing that exists in one possible world must by definnition exist in all possible-worlds; like 2 + 3 = 5, which, because it exists in a possible world and is necessary also exists in all. "Then, if God exists in a possible world, and He is necessary, then we have proven that He exists in all possible-world; correct?" You nod. "And the extent world is a possible-world?" Again, you nod. "Then" the Curator finishes, "if God is necessary, then He must exist in the extent world."

"How then, do we know that God is necessary?" you ask. In response, the Curator hands you a pen and paper, and then tells you to draw a triangle with four sides. You respond that you cannot. She tries again, ordering you to draw a triangle whose interior angles do not add up to one-hundred and eighty degrees. Again, you say that you cannot. "That is because," the Curator explains, "those properties are intrinsic to the concept of a triangle. The same applies to God, there are properties which are intrinsic to His concept. One of these properties is that He is Maximally-Great. A Maximally-Great Being possesses all properties which it is better to have rather than not to have, and possesses them to the maximal extent. This means that the Maximally-Great Being possesses the maximum of intelligence, compassion, love, benevolence, et cetera. Now, is it greater to exist or not to exist?" You respond that it is greater to exist. "That is correct, and so we cannot speak of a Maximally-Great Being who does not exist, because a Maximally-Great Being includes "existence" in its concept. We can only say that the Maximally-Great Being is impossible (that is, that He can exist in no possible-world), or that He exists necesarily (because existence is within His ontology); to say 'a Maximally-Great Being does not exist' is to say 'A Maximally-Great Being who is not a Maximally-Great Being does not exist' - and that is nonsense; it would be like saying 'I see a triangle with four sides.' How did you respond when I asked if God's existence is possible again?"

The conclusion seems inevitable, since God's existence is possible, and therefore He exists in a possible-world - and His existence is necessary, and therefore if He exists in one possible-world He must exist in all - it is the logical conclusion that God exists in all possible-worlds. Since the extent world is a possible-world, it then naturally follows that God exists in the extent world as well. The Curator leaves you as you return to the extent world, to tell Judechild what you think of all this.

 

[OllieFranz]

Some of your statements (3 = 8, 4 = 9) are redundant. One of your statements (2) contains unexamined assumptions ("maximally-great" = "infinitely great" and "infinitely great" = "necessary") that may or may not be self-evident. And your first conclusion (5) relies on a hidden assumption, which you obliquely acknowledge by restating premise (1) as though the hidden assumption was proved. (being able to be conceptualized = physically [or perhaps metaphysically?] exists)

That's not to say that the Ontological argument itself fails, just that your specific formulation of it is flawed.

 

[judechild]

I know that I re-stated 3 and 4, which is why I wrote (re-stated) in from of 9; I simply forgot to add it after eight. The re-statements are there because I am trying to find a way of teaching this argument to people who are not trained philosophically, so that they can understand the argument.

In point 2, I do not make the assumption that "maximally-great" equals "infinitely great" because the latter never shows up in my proof; while the axiom "a maximally-great being is a necessary being" is accepted by most modal logicians, as I explain in depth in paragraph four of the narration. But I can see that I'll probably need to amend that, because I'm trying to teach this argument and that may cause confusion (though I tried to head that off in the "definitions" section when I wrote: "A being which possesses all things that it is better to have than not to have, and possesses them to the maximal extent.")

Finally, the part on premise five, I'll amend to "Therefore, God either necessarily exists or God is impossible;" which is sufficiently supported by the previous four premises since an extent, necessary being must exist in all possible worlds; so the only way that God cannot exist in this world is if the idea of God is logically incomprehensible.

 

[OllieFranz]

A being that is "maximally-great" without being "infinitely-great" is not the God whose existence you are attempting to prove. But I can conceptualize worlds in which any given trait has a non-infinite maximum. So the minimally necessary "maximally-great" being is not God. Not as long as I can imagine a possible world where one or more of His attributes is not infinite.

The traditional way of expressing statement 2 is: A "perfect" being cannot be totally perfect if He does not exist, so if He is perfect, He must necessarily exist. I can understand why you rephrased it, since there is a whiff of bootstrapping in that phrasing.

 

[anunbeliever]

In point 2, I do not make the assumption that "maximally-great" equals "infinitely great" because the latter never shows up in my proof; while the axiom "a maximally-great being is a necessary being" is accepted by most modal logicians, as I explain in depth in paragraph four of the narration.

I still cannot see why point 2 is a given - why is a maximally great being necessary in any possible world?

 

[judechild]

A being that is "maximally-great" without being "infinitely-great" is not the God whose existence you are attempting to prove. But I can conceptualize worlds in which any given trait has a non-infinite maximum. So the minimally necessary "maximally-great" being is not God. Not as long as I can imagine a possible world where one or more of His attributes is not infinite.

"Infinitely-great" is not necessary to prove, because "maximally-great" implies great to the maximum extent, and to say that infinitely-great is beyond the maximal extent is senseless. Saying that God is "maximally intelligent" means to say that by His ontology He has no imperfection in the area of intelligence - but with a discrete trait such as existence, He either exists (and exists maximally), or He does not.

The traditional way of expressing statement 2 is: A "perfect" being cannot be totally perfect if He does not exist, so if He is perfect, He must necessarily exist. I can understand why you rephrased it, since there is a whiff of bootstrapping in that phrasing.

Yes, I do know the historical conceptions, but St. Anselm and his immediate successors didn't use modal-logic, as I am.

I still cannot see why point 2 is a given - why is a maximally great being necessary in any possible world?

Because if a necessary thing (such as 2 + 3 = 5) exists in one possible world, then it exists in all possible-worlds. So, if God is a necessary being, then He must exists in all possible worlds - and since this is a possible world, it follows that He exists in this extent world.

A maximally-great being is necessary for the same reason as it is necessary that when you draw a triangle, the interior-angles must equal 180 degrees. If you try to draw a triangle in any other way, you are taking back what you gave by trying to draw a triange which is not a triangle. Like 180 degrees is a property of a triangle, existence is a property of the Maximally-Great Being. This is because it is greater to exist in the extent world than not to exist, and so if we're talking about the Maximally-great Being, existence is a part of that concept. Itaque, just as it would be senseless for me to say "I have an idea of a triangle with 185 degrees" it would also make no sense to say "I have an idea of a maximally-great Being that does not actually exist." Since the concept of a maximally-great Being exists necessarily, it follows that either the concept of a maximally-great Being is impossible, or that Being exists in all possible-worlds and therefore in the extent world.

I say something similar in paragraph 4 of the narration.

 

[IisJustMe]

A being that is "maximally-great" without being "infinitely-great" is not the God whose existence you are attempting to prove. But I can conceptualize worlds in which any given trait has a non-infinite maximum. So the minimally necessary "maximally-great" being is not God. Not as long as I can imagine a possible world where one or more of His attributes is not infinite.

What you can "imagine" is totally irrelevant to the attibutes of the living God. Sorry to burst your bubble, but you're just not that important.

 

[OllieFranz]

"Infinitely-great" is not necessary to prove, because "maximally-great" implies great to the maximum extent, and to say that infinitely-great is beyond the maximal extent is senseless. Saying that God is "maximally intelligent" means to say that by His ontology He has no imperfection in the area of intelligence - but with a discrete trait such as existence, He either exists (and exists maximally), or He does not.

Again, if in a given possible world, a trait such as "inelligent" has a finite maximum and in another, there is no such limit, then maximally intelligent does not exist as a necessary trait. A being posessing intelligence at the level of the cap in the first world falls short of maximal in the second, ans a being of infinite intelligence, while maximal in the second, cannot exist in the first.

A maximally-great being is necessary for the same reason as it is necessary that when you draw a triangle, the interior-angles must equal 180 degrees. If you try to draw a triangle in any other way, you are taking back what you gave by trying to draw a triange which is not a triangle. Like 180 degrees is a property of a triangle, existence is a property of the Maximally-Great Being. This is because it is greater to exist in the extent world than not to exist, and so if we're talking about the Maximally-great Being, existence is a part of that concept. Itaque, just as it would be senseless for me to say "I have an idea of a triangle with 185 degrees" it would also make no sense to say "I have an idea of a maximally-great Being that does not actually exist." Since the concept of a maximally-great Being exists necessarily, it follows that either the concept of a maximally-great Being is impossible, or that Being exists in all possible-worlds and therefore in the extent world.

But the formula that the sum of the interior angles equals 180° is not universal. It only applies in Euclidean Geometry. In Non-Euclidean Geometry, the sum is never 180°. In the "hyperbolic" version of non-Euclidean Geometry it is always less than 180°. In the "elliptical" version of non-Euclidean Geometry, which can be demonstrated on the surface of a sphere, it is always greater than 180°. Exactly how much greater (or less) depends on two things, the size of the triangle, and the curvature of the space. It only approaches 180° as a limit in two cases, when the triangle becomes infinitely small or when the space becomes infinitely large and flat, at which point it becomes Euclidean space.

Under General Relativity, we have discovered that the space in the extant world is not infinite, and if we define a "straight line" by the path an unimpeded beam of light takes to get from point A to point B, then the extant world is "elliptical." But it is so vast, and most of the triangles we can work with are so small in comparison, that the sum of their interior angles is almost immeasurably close to 180°.

It is possible that we are wrong to define a "straight line" in that manner, and that the extant world is Euclidean and flat, but it is not "necessary" in the way that you have defined it.

What you can "imagine" is totally irrelevant to the attributes of the living God. Sorry to burst your bubble, but you're just not that important.

You misunderstand. I am not questioning God's existence. I believe in God. I am examining the logic in the OP. And the Ontological Argument as phrased by Judechild does not prove the existence of the God I believe in, but only the possibility of a lesser being.

 

[anunbeliever]

Because if a necessary thing (such as 2 + 3 = 5) exists in one possible world, then it exists in all possible-worlds.

I disagree with this. 2 + 3 = 5 is correct in this universe because the laws of mathematics define it. A different universe with different laws may have 2 + 3 = 7. However i would agree that 2 + 3 = 5 anywhere in this universe would apply where-ever the basic rules of our mathematics are in effect.

A maximally-great being is necessary for the same reason as it is necessary that when you draw a triangle, the interior-angles must equal 180 degrees....existence is a property of the Maximally-Great Being.

I could define existence as a property of any theoretical being. That does not make that being's existence a given. Also, as others have discussed, it depends on the actual definition of "maximally great being". If i defined it as "the strongest living human" or "the most intelligent living human" or such, then its existence would be 100% since we know humans exist and, at any given time, one of them would be the best for a given metric.

I could extend that definition to "the strongest living being" or "the most intelligent living being". The winner may well still be human if there are no smarter/stronger aliens out there. If there are many other populated planets, the winner may well be someone from there. I wouldnt know without data to compare them. If the Christian god exists, then he would be the winner of this particular metric.

either the concept of a maximally-great Being is impossible, or that Being exists in all possible-worlds and therefore in the extent world.

Thats the crux of it. Either the omnipotent/omniscient God of Christianity exists or he doesnt. The proof is therefore no closer to proving anything. All it says is "if God exists then he exists".

 

[judechild]

I disagree with this. 2 + 3 = 5 is correct in this universe because the laws of mathematics define it. A different universe with different laws may have 2 + 3 = 7. However i would agree that 2 + 3 = 5 anywhere in this universe would apply where-ever the basic rules of our mathematics are in effect.

That is simply incorrect. 2 + 3 cannot possibly equal anyting other than five, no matter what possible world you are in. The only way you can say that 2 + 3 = 7 is if you linguistically take the symbols to mean something other than what they represent in our usage. To say the 2 + 3 = 7 in any other sense is meaningless because it can exist in no possible world.

I could define existence as a property of any theoretical being. That does not make that being's existence a given. Also, as others have discussed, it depends on the actual definition of "maximally great being". If i defined it as "the strongest living human" or "the most intelligent living human" or such, then its existence would be 100% since we know humans exist and, at any given time, one of them would be the best for a given metric.

You have missed the point. Existence (real existence, of course) is not the property of any theoretical being, because Mickey Mouse does not actually exist. You are correct that the strongest living human actually exists, but that is because humans actually exist, and so one is necessarily the strongest - but you've failed to draw a meaningful comparison, because nobody would say that "the strongest living human" is maximally-great. That means that that human does not necessarily possess all properties that it is greater to have than not to have. If that human does not necessarily possess all properties that it is greater to have than not have, then that human is not a necessary being. Since that human is not a necessary being, you have not drawn a relevant comparison.

I could extend that definition to "the strongest living being" or "the most intelligent living being".

The comparison is still irrelevent, for the same reason: the strongest living being is not a necessary being.

Thats the crux of it. Either the omnipotent/omniscient God of Christianity exists or he doesnt. The proof is therefore no closer to proving anything. All it says is "if God exists then he exists".

It does not say "if God exists then He exists." What it does say is "If God is a necessary being - which, as a Maximally-great being He is - then if it is possible that He exists, then He exists (hypothetically) in a possible world. But necessary beings (including mathematical laws) exist in all possible worlds, and so if God exists in any possible world then He exists in all possible worlds. If He exists in all possible worlds, then He exists in the extent world.

And to the previous poster, it is assumed that maximally-great is the greatest possible, irrespective of the possible worlds.

 

[BuffMonkey5]

Well, this is an interesting argument. I think it needs a little re-examining before you teach it to anyone though. To show why, let me restate your argument. I've added some hidden premises such as "It is greater to exist than to not exist" which I think you wanted to be derived from your definitions of maximally-great. I also changed the language a bit so that we can get some universal quantifiers in the argument to make our lives easier.

Argument One:

1. The idea of God as a maximally-great being is possible.
2. The extent world is a possible world.
3. It is greater to exist than to not exist.
4. For all (x), if (x) exists in all possible worlds, it is necessary.
5. For all (x), if (x) is maximally-great, it exists in all possible worlds.
6. For all (x), if (x) is maximally-great, it is necessary.
7. God is either necessary or impossible.
8. The existence of God is not impossible.

9. Therefore, God exists in the extent world.

Wow. I think this is what you were trying to say, no? If it isn't, I'm terribly sorry. But I THINK this is it. Anyways, let's go over the argument one premise at a time.

NUMBER ONE: This is true, and I don't think it's very controversial. The idea of a maximally great god isn't hard to formulate, and many people can do this.

NUMBER TWO: Another non-controversial premise by definition. We're off to a good start!

NUMBER THREE: Well, I'm not sure if EVERYONE would agree with this premise, but I'll give it to you for the sake of argument.

NUMBER FOUR: Okay, here's where we get into trouble. This isn't true, and the majority of logicians will agree. Now, before you get riled up, let me just say that you are VERY close to the correct definition of what it means to be necessary. At the moment, you are prescribing names or BEINGS as necessary or possible. As a logician, you can't do this. You can only say that certain claims, propositions, or statements are either necessary or possible. So the claim "2 + 3 = 5" can be (and is) necessary, and the statement "God exists" can be possible, but the being God cannot be either. Does this make sense?

The definition of necessary is this: A proposition is necessary if and only if it is true in all possible worlds.

And the definition of possible is this: A proposition is possible if and only if it is true in at least one possible world.

So we cannot have a universal quantifier here. But that's easily fixed with the above definition.

NUMBER FIVE: I know what you're trying to do here. By your definition of maximally-great, a being that is maximally great must possess greatness to a maximal extent. So you therefore extend existence to not only one possible world, but ALL possible worlds to satisfy this notion of "maximal extentness".

Well, that introduces a BIG problem in modal logic, and it's probably not a road you want to travel down. (But hey, maybe you do, I'm not sure.) If you do, you have to deal with the problem of trans-world identity. This basically states that no single individual can exist in more than one possible world. If they did, they live in different possible worlds, and they will generally have different properties (observing different things at different times, doing different things at different times, knowing different things, etc.). The principle of the indiscernibility of identicals indicates that identical things have the same properties. As you can hopefully see, there are some inconsistencies here. Of course, if we subscribe to a counter-part theory, we can avoid all of this. But even if we do, we have to amend your premise.

NUMBER SIX: This basically is derived from hypothetical syllogism in conjunction with some quantifier rules. It's completely allowed if the premises are true, but as we have seen, they may not be…

NUMBER SEVEN: This was the conclusion of your first argument… It's not actually clear why you decided to end your first argument with a disjunction since it would have been more powerful to just end it with a simple sentence. But you are allowed to do this if have proved either statement "God is necessary" or "God is impossible" as true. Unfortunately, you haven't proved either.

You may argue that you have, in fact, proved that God is necessary if all of the preceding premises are true. This may SEEM to be the case, but it definitely isn't. This is because it all hinges on the analysis of premise one, "The idea of God as a maximally-great being is possible."

You seem to analyze premise one to mean "The existence of a maximally-great God is possible". I hope you can see that by adding "the IDEA" to the premise, you get a VERY different statement.

And you are not allowed to conclude that the IDEA is maximally-great and therefore necessary, because premise one only states is that the idea is merely possible.

You can try to avoid all of this by amending premise one to read "The existence of a maximally-great God is possible" where the statement "a maximally-great God exists" is true in at least one possible world. I think this may pass as true, and it fits into your argument nicely.

NUMBER EIGHT: Once again, this hinges on premise one, and cannot be derived without that premise being amended.

NUMBER NINE (THE CONCLUSION): Well, it doesn't follow from your argument… You're close, but you're quite not there.

AND THAT'S THAT.

At the moment your argument is lacking in validity. Even if you do incorporate my suggestions, I'm not sure it would be either valid or sound. You have to some how show that maximal-greatness is an actualized state of affair in all possible worlds. That's going to be tough.

 

[razeontherock]

I think it's simpler to define God. Reality exists, and took power to come into being. G-d is that Power. His existence is undeniable.

This is a mere definition. Trying to make that definition branch out into anything else (other than pure Deism) only works via the resurrection of Christ, from the dead.

To any born again Christian, that is as real as the ground under our feet.