The Ontological Argument For God's Existence
To be clear as to exactly what the ontological argument says, one very simple form goes as follows:
1. God is the greatest possible being.
2. It is possible that God exists.
3. If God does not exist, He would be inferior to a God which did exist.
4. If (1), (2), (3) then God exists.
5. Therefore, God exists.
It just happens that people have made this argument much more rigorous. For instance, Godel created a version of the ontological argument using modal logic that proceeds as follows: For those inclined to work through how this argument functions, it's available here:
http://skepticsplay.blogspot.com/2009/06/godels-ontological-argument-step-by.html
I find the ontological argument unpersuasive once effort is made to understand it. The casting of the argument using model logic cannot whitewash its flaws.
Here is my breakdown.
1. God is the greatest possible being. To better understand the fallacy of this argument, let's start a parallel argument.
A. Pegasus is the greatest possible flying horse. The word possible is the operative predicate, indicating that there are none better horses, flying or otherwise.
2. It is possible that God exists.
B. It is possible that Pegasus exists.
On what basis should I concede that? It seems to me that the moment that you have a ground for a possibility that X exists, it must possibly exist.
3. If God does not exist, He would be inferior to a God which did exist.
C. If Pegasus did not exist, He would be inferior to a flying horse that did exist.
Now, I'm not expert in modal logic, but this seems gibberish, as an attempt is to prove existence in the using the negative subjuctive: "If X does not exist, therefore Y must exist." By assertion, we are creating the existence of flying horses.
4. If (1), (2), (3) then God exists.
D. If (A), (B), and (C), then Pegasus exists.
5. Therefore, God exists.
E. Therefore, Pegasus exists.
I don't think that follows.
A response from a reader:
Well, it is the consensus opinion that there are severe problems with the ontological argument. I should note that I do not believe in the ontological argument (in fact, I don't believe in God at all.) However, the reasons which you have cited are not the faults which are usually found with the ontological argument. In fact, if I understand your reasons correctly, then much of modern analytic metaphysics is unquestionably false. Given that this is a large body of serious academic work, it is worthwhile to at least try to understand some of the orthodox responses to your comments. I reserve neutrality as to my own position on this statements; I am merely pointing you to the accepted answers, not whether or not I personally accept them (though I do think they would be difficult to properly refute.)You seem to find fault with the modal notion of "possible" (which is sometimes also refered to as "contingency", though that has a slightly different meaning.)
You wrote:
2. It is possible that God exists.
B. It is possible that Pegasus exists.
On what basis should I concede that? It seems to me that the moment that you have a ground for a possibility that X exists, it must possibly exist. Strikes me as nonsensical.
In modern analytic metaphysics, X is said to possibly exist if we can form consistent propositions about it. Unless the notion of pegasus is somehow contradictory we must accept that it possibly exists precisely because, and only because, it is non-contradictory. We are not usually entitled to say that X has necessary existence only in virtue of its possible existence, and this is something that is strange about the ontological argument. Usually, philosophers find it sufficient to say that if they can imagine it, then it exists at some possible world (which is equivalent to saying that it is a non-contradictory notion.) In other words, if we can imagine it, then it is possible. Contradictory notions, meanwhile, are termed impossible. Modal logic gives us the ability to quantify over these varies different modes of existence - necessary, possible, and impossible. Therefore, modal logic is the formal tool that we need to express sentences containing various different modalities (i.e. modes of existence.)I should note that there are many things which are possible but do not exist in our world. I think it is non-controversial that Pegasus is an object of that kind (i.e. Pegasus is possible, but does not exist in our universe.) Of course, there are philosophers who believe in all kinds of things, so you can find philosophers who identify themselves as "modal realists". They believe that all possible worlds are real, whatever that might mean. This is different from the multiverse theory, though there are some who believe that these are the same thing. Most philosophers feel that these ideas are silly. I therefore will not spend more time on them.
What you wrote, while ultimately at odds with philosophical orthodoxy, is not entirely different from one of the standard refutations of the ontological argument. Personally, I like to formulate a parallel argument using the "ultimate taco":
1*. The Greatest Taco is the greatest possible taco.
2*. It is possible that the Greatest Taco exists.
3*. If the Greatest Taco does not exist, it would be inferior to a taco which did exist.
4*. If (1), (2), (3) then the Greatest Taco exists.
5*. Therefore, the Greatest Taco exists.
Now, the flaw here cannot be that the argument is invalid. After all, it is a simple modus ponens argument and its validity can be trivially shown. What we are concerned with is its soundness. I think it is non-controversial that the Greatest Taco does not exist. Therefore, we can conclude that the taco argument must make a mistake somewhere.
How is this different from the Pegasus argument? It's different because I did not attack the ontological argument on either the grounds that you cite (i.e. your problem with modality or your problem with negative subjunctives. You might be wondering why I did not give the orthodox response to your worry about negative subjunctives. I have to confess that I am not familiar with the formal fallacy that you are indicating if, in fact, such a fallacy exists.) Rather, this is simply a reductio argument showing that something must be wrong with arguments of this kind; the exact error is not specified.There is a problem with this counterargument (and so we begin the counter-counter-argument!) The first problem is that it does not tell us where the issue occurs in arguments of this kind. Maybe there is a Greatest Taco, greater than any other taco and perhaps Pegasus exists as well. We doubt that these two statements are true, but on what grounds do we come to believe them? Perhaps an evil demon is tricking us into believing that super tacos and flying horses don't exist. Egads -- we've been deceived our entire lives! But most people are willing to think that this response is probably false, at least on the basis of inductive evidence.The second problem with this counterargument is the possibility that Anselm meant something else, something more subtle. Examine premise (1*) of this argument and premise (1) of the ontological argument. These premises are slightly different:1*. The Greatest Taco is the greatest possible taco.1. God is the greatest possible being.In premise (1), what is a "being"? And, in particular, what exactly did Anselm mean? If he just meant object, thing, or entity, then this is very different from saying that God is the greatest possible "supernatural man with a beard". It's not that God is the greatest possible god; it's that, of all things/objects that could possibly exist, God is the greatest. So, pick out any object in the world and God will be greater than that object. Toasters? Yep, God is greater. Laptops? Yep, God is greater. Janet Reno? Yep, God is greater. Burger King? Still, God is greater. I think you get the picture.But this is not true of premise (1*). Here, we are told that the Greatest Taco is the greatest possible taco. Maybe toasters are superior to tacos for some reason. I don't why that would be true, but bare with me. The idea is that proposition (1*) only speaks about possible tacos and not the full set of possible objects. Thus, we should be able to identify objects, either possible or actually existent, which are superior to the Greatest Taco, if, in fact, no possible taco is the greatest possible object.Unless, that is, we change premise (1*) to read:1**. The Greatest Taco is the greatest possible thing.Now, we claim that premise (1) and premise (1**) are equivalent modulo the name of the greatest possible thing. One might think, on a variety of different grounds, that there can only be one greatest possible thing (i.e. "greatest possible thing" is a unique object.) If this uniqueness claim holds, then God is the Greatest Taco and the Greatest Taco is God. You might object here on the grounds that relating God to tacos is clearly absurd. But what this really shows is that any object, when it is given the status of "greatest possible thing", must have the properties of God. We can imagine a taco that is the most intelligent, the most beautiful, the most good, the most merciful, etc, possible. Such a taco doesn't really have the properties of taco-ness; it has the properties of Godness. We probably wouldn't call such an object a "taco" since it does not have the properties we expect tacos to have. Just the same, if (1**) is true, then God and the Greatest Taco are identical.In case you're sceptical about the uniqueness claims, one simple way to argue for the uniqueness of the greatest possible thing is just to state that a non-unique thing is always inferior to a unique thing. Therefore, the greatest possible thing must be unique in virtue of its being the greatest possible.Another problem that you might cite in the ontological argument is the vagueness of the term "greatest". In virtue of what is God said to be the greatest? He obviously isn't the greatest evil. He's also not the greatest womanizer or the greatest misogynist. On all of these qualities, God seems to be the polar opposite (at least in the conception of God that mainstream Abrahamaic religions profess.) Yet, if we just say that He is the greatest possible in all categories, we are left with deducing clearly false propositions like this. There do exist solutions to this vagueness problem in the literature; however, none of them are really satisfying to me.There is another problem, though it is much more technical. In the ontological argument, the property of existence is ascribed to God. Further, He is said to be the greatest possible at existing; i.e. a non-existent deity is inferior to an existent deity. However, this is at odds with how existence is normally understood in the philosophical and logic literatures. In the literature, the orthodox position is that existence is a quantifier. But if existence is a quantifier, then it is not something which can be ascribed to an object. -- i.e. there would be no such thing as an existence predicate. However, it is impossible to formulate the ontological argument without an existence predicate. I understand that this last counterargument is still controversial. I also understand that there exists the position that existence is a second order predicate. I do not know very much about this last position nor do I know how it relates to the ontological argument.
1. God is the greatest possible being.
2. It is possible that God exists.
3. If God does not exist, He would be inferior to a God which did exist.
4. If (1), (2), (3) then God exists.
5. Therefore, God exists.
It just happens that people have made this argument much more rigorous. For instance, Godel created a version of the ontological argument using modal logic that proceeds as follows: For those inclined to work through how this argument functions, it's available here:
http://skepticsplay.blogspot.com/2009/06/godels-ontological-argument-step-by.html
I find the ontological argument unpersuasive once effort is made to understand it. The casting of the argument using model logic cannot whitewash its flaws.
Here is my breakdown.
1. God is the greatest possible being. To better understand the fallacy of this argument, let's start a parallel argument.
A. Pegasus is the greatest possible flying horse. The word possible is the operative predicate, indicating that there are none better horses, flying or otherwise.
2. It is possible that God exists.
B. It is possible that Pegasus exists.
On what basis should I concede that? It seems to me that the moment that you have a ground for a possibility that X exists, it must possibly exist.
3. If God does not exist, He would be inferior to a God which did exist.
C. If Pegasus did not exist, He would be inferior to a flying horse that did exist.
Now, I'm not expert in modal logic, but this seems gibberish, as an attempt is to prove existence in the using the negative subjuctive: "If X does not exist, therefore Y must exist." By assertion, we are creating the existence of flying horses.
4. If (1), (2), (3) then God exists.
D. If (A), (B), and (C), then Pegasus exists.
5. Therefore, God exists.
E. Therefore, Pegasus exists.
I don't think that follows.
A response from a reader:
Well, it is the consensus opinion that there are severe problems with the ontological argument. I should note that I do not believe in the ontological argument (in fact, I don't believe in God at all.) However, the reasons which you have cited are not the faults which are usually found with the ontological argument. In fact, if I understand your reasons correctly, then much of modern analytic metaphysics is unquestionably false. Given that this is a large body of serious academic work, it is worthwhile to at least try to understand some of the orthodox responses to your comments. I reserve neutrality as to my own position on this statements; I am merely pointing you to the accepted answers, not whether or not I personally accept them (though I do think they would be difficult to properly refute.)You seem to find fault with the modal notion of "possible" (which is sometimes also refered to as "contingency", though that has a slightly different meaning.)
You wrote:
2. It is possible that God exists.
B. It is possible that Pegasus exists.
On what basis should I concede that? It seems to me that the moment that you have a ground for a possibility that X exists, it must possibly exist. Strikes me as nonsensical.
In modern analytic metaphysics, X is said to possibly exist if we can form consistent propositions about it. Unless the notion of pegasus is somehow contradictory we must accept that it possibly exists precisely because, and only because, it is non-contradictory. We are not usually entitled to say that X has necessary existence only in virtue of its possible existence, and this is something that is strange about the ontological argument. Usually, philosophers find it sufficient to say that if they can imagine it, then it exists at some possible world (which is equivalent to saying that it is a non-contradictory notion.) In other words, if we can imagine it, then it is possible. Contradictory notions, meanwhile, are termed impossible. Modal logic gives us the ability to quantify over these varies different modes of existence - necessary, possible, and impossible. Therefore, modal logic is the formal tool that we need to express sentences containing various different modalities (i.e. modes of existence.)I should note that there are many things which are possible but do not exist in our world. I think it is non-controversial that Pegasus is an object of that kind (i.e. Pegasus is possible, but does not exist in our universe.) Of course, there are philosophers who believe in all kinds of things, so you can find philosophers who identify themselves as "modal realists". They believe that all possible worlds are real, whatever that might mean. This is different from the multiverse theory, though there are some who believe that these are the same thing. Most philosophers feel that these ideas are silly. I therefore will not spend more time on them.
What you wrote, while ultimately at odds with philosophical orthodoxy, is not entirely different from one of the standard refutations of the ontological argument. Personally, I like to formulate a parallel argument using the "ultimate taco":
1*. The Greatest Taco is the greatest possible taco.
2*. It is possible that the Greatest Taco exists.
3*. If the Greatest Taco does not exist, it would be inferior to a taco which did exist.
4*. If (1), (2), (3) then the Greatest Taco exists.
5*. Therefore, the Greatest Taco exists.
Now, the flaw here cannot be that the argument is invalid. After all, it is a simple modus ponens argument and its validity can be trivially shown. What we are concerned with is its soundness. I think it is non-controversial that the Greatest Taco does not exist. Therefore, we can conclude that the taco argument must make a mistake somewhere.
How is this different from the Pegasus argument? It's different because I did not attack the ontological argument on either the grounds that you cite (i.e. your problem with modality or your problem with negative subjunctives. You might be wondering why I did not give the orthodox response to your worry about negative subjunctives. I have to confess that I am not familiar with the formal fallacy that you are indicating if, in fact, such a fallacy exists.) Rather, this is simply a reductio argument showing that something must be wrong with arguments of this kind; the exact error is not specified.There is a problem with this counterargument (and so we begin the counter-counter-argument!) The first problem is that it does not tell us where the issue occurs in arguments of this kind. Maybe there is a Greatest Taco, greater than any other taco and perhaps Pegasus exists as well. We doubt that these two statements are true, but on what grounds do we come to believe them? Perhaps an evil demon is tricking us into believing that super tacos and flying horses don't exist. Egads -- we've been deceived our entire lives! But most people are willing to think that this response is probably false, at least on the basis of inductive evidence.The second problem with this counterargument is the possibility that Anselm meant something else, something more subtle. Examine premise (1*) of this argument and premise (1) of the ontological argument. These premises are slightly different:1*. The Greatest Taco is the greatest possible taco.1. God is the greatest possible being.In premise (1), what is a "being"? And, in particular, what exactly did Anselm mean? If he just meant object, thing, or entity, then this is very different from saying that God is the greatest possible "supernatural man with a beard". It's not that God is the greatest possible god; it's that, of all things/objects that could possibly exist, God is the greatest. So, pick out any object in the world and God will be greater than that object. Toasters? Yep, God is greater. Laptops? Yep, God is greater. Janet Reno? Yep, God is greater. Burger King? Still, God is greater. I think you get the picture.But this is not true of premise (1*). Here, we are told that the Greatest Taco is the greatest possible taco. Maybe toasters are superior to tacos for some reason. I don't why that would be true, but bare with me. The idea is that proposition (1*) only speaks about possible tacos and not the full set of possible objects. Thus, we should be able to identify objects, either possible or actually existent, which are superior to the Greatest Taco, if, in fact, no possible taco is the greatest possible object.Unless, that is, we change premise (1*) to read:1**. The Greatest Taco is the greatest possible thing.Now, we claim that premise (1) and premise (1**) are equivalent modulo the name of the greatest possible thing. One might think, on a variety of different grounds, that there can only be one greatest possible thing (i.e. "greatest possible thing" is a unique object.) If this uniqueness claim holds, then God is the Greatest Taco and the Greatest Taco is God. You might object here on the grounds that relating God to tacos is clearly absurd. But what this really shows is that any object, when it is given the status of "greatest possible thing", must have the properties of God. We can imagine a taco that is the most intelligent, the most beautiful, the most good, the most merciful, etc, possible. Such a taco doesn't really have the properties of taco-ness; it has the properties of Godness. We probably wouldn't call such an object a "taco" since it does not have the properties we expect tacos to have. Just the same, if (1**) is true, then God and the Greatest Taco are identical.In case you're sceptical about the uniqueness claims, one simple way to argue for the uniqueness of the greatest possible thing is just to state that a non-unique thing is always inferior to a unique thing. Therefore, the greatest possible thing must be unique in virtue of its being the greatest possible.Another problem that you might cite in the ontological argument is the vagueness of the term "greatest". In virtue of what is God said to be the greatest? He obviously isn't the greatest evil. He's also not the greatest womanizer or the greatest misogynist. On all of these qualities, God seems to be the polar opposite (at least in the conception of God that mainstream Abrahamaic religions profess.) Yet, if we just say that He is the greatest possible in all categories, we are left with deducing clearly false propositions like this. There do exist solutions to this vagueness problem in the literature; however, none of them are really satisfying to me.There is another problem, though it is much more technical. In the ontological argument, the property of existence is ascribed to God. Further, He is said to be the greatest possible at existing; i.e. a non-existent deity is inferior to an existent deity. However, this is at odds with how existence is normally understood in the philosophical and logic literatures. In the literature, the orthodox position is that existence is a quantifier. But if existence is a quantifier, then it is not something which can be ascribed to an object. -- i.e. there would be no such thing as an existence predicate. However, it is impossible to formulate the ontological argument without an existence predicate. I understand that this last counterargument is still controversial. I also understand that there exists the position that existence is a second order predicate. I do not know very much about this last position nor do I know how it relates to the ontological argument.
A description of the problem of having existence be a predicate (at least as formulated by Kant) is available here:
As for why the ontological argument cannot be formulated without having existence as a predicate, we have to turn back to examine what exactly it is that the argument says. Let's consider a modified form of the argument that I already gave:1. God is the greatest possible thing.2. It is possible that there exists an x such that x=God.3. If God does not exist, He would be inferior to a thing which did exist.4. If (1), (2), (3) then God exists.5. Therefore, God exists.However, premise (3) now has problems. First, I note that premise (3), as currently expressed, cannot possibly be coherent if existence is a quantifier since it was in that sentence as a predicate. Namely, proposition (3) is a sentence of the kind "x is p" (expressible in predicate logic as ). Now we look for a way to suitably alter (3) without changing it's meaning.Consider the sentence "If there does not exist x, such that x=God, then there exists some existent t such that God is inferior to t." We might formalize this as: inf where G is God, t is a thing which exists. and inf is a order relation such that if AinfB then A is inferior to B. But why would this proposition be true? Since we have existentially quantified over G, and not attributed some property to it, there is no property by the lights of which G is inferior to t. In other words, the relation tinfG returns false whenever A=G and B=t. But that's not at all the idea that we wished to express; we wished to express the idea that a non-existent God would be inferior to an existent God.
Labels: apologetics
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