Modified Version of Anselm's Ontological Argument
Here is a modified version of Anselm's ontological argument for Gods existence and how it answers an objection from Kant. First I will list the original argument followed by its modified version.
Original:
1. That than which nothing greater can be conceived (TTWNGCBC) exists in thought.
2. It is greater to exist in thought and in actuality than to exist just in thought.
3. TTWNGCBC exists in actuality.
4. If TTWNGCBC exists in actuality, then God exists in actuality.
5. God exists in actuality
Modified:
1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent.
Kant claims that existence is not a real predicate, meaning that existence cannot be a property or characteristic of something. He claims this because when we conceive of something in our minds, we conceive of it existing. There is no other way to conceive it or picture it if it lacks existence. Something has to exist in order to have the property of existence. Since what we conceive of has to have the property of existence, there is theoretically no meaning behind the property and it is an innate characteristic to anything. This is an issue for Anselms argument, because he claims that existence is a property of God as the perfect being must exist. If existence is not a property of God or the perfect being, then there is no conclusive claim about the existence of God.
The solution to this problem lies in the fact that more than one mode of existence exists. Even if existence is not a real predicate, Gods existence is. This is because God exists either necessarily or impossibly. He cannot exist contingently. We all exist contingently because we may or may not exist and have the ability to not exist. God on the other hand, cannot exist and have the potential for nonexistence (or not-exist and have the potential for existence). If that were the case, he would not be God. Therefore, Kants argument only applies to contingent existence. His argument is no threat to Anselms. To better define this we modified Anselm's argument in such a way.
Original:
1. That than which nothing greater can be conceived (TTWNGCBC) exists in thought.
2. It is greater to exist in thought and in actuality than to exist just in thought.
3. TTWNGCBC exists in actuality.
4. If TTWNGCBC exists in actuality, then God exists in actuality.
5. God exists in actuality
Modified:
1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent.
Kant claims that existence is not a real predicate, meaning that existence cannot be a property or characteristic of something. He claims this because when we conceive of something in our minds, we conceive of it existing. There is no other way to conceive it or picture it if it lacks existence. Something has to exist in order to have the property of existence. Since what we conceive of has to have the property of existence, there is theoretically no meaning behind the property and it is an innate characteristic to anything. This is an issue for Anselms argument, because he claims that existence is a property of God as the perfect being must exist. If existence is not a property of God or the perfect being, then there is no conclusive claim about the existence of God.
The solution to this problem lies in the fact that more than one mode of existence exists. Even if existence is not a real predicate, Gods existence is. This is because God exists either necessarily or impossibly. He cannot exist contingently. We all exist contingently because we may or may not exist and have the ability to not exist. God on the other hand, cannot exist and have the potential for nonexistence (or not-exist and have the potential for existence). If that were the case, he would not be God. Therefore, Kants argument only applies to contingent existence. His argument is no threat to Anselms. To better define this we modified Anselm's argument in such a way.
Comments (88)
That is your modified argument in a nutshell.
Its a good argument only in so far as we include its contingency as the necessity part of the argument is an unfounded conclusion right from the start.
1. I can conceive of nothing greater than MO (my owner), who takes care of me, feeds me, provides me catnip and a comfortable place to live.
2. If MO existed contingently, there would be something greater
3. Nothing is greater than MO
4. Thererfore, MO exists necessarily
5. Therefore, MO is God.
The flaw is
2. Nothing is greater than TTWNGCBC
Any limitation in what we can conceive, doesnt imply anything about what exists.
Isn't that perfect pink unicorn (PPU) eventually going to turn into god? For example, if the PPU isn't all-loving, I can think of a PPU that is. If the PPU isn't all-knowing, I can think of a PPU that is, etc. Eventually, the perfect PPU will be an omniobenevolent, omniscient, omnipotent necessarily existing thing. God, in other words.
Russell set Kant's objection out much more clearly. this is an oversimplification, but...
Existence is taken as a second-order predicate.
First-order predicates apply to (range over) individuals, and are written using the letters f,g,h... We write "f(a)" for the predication "a is f".
But if we want to say that something about the predicate, we need to move up a level. So if we want to say that something has the predicate f, we use an existential quantifier. So "Some thing has the predicate f" or "Something is f" have to be written:
"There exists an x such that x is f".
Notice that the existential quantifier - the existential predicate, if you will - haas the predicate "f" within it's scope? It ranges over predicates. "f" is a first-order predicate, "?" is a second-order predicate.
The result, is that the formula ?(a) - "The individual a exists" - is ill-formed. It says nothing.
The upshot of all this is that it is pretty much impossible to set out the structure of the ontological argument in first-order logic. Or if you prefer, that the argument does not make sense.
Hence it is not valid.
You only do OP's?
I've seen this argument before but never fully understood it. Can you provide a reference which elaborates? Why can't existence be regarded as a first-order predicate?
Letting "a" stand for "exists" we have:
f(a) is false if f is "the first even prime number after 2"
f(a) is true if f is "the first odd prime number after 2"
Also, if "a" is "is green" then f(a) is true if f is "grass". But does that make "is a color" a second order predicate because we can say "green is a color"? i.e., "a" means "is a color" and f refers to green.
Your argument appears to be:
1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists
The conclusion doesn't follow.
One of these is true:
1. I conceive of [an entity which is all powerful and all knowing and exists] and this entity doesn't exist
2. I conceive of [an entity which is all powerful and all knowing and exists] and this entity exists
The thing conceived (as shown in brackets) is the same in both cases. Anselm's argument makes a fallacious reinterpretation of these as something like:
3. I conceive of [an entity which is all powerful and all knowing and exists and doesn't exist]
4. I conceive of [an entity which is all powerful and all knowing and exists and exists]
He then claims that because the thing conceived (as shown in brackets) in 4) is "greater" than in 3) then 2) must be true, which again is a fallacious reinterpretation.
. By whatever and by whatever number of predicateseven to the complete determination of itI may cogitate a thing, I do not in the least augment the object of my conception by the addition of the statement: This thing exists.
(CPR A600/B628)
Quoting Michael
2) positing and this entity exists, is precisely the fallacy in the original argument expounded in the Kantian objection to it.
The OP is full of holes, but your breakdown is agreeable.
It can. It's called Free Logic. But one of the results of free logic is that the existence of something cannot be the result of a deduction.
I took that from a recent article by Andrew Stephenson "Existence and Modality in Kant: Lessons from Barcan" in The Philosophical Journal. Is it the case that if something is possible then there must be something that possibly instantiates it? I don't know, but I'm gathering the de re/de dicto distinction might help show why the modified version won't work, @Epicero
I don't quite get the issue. We seem to understand what we mean when we ask whether or not ghosts or aliens or tachyons exist.
In the first version:
2. It is greater to exist in thought and in actuality than to exist just in thought.
Here, "It" slides from the thought of (1) into a being. In some sense (though such arguments seem quaint to modern eyes), the thought of an existent being is "greater" than the thought of that same but nonexistent being. But whether or not the being exists in actuality does not impact the "greatness" of the thought. The thought remains identical across universes where the being exists and doesn't exist.
I think is making this same point, but more clearly.
Quoting Banno
This is not a refutation. So, it requires 2nd order logic. So what?
So you can set it out in a second order formalism?
Go on, then.
When a painter considers beforehand what he is going to paint, he has it in his understanding What is Anslem trying to say here, or how should one understand this? I think he would demonstrate that it is in his understanding by articulating or describing what he plans to paint. This shows what is in his understanding. If he was unable to articulate, this would demonstrate that nothing was in his understanding.
But when he has painted it, he both has it in his understanding and understands that what he has now produced exists. I do not think Anslem is saying that the painter is reporting on what he is perceiving (though it is implied that it happened), but more reflecting on what he has produced, and that he can say it exists whether he is perceiving it or not.
How did Anselm demonstrate his understanding of God. He provided us with definition, God is a being than which none greater can be thought. It must be accepted to get one started in the deductive reasoning like one does with geometric proofs (consider Euclids Elements, "A point is that which has position but not dimensions.") From a definition, Anselm concludes that God exists because to exist in reality is greater than just existing in understanding. Unlike the painting example, Anselm is not reflecting on an experience of God in reality like the painter did with his painting, but reflecting on the "ideas of God" that makes him understand "God exists." And this is where, to some, the argument is not satisfying. Anselm gets to God exists not by the example most would agree they understand by to exist in reality like the painting example.
So we are left with:
Chapter 2 (Proslogion)
What exists exactly? Answer, A being than which none greater can be thought.
And what is that? Answer, a being that exists in reality as well as in understanding. This is greater than just "in understanding."
And what being is that Answer, A being than which none greater can be thought.
Chapter 3 (Proslogion)
What exists exactly? Answer, A being than which none greater can be thought.
And what is that? Answer, "A being that necessarily exists" This is greater than a being that contingently exists."
And what being is that Answer, A being than which none greater can be thought.
Could you lay out how you arrived at this representation please?
It does not begin with "if God exists", it begins with something equivalent to saying "that which there is nothing greater cannot be contingent". What falls into this category is God, and so the set-up connecting existence with non-contingency produces the conclusion. Denying that the category exists seems a contradiction in terms, as well as raises difficult questions about what the denier thinks. It is like saying "there's no greatest number".
1), 2), 3) is simplified to:
a) If some X is TTWNGCBC then X necessarily exists
Given 4), replace "TTWNGCBC" with "God":
b) If some X is God then X necessarily exists
Or in other words:
1. If God exists then God necessarily exists
Hence why the argument is just:
1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists
Clearly a non sequitur.
Quoting Michael
If TTWNGCBC existed contingently, then it would not exist necessarily, but something else would be TTWNGCBC.
Removing those parts is allowing you to make the argument look as if it's a non-argument.
Quoting Michael
No, the argument is "If some X is TTWNGCBC, then X necessarily exists".
If some X is TTWNGCBC then X necessarily exists
If some X is TTWNGCBC then X is God
If some X is God then X necessarily exists
Therefore, God (necessarily) exists
This is what the argument amounts to. The conclusion is a non sequitur.
I don't think that's a non sequitur, it's just not a fully formed argument. It's just 3 axioms followed by a conclusion. You could have switched "God" and "X" on the 3rd line though, that would've made it a valid and sound argument.
It could go:
If some X is TTWNGCBC, then X necessarily exists
God is an X.
Therefore, God (necessarily) exists.
Not a non sequitur.
Then this begs the question, as the second premise just asserts that God exists.
I'll be more explicit with my terms to make this clearer:
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. If there exists something which is God then this thing necessarily exists
4. Therefore, God (necessarily) exists
This is the fallacious argument that the OP has given.
Could you elaborate on what I'm misunderstanding? I see that quantifier being used in the article cited to argue for the existence of certain numbers. I don't see the difference to how it's being used in this argument.
TTWNGCBC is a concept, just like numbers are, so using a quantifier that means "there exists" to express the condition that something fits the definition of that concept should not beg the question, even if the conclusion is that that something exists.
Quoting Michael
3. in the above isn't in the original argument by the OP. They don't give the condition "if there exists God..." in the argument. It isn't necessary to include and I don't see a fallacy in the argument without it. All that is necessary is stating that God fits the definition of TTWNGCBC in some way, which the OP did in point 4.
Then the argument is:
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. Therefore, God (necessarily) exists
Which again is invalid.
Actually it would be
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. TTWNGCBC is God (or vice versa).
4. Therefore, God (necessarily) exists.
Although it isn't optimal, it appears to be valid and sound.
Quoting Michael
How so?
How does 2 differ from 3?
Quoting Hallucinogen
Because the conclusion doesn't follow. You would need an additional premise such as:
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. There exists something which is TTWNGCBC
4. Therefore, God (necessarily) exists.
But 3) is an empirical claim that needs to be shown. It's not something that's true a priori.
The mistake the OP (and Anselm) makes is to derive 3) from 1), but that's a non sequitur.
1. If God exists then it is necessary that God exists
2. It is possible that God exists
3. Therefore, it is possible that it is necessary that God exists
4. If it is possible that it is necessary that God exists then it is necessary that God exists
5. Therefore, it is necessary that God exists
In formal logic:
[math]\exists xGx\to\Box\exists xGx\\\Diamond\exists xGx\\\therefore\Diamond\Box\exists xGx\\\Diamond\Box\exists xGx\to\Box\exists xGx\\\therefore\Box\exists xGx[/math]
3 is not an axiom, just a definitional fact. 2. isn't necessary, I just left it there because you put it there. See:
Quoting Hallucinogen
Quoting Michael
Oh right. But I was assuming that by "If there exists something which is TTWNGCBC", you meant the same thing as "If some X is TTWNGCBC," in the arguments you gave when you were previously attacking it. I wouldn't try to defend this argument beginning with "If there exists something which is TTWNGCBC", because of the flaw you've pointed out, so I would have to insist on going back to the way you originally simplified it, to "If some X is TTWNGCBC (...)"
Showing that "there exists something which is TTWNGCBC" is the intent of the argument, so I suppose you would have to express it in a way that does not require the satisfaction of an empirical claim, as I have done above.
Yes, they mean the same thing.
Quoting Hallucinogen
Then the argument is invalid. To make your argument more precise:
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. God is defined as TTWNGCBC
3. Therefore, God (necessarily) exists
It's still missing the premise that asserts that there exists something which is TTWNGCBC, which as you say is the very intent of the argument.
To make this clearer by analogy:
1. If there exists something which is the greatest conceivable vampire then this thing necessarily exists
2. Dracula is defined as the greatest conceivable vampire
3. Therefore, Dracula exists
The conclusion doesn't follow. I'd need as a premise that the greatest conceivable vampire exists.
It doesn't need one; the argument is still valid.
Quoting Michael
Line 1 connects anything that fits the definition of TTWNGCBC (since you're allowing it to mean the same thing as "if some X is...") with it necessarily existing. So once a concept is identified as fitting that definition, it is shown to in fact exist.
Your objection seems to me to undermine the very capacity of logical and mathematical generalizations to prove anything about the world. All I need is for God to fit the definition of something which is a valid generalization of the logical and mathematical relationships between things that I already know to exist.
Quoting Michael
It's a false analogy. Vampires aren't non-contingent entities.
The greatest conceivable vampire is.
A vampire that exists is greater than a vampire that doesnt exist.
A vampire that necessarily exists is greater than a vampire that non-necessarily exists.
Therefore, the greatest conceivable vampire is one that necessarily exists.
Replacing the word vampire with intelligence or entity or thing doesnt change the logic.
https://plato.stanford.edu/entries/ontological-arguments/#PlaOntArg
The counter model looks right.
There might be something in the " suitable assumptions about the nature of accessibility relations between possible worlds", butI don't see it. It's invalid in all six, according to the tree proof generator.
So I'm left to supposing that it's down to how we pass
??xGx??xGx looks invalid. there can be a world in which ??xGx is true, and yet ?xGx false - It is possible to have green cows, but there are no green cows.
Given the definition of maximal greatness as being necessarily maximally excellent, the argument is ?? ?xGx? ??xGx.
It is possible that something is necessarily maximally excellent, therefore it necessary that something is maximally excellent.
I think its interpreting this as an inference rather than as a premise:
?xGx ? ??xGx
But that's just an instance of ?p?p, which is pretty clearly invalid.
Quoting Michael
p??p. Invalid.
??p ? ?p is valid.
Quoting Banno
This is given as a premise, not an inference. Its either true or false. If I gave this argument, would you reply by saying that 1) is invalid?
1. p?q
2. p
3. q
Firstly it over complicates things, if cat, fish, dog is impossible (non-existent) then by fact of existence cat, fish, dog exist then cat, fish, dog exist.
Where does contingency come into it ?
Either it is not possible that God exists or it is necessary that God exists
It is possible that God exists
Therefore, it is necessary that God exists
¬??xGx ? ??xGx
??xGx
??xGx
Its like saying its possible that my next coin flip will be tail. So if I do flip it it will be tails. (By necessity)
https://www.umsu.de/trees/#((~3~9~7xGx~2~8~7xGx)~1~9~7xGx)~5~8~7xGx
The question then is whether or not there is a satisfactory definition of God of which both ¬??xGx ? ??xGx and ??xGx are true.
The second premise is true if the definition doesn't contain a contradiction.
The first premise appears to be an application of the Buridan formula, ?x?Dx ? ??xDx, where Gx is defined as ?Dx, and Dx is defined as something like "x is the demiurge".
The full argument then is:
1. ?x?Dx ? ??xDx
2. ??x?Dx
3. ? ???xDx
4. ? ??xDx
What's interesting is that according to that website 1-3 is valid, 3-4 is valid, but 1-4 is invalid. That strikes me as a contradiction.
The countermodel is:
Worlds: { w0 }
Individuals: { 0 }
@: w0
D: { }
If the definition is "a something a greater than which cannot be conceived", I'm not convinced. There's the obvious comparison of "A number a larger than which cannot be conceived" - the idea is not coherent.
For the sake of argument I'm using the more simplistic definition "the demiurge of all possible worlds".
Yes, I've already argued with others that Anselm's argument is invalid. I'm now trying to find the strongest kind of ontological argument. It's a more worthy topic of discussion.
But "the demiurge of all possible worlds" might need some work...
?xGx ? ?x?Fx
??x?Fx
? ?xGx
Proof
But given that ??x?Fx ? ?x?Fx is valid, ??x?Fx begs the question.
Also as a counterargument:
?xGx ? ?x?Fx
?¬?xFx
? ¬?xGx
Proof
But given that ?¬?xFx ? ¬?x?Fx is valid, ?¬?xFx also begs the question.
So at least with respect to the modal ontological argument there is no reason to believe either that God exists or that God doesnt.
I'll use an argument formed from Anselm's text to show the argument isn't sound. It's taken from the English text of the Proslogion chapter 2. I think this is a better version of the argument, but it still doesn't work.
Premise (1) The fool hears and understands "a being than which none greater can be thought."
Premise (2) If the fool hears and understands, then it exists in his understanding.
Intermediate Conclusion: (3) The being than which none greater can be thought exists in the fool's understanding. Follows from (1) and (2) Modus Ponens
Premise (4) The being than which none greater can be thought exists in the understanding alone. (This would be the atheist's position according to Anselm.)
Premise (5) A being of which none greater can be thought can exist in reality.
Premise (6) A being that exists in reality is greater than a being existing in the understanding alone.
Intermediate Conclusion: (7) The being of which none greater can be thought existing in reality would be greater than the same being existing in the understanding alone. Follows from (5) and (6)
Final Conclusion: (8) A being than which none greater can be thought existing in reality would be greater than the same being existing in the mind/thought. Follows from (4) and (7)]
This presumably shows that the atheist position is contradictory, and therefore false. Why? Because the atheist's position is that a being than which none greater can be thought exists in the understanding alone. However, this cannot be so, because one could add a further attribute that would make it greater, viz., existing in reality. Thus, it can't exist in the understanding alone. It would be similar to saying that 10 is the greatest number. However, someone replies, no, I can add 1 to the number 10 and get 11, so 11 is the greatest number.
Since this argument is deductive it is valid. However, it must also be sound, i.e., the premises must be true, to be a good argument. The first premise with a problem is (2). How can a being exist in the understanding? Only a concept can exist in the understanding. We have the concept unicorn, but that doesn't mean unicorns are running around in my mind. Moreover, if you change the premise to only the concept existing in the understanding, then the argument is no longer valid. Why? Because if you add to the concept existing in reality you would still just have a concept existing in reality, not the being itself.
Finally, many find the argument dubious for other reasons, viz., trying to prove the existence of something from the concept alone, which others have pointed out in this thread, is very problematic to say the least.
Perhaps a naive question here, but does the word "greater" have some special meaning/usage in a philosophical discussion apart from the plain language meaning/usage?
I believe Anselm is trying to distinguish between two different ideas, "understanding that something exists in reality" and "experiencing that something exists in reality." As he says in Chapter 2 "And so. O lord, since thou givest understanding to faith, give me to understand-as far as thou knows it to be good for me-that thou exist, as we believe, and that thou art what we believe thee to be."
Unlike the painter and painting example, where producing a painting is the reason he understands the painting exists in reality, it is the idea of "a being than which none greater can be thought" and its deductive implication that Anselm understands such a concept of a being "exists in reality." So, when you say, "....you would still just have a concept exist in reality, not the being itself.", what is this idea trying to express? That the deductive argument should produce some experience of "the being of God"? Demonstrate some experience we had corresponds to this idea of "a being than which none greater can be thought."? It is a deductive argument, it is about ideas. Geometric proofs are about ideas, which does not mean it will have any successful application in reality.
Whether the argument is sound, how can we fairly access this? How does one evaluate the "truth" of "God is a being than which no greater can be thought", and "Existing in reality" is greater than "existing in understanding" in order to determine soundness. What should we do, take a poll on how many people agree with these premises?
Maybe what this argument ultimately demonstrates is the vacuousness of using general concepts and deductive reasoning whether one thinks something exist or not.
That experience is the final arbiter.
Goats eat everything; therefore there is something that eats everything. therefore It is possible that something eats everything.
So you have a proof of the Great Goat:
Either it is not possible that something eats everything or it is necessary that something eats everything.
It is possible that something eats everything.
Therefore it is necessary that something eats everything.
And this we all call the Great Goat.
A few more small steps and we have that everything is a goat.
Well, it's not a proof, but it is a valid argument.
I've never liked this one. Possibly necessary => necessary doesn't seem, to me, to be an adequate model of what a Godlike "necessary being" would look like.
Roughly, possibility means "exists in one (connected) possible world", and necessary means "exists in all (connected) possible worlds". It isn't exactly an account of what it would mean for a God to be a necessary existent in a world where they exist.
If you read premise one as "If god exists (in a world) then god exists in all worlds connected to that world", that's quite different from "If god exists (in a world), then their existence in that world is an essential property of it". If we take the sense of necessity of God's existence as "one whose essence includes existence", that sense of essentiality does not resemble necessity as a quantifier over possible worlds. Why? Essentiality concerns one entity in the world it's in - as a property of that entity. Necessity concerns one entity's behaviour in all worlds.
In other news, it doesn't tell you if the necessary existent is a god. Just that if a predicate behaves like premise 1, then it exists in all possible worlds. Could be the goat.
It does seem to trade on an ambiguous interpretation of the phrase "necessary". Modality is tricky. When I say that it is possible that it will rain tomorrow, I'm not simply saying that there is some possible world (e.g. parallel world) where it will rain tomorrow, but rather saying that the actual world might be such a world.
Is there a form of modal logic that can make this distinction?
No idea. SEP has a related article.
Does it show that a modally necessary God exists? Is ???xGx true and does ???xGx entail ??xGx?
First quibble: it isn't demonstrated to be any particular god, just an entity which satisfies G. The only thing which makes it god-ish is that G is associated with god. It would need to be argued that any given god has the property G, which is established independently (and is a theological thing, right). Moreover, it would need to be argued that an entity could, in principle, have that property.
Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds?
An example of that quibble: it was possibly physically necessary that the luminiferous aether existed, therefore it was physically necessary that the luminiferous aether existed, therefore the luminiferous aether existed. A sense of metaphysical necessity which lets you do this conjuring trick is... well, it needs a good argument to support.
Third quibble: you can always deny that it's possible that any particular god exists. And in that case the entity in question would not exist in any world.
Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example.
I did offer a more substantial notion of God here. The argument attempts to show that there exists something which necessarily created the world.
But you are right that we can posit any entity. So if anything it's a reductio ad absurdum against the assumption that ??x?Fx is true for every logically consistent Fx.
Quoting fdrake
The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument.
On this point, consider this:
1. ?xFx ? ?x?y(Fy ? (x = y))
2. ??x?(Fx ? Ax) ? ?x?(Fx ? Ax)
3. ??x?(Fx ? ¬Ax) ? ?x?(Fx ? ¬Ax)
The first premise asserts that if there is an x such that Fx then there is exactly one x such that Fx. The second asserts that there is an x such that it is necessary that both Fx and Ax. The third asserts that there is an x such that it is necessary that both Fx and ¬Ax. Obviously this is a contradiction.
If we take Fx to mean something like "x is the sole creator of the world" then 1 is true, and as both 2 and 3 are valid under S5 it must be that one or both antecedents are false, and so one or both of these is true:
4. ¬??x?(Fx ? Ax)
5. ¬??x?(Fx ? ¬Ax)
Therefore we cannot assume that ??x?Px is true for any logically consistent Px, and so cannot assume that it is possible that something necessarily created the world.
Or we have to reject S5, but if we reject S5 then the modal ontological argument is invalid as possibly necessary wouldnt entail necessary.
Eh, possibly necessary => necessary is reasonably easy to argue against. I don't like it for the above stated reasons. That lets you conjure up the luminiferous aether, assuming the "true logic of metaphysics" lets you do possibly necessary implies necessary. In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means).
I wouldn't want to deny that S5 has applications, just that demonstrating it as the "true logic of metaphysics" is a project unto itself. That a logic applies to a domain isn't something that can be taken for granted, I think. The above argument regarding physical necessity is a reason to reject the application of any logic which allows the inference pattern (possibly necessary => necessary) to metaphysics in general.
Given my previous post that shows that under S5 we cannot assume that ??x?Px is true for any logically consistent Px, the third alternative is that possibly necessary under S5 means something different to what it means under other systems (or natural English).
Aye! Nothing tells you the meaning of the two modal operators other than the context they're applied to.
I admit that whether the abstract property of greatness exists independently of speakers and their evaluations can be debated philosophically.
But this leaves the ontological argument, even if logically valid, only as sound as the notion that greatness exists independently of the evaluation of some rational being, rather than existing only as such an evaluation.
IMO, my evaluation of X is not a property of X.
You can't add anything to or subtract anything from an apple that does not exist, except in thought.
Quoting Banno
It is not an existent apple, but is merely the thought of an apple; am imagined or non-existent apple.
Assume X has the property 'existence'.
Now ask; does X exist distinct from its property 'existence'?
Two answers:
1. X does not exist. Therefore it cannot have properties, let alone 'existence'.
2. X exists. This makes existence as a property superfluous, since X exists anyway, whence X is existence.
This proves existence cannot be a property.
A property can be physical or chemical etc, it can describe a change or variable attribute.
A state is an instantaneous observation, such as solid, liquid, gas. A property is variable and can cause movement from one state to another. Existence is a state that can change into a state of non-existence.
'State' and 'property' are not synonymous.
If god has an existent state then can that state change into a non-existent state?
Even cyclical or oscillating universe hypotheses still intuit a 'spark' to start the process that then becomes eternal. The eternal god posit suffers from the same problem, 'what sparked god?' and what sparked the spark. That's why it's called an 'infinite' regression.
An ontological argument for god has no significance at all, to theism as it is at it's best, a very poor argument for the existence of A god or first cause mind with an intent/need to create. It offers nothing to the theist by way of supporting evidence that their god flavour exists. Allah and Yahweh remain as likely, as the spider god or the energy god or any, from an infinity of potential god descriptions/properties.
This ontology stuff is so easy!
What does this mean? Are you saying that the words "existence" and "God" are synonyms? As a fluent English speaker I'd have to disagree. At the very least, "God" is proper noun and "existence" an improper noun, so clearly there is at least some distinction between the words.
What's the verb form of "God"? For "existence" it's "exists". So how would you rephrase the sentence "there exists more than one apple"? Maybe "there gods more than one apple"? Doesn't make much sense to me.
Or are you perhaps just asserting pantheism? If so then what evidence or reasoning leads you to believe that the universe is "divine" (or whatever it is that distinguishes a pantheistic universe from a non-pantheistic universe)?
The verb for God is 'becoming' ie. evolving properties.
More than one apple? There is existence and it can have many apples as properties. Pantheism? No. Existence is eternal. It becomes creation.
Why use the word "God" at all? Why not just say that there was some inanimate, formless chaos that happened (without intention) to form into the space and time and matter and energy that we are familiar with?
Using the word "God" brings in all sorts of additional, religious baggage.