The Ontological Argument is probably the most widely misunderstood and maligned of all the theistic arguments. Counters to it often entail little more than mud-slinging, calling such an argument “wordplay” or “trickery,” but few get to the meat of the argument. Often counter-arguments include attempts to parody the argument (as here) or a dismissive strategy. But does anyone truly confront the argument? Rarely. Here I’ll present two forms of the ontological argument, and discuss them in some detail.
The first version of the argument that I will present is Alvin Plantinga’s “Victorious Modal” version of the argument. I actually don’t think this is the strongest version of the ontological argument, but it is one step towards the strongest version. First, the argument:
“1) The property of being maximally great is exemplified in some possible world
2) The property of being maximally great is equivalent, by definition, to the property of being maximally excellent in every possible world
3) The property of being maximally excellent entails the properties of [at least] omniscience, omnipotence, and moral perfection
4) A universal property is one that is exemplified in every possible world or none
5) Any property that is equivalent to some property that holds in every possible world is a universal property
Therefore,
6) There exists a being that is essentially omniscient, omnipotent, and morally perfect (God) (Maydole, 573)”
Now let’s analyze this argument. The long story short is that this argument is logically valid. The conclusions follow from the premises. This can be shown with deductive symbolic logic (Maydole, 590). Thus, one cannot argue against it as being invalid, rather, the argument must be attacked for soundness.
Let’s sum it up in easier-to-understand language, shall we? The first premise simply claims that in some possible world (out of infinite or nearly infinite), the property of “maximal greatness” is exemplified, that is, some body has this property. Premise 2) argues that this property is equivalent to maximal excellence, which is explained in 3) as (basically) the attributes generally believed to be possessed by God in classical theism. Premise 4) states the obviously true statement that if a property is universal it is in either every possible world or none. This is a simple tautology, it is true by definition. One could just as easily say a property that exists in every possible world or none is universal. X = X, this is true. Then, Plantinga argues 5) that maximal greatness is a universal property. This is key to understanding the argument. Basically, in his book God, Freedom, and Evil (and elsewhere), Plantinga makes the point that if a being is maximally great, then that simply entails being maximally great in all possible worlds. For a being that is maximally great in, say 200 worlds is not greater than one that exists in 2,000, but then this continues up the ladder until you have a being that is maximally great in all possible worlds, which then excludes the possibility of other beings with that property (for they would then, necessarily, not be the maximally great being). Finally, premise 6) follows from the previous premises (for if the maximally great/excellent being exists in all possible worlds, it exists in our own).
The question for this argument is then whether it is true. The premise on which this argument hinges is 1) “The property of being maximally great is exemplified in some possible world”. This seems to be perfectly clear. Denial of this premise means that one would have to argue that it is logically impossible for maximal greatness to be exemplified in any possible world at all, not just our own. This means someone must have infinite knowledge of all possible worlds. Therefore, it seems as though this argument is almost airtight. But suppose someone insists that one can deny premise 1), well then the whole argument falls apart. I must admit I don’t see how anyone could logically do so, but I don’t doubt that people will do so. So if someone wants to deny premise 1), and then–in my opinion–become rather dishonest intellectually, they can deny the soundness of the argument.
I don’t think that there is a way around this argument, but it is actually possible to make the Ontological Argument even stronger.
The most powerful version of the ontological argument, in my opinion, is presented in the book God and Necessity by Stephen E. Parrish (previously discussed here).
The argument goes as follows:
1) The concept of the GPB is coherent (and thus broadly logically possible)
2) Necessarily, a being who is the GPB is necessarily existent, and would have (at least) omnipotence, omniscience, and moral perfection essentially.
3) If the concept of the GPB is coherent, then it exists in all possible worlds.
4) But if it exists in all possible worlds, then it exists in the actual world.
5) The GPB exists (Parrish, 82)
This argument is also deductively valid. Premise 1) argues that the Greatest Possible Being is coherent–that is, there is no logical contradiction within such a being. 2) further defines what a GPB would be (Plantinga’s argument outlines this thoroughly). Premise 3) states the major part of the argument in a different way. Rather than arguing that it is possible that “maximal greatness” is exemplified in some possible world, Parrish argues that the concept of the GPB entails logical necessity along with such maximal greatness, and thus 3) follows from the previous premises, just as Plantinga’s version of the argument does. The key is to remember that in Parrish’s version of the argument, the coherence of the GPB is what is important, not the possibility (for if it is coherent, it is possible). 4) This is tautologically true. 5) follows from the previous premises.
What Parrish does here is actually takes out the possibility of denying premise 1) in Plantinga’s argument. Let’s look into this closely. Parrish argues that the concept of the Greatest Possible Being is coherent. Why is this so important? Well, because if we grant for a moment that the GPB exists, such a being could not fail to exist due to some kind of chance mistake or having some other being or thing prevent the GPB’s existence (Parrish, 105). The first point (that chance could not prevent the GPB’s existence) is true because the GPB would be logically necessary (it would either exist or not exist in all possible worlds). This claim is reinforced by the idea of maximal greatness being a universal property (above). The second point (nothing else could prevent the GPB’s existence) seems quite obvious. If there were a being or body or thing, etc. that could prevent the GPB’s existence, the GPB would clearly not be the Greatest Possible Being. If some other being were powerful enough to prevent the GPB’s existence, then that being would be greater.
So the only thing that could prevent the GPB from existing is self-contradiction within the concept.
Why is this? Well, after a little investigation it seems pretty clear. If the GPB is a coherent (and logically possible) concept, then such a being does exist. Let us say that the GPB is coherent. Let us then take some world, W, and see whether the GPB can fail to exist.
The concept of the GPB includes logical necessity in all possible worlds. The GPB has all the properties of maximal greatness. This means that these properties are universals. We can simply refer back to the argument above. If the GPB exists and has omnipotence, omniscience, etc. then it must exist universally, because, again, if some being is the GPB in only 200/1,000,000,000 possible worlds, the being that is GPB in 2,000 is greater. But this seems ridiculous, for the truly Greatest Possible Being must exist in all of them, for if there was a possibility for some being to exist in all the worlds that the GPB exists in +1 and exemplify the maximally great attributes, then that being would be the GPB (and the previous one would not really have omniscience, etc., for the GPB would be more powerful, existing in all possible worlds, and being sovereign in all possible worlds) . Now let us return to W. It now seems completely clear that W could not be such that, if the GPB is coherent (and therefore possible), W could not fail to exemplify the GPB.
But have we then demonstrated that coherence is really the issue here? Is it possible that we are just thinking up some thing, calling it the GPB, and then arguing it into “supposed” existence? Logically, it does not seem so.
The reason is because we are arguing that the GPB entails these properties. Things have, essentially properties. I exemplify the property of “having fingers.” I also exemplify the properties of “being finite,” “being human,” “having two feet,” etc. These properties don’t belong to me simply because someone sat around and decided to assign them to me, rather they belong to me because of the kind of thing I am. (Parrish argues similarly, 55). But in the same way, we could answer such objections by saying that these properties are part of the concept of God because that’s the kind of thing God is. Certainly, there have been all kinds of “gods” claimed throughout history that are finite in power or activity, but those aren’t the “gods” whose existence we are arguing for. Rather, we are arguing for the existence of the God of classical theism, and that God has such properties as necessary existence (in the analytic sense), omnipotence, omniscience, etc. This objection really doesn’t have any weight. But again, let’s assume for the sake of argument that it does.
Let’s assume that the objection may be true. We are just taking some “X” and arbitrarily saying that it is omnipotent, necessary, etc. Does that preclude such an object existing? I don’t see how this could be true. But even further, some claim that this doesn’t match up with Christianity’s concept of God. This seems preposterous. One needs only to open a Bible to find that, while words like “omnipotence” are not used, words like “Almighty”, “Most High”, and the like constantly are. And what kind of objection is this really? Is the person making this objection going to concede that it is possible that there exists some nearly-omnipotent-but-not-actually-omnipotent creator of the universe? No, the objection is beyond logic and into emotional repugnance at the thought of God actually existing.
But we can even go further. For let us simply define God as the Greatest Possible being. This seems like it could very easily operate as a definition of what “God” is, at least on classical theism. Well then, what properties might this Greatest Possible Being have? And then we simply build them up. Omnipotence seems obvious, as does omniscience, as does necessity, etc. So this isn’t some arbitrary assigning-to of properties, but rather such properties are part of the GPB simply because of what the GPB actually is, if the GPB existed.
Now we can return to the matter at hand. Does God exist? Well it follows from all of this that yes, God does exist. The theist has established that there are some arguments that deductively prove that God does exist. The only “way out” for the atheist is to attack premise one and argue that the concept of the GPB is, in fact, contradictory. And let’s be honest, there have been many attempts to do so. I can’t possibly go into all of them here, but I can state simply that I remain unconvinced. Often these arguments are things like “Omnipotence and omniscience are impossible to have, because if God knows in advance what He’s going to do, He can’t do anything else!” This argument is obviously false, for simply knowing what is going to happen is not causation. I know that a sheep is an animal, this does not cause the sheep to be an animal. I know that I am going to finish typing this post, that does not cause me to do so. Rather, I choose to continue typing and finish this post.
Of course, one might say “You can’t really know you’re going to finish this post! Your computer might explode and you may get brain washed, etc.” Well that is a whole different debate, but I think that such objections, ironically, actually apply not at all to God. For if God is omniscient and omnipotent, it seems clear that God actually would be above such things! For nothing could prevent God from finishing something He knows He’s going to do! Not only that, but God’s knowledge is such that He actually would know He is going to do something, and freely chooses to do so. I don’t see why God’s foreknowledge of an event somehow limits omnipotence, especially when one considers that God is part of agent-causation, so God chooses to do the things He is going to do. Thus, the argument falls apart.
But now I’m already farther off track than I was (and thus preventing myself from finishing this post, AH the irony!). Suffice to say that I very much doubt that any objection to the coherence of the GPB even comes close to succeeding. But then, if that is true, God exists.
Therefore God exists.
(Edit: I’ve included below a proof of Plantinga’s argument)
Let
Ax=df x is maximally great
Bx=df x is maximally excellent
W (Y) =df Y is a universal property
Ox = df x is omniscient, omnipotent, and morally perfect 1) ◊ (∃x)Ax pr
2) □(x)(Ax iff □Bx) pr
3) □(x)(Bx⊃Ox) pr
4) (Y)[W(Y) iff (□(∃x)Yx ∨ (□~(∃x)Yx)] pr
5) (Y)[(∃Z)□(x)(Yx iff □Zx)⊃ W(Y)] pr
6) (∃Z)□(x)(Ax iff □Zx) 2, Existential Generalization
7) [(∃Z)□(x)(Ax iff □Zx)⊃W(A)] 5, Universal Instantiation
8 ) W(A) iff (□(∃x)Ax ∨ (□~(∃x)Ax) 4, Universal Instantiation
9) W (A) 6, 7 Modus Ponens
10) W(A)⊃ (□(∃x)Ax ∨ (□~(∃x)Ax) 8, Equivalence, Simplification
11) □(∃x)Ax (□~(∃x)Ax) 9, 10 Modus Ponens
12) ~◊~~(∃x)Ax ∨ (□(∃x)Ax) 11, Communication, Modal Equivalence
13) ◊(∃x)Ax ⊃ □(∃x)Ax Double Negation, Impl
14) □(∃x)Ax 1, 13 Modus Ponens
15) □(x)(Ax iff □Bx) ⊃ (□(∃x)Ax ⊃ □(∃x)□Bx) theorem
16) □(∃x)□Bx 14, 15 Modus Ponens (twice)
17) □(x)(Bx ⊃ Ox) ⊃ (□(∃x)□Bx ⊃ □(∃x)□Ox theorem
18) □(∃x)□Bx 16, 17 Modus Ponens (twice)
19) (∃x)□Bx 18, Necessity Elimination
(taken directly from Maydole)
Sources:
Maydole, Robert E. “The Ontological Argument.” The Blackwell Companion to Natural Theology. Edited William Lane Craig and J.P. Moreland. Blackwell, 2009.
Parrish, Stephen E. God and Necessity. University Press of America. 1997.
——
The preceding post is the property of J.W. Wartick (apart from citations, which are the property of their respective owners) and should not be reproduced in part or in whole without the expressed consent of the author.
Thanks for this post! I have always been interested in the ontological argument, and this is a good summary of some of the points.
Posted by zenothales | February 19, 2010, 10:32 AMI only read the first argument. I would agree that it is intellectually dishonest to claim knowledge of infinite or even near infinite worlds. Claiming knowledge of anything that is infinite or near infinite also seems obviously intellectually dishonest. The door swings both ways, brother. You can’t have it both ways…
Posted by Mateo | February 21, 2010, 1:07 AMDo we have knowledge of numbers? They are an infinite set. Do we have knowledge of pi? It is infinite. Do you think we have knowledge of modal properties? They are infinite. It is actually intellectually dishonest to say that we don’t have knowledge of infinite things, not just because we do (in the cases above), but also because if someone claims that:
1) We don’t have knowledge of x
then it is impossible for us to know 1), for we would then:
2) Know that we don’t have knowledge of x
But 2) is a type of knowledge about x to begin with.
so 1 ) is obviously false.
Sorry, but this objection fails on many levels.
Posted by J.W. Wartick | February 21, 2010, 4:32 PMHi Joseph,
I like your blog. Lots of interesting topics. I signed up to receive updates by email.
Have a good week!
Chris
Posted by fleance7 | February 22, 2010, 1:58 PMThanks Chris!
I’ve enjoyed reading the updates to your blog as well, I appreciate seeing others out there writing on these topics from a Biblical Christian perspective.
God bless,
-J.W.
Posted by J.W. Wartick | February 22, 2010, 2:02 PM“The property of being maximally great is exemplified in some possible world”
This property could only be held by what you call god… which makes the first premise read as:
“’god’ is ‘possible’ in some possible world”.
I think this is a logical and fair interpretation
which means you stated your conclusion right in your premise
thats called ‘begging the question’ which makes the entire argument null and void.
Posted by Mateo | February 22, 2010, 10:38 PMWrong. The argument is deductively valid, the only way to attack it is to attack a premise (and the only premise to attack would pretty obviously be 1).
I can show it in two ways, the first simply with words, the second with symbolic logic. And because the argument is deductively valid (see below), this objection is clearly false, for a valid argument cannot beg the question.
Words:
Begging the question would mean that the argument is basically A, B, therefore A.
But even on your own redefinition of terms it is not doing that. The conclusion is that God exists, but the premise (which you argue shows question-begging) is that it is possible that maximal excellence is exemplified in some possible world. Now even if we allow for the redefinition of terms that you argue for, the argument is still not question begging, because it would still have these terms: A (possibly, God exists), B (If A, then God exists), therefore, C (God exists).
But your redefinition is not even justified, because something is not necessarily equivalent to its properties. Indeed, if God exists, maximal excellence would be a property essential to God’s nature, but that does not mean that the two are the same, in the same way as me having the property (arguably) of being a rational animal (following Aristotle’s rather obscure definition) does not mean that rational animal = J.W. necessarily. A property is not the thing itself, but something about the thing. So your objection fails in this way as well.
Now it seems that perhaps your objection is that somehow the statement “’god’ is ‘possible’ in some possible world” is question begging on its own. This is just a misunderstanding, for it is obviously a tautology. If God is possible, then God is possible in some possible world, that’s exactly what “possibility” is. Further, this statement itself is a premise not a syllogism, so I don’t know how it could be question begging. The premise, on your redefinition (which doesn’t work anyway, above) is simply a premise. A premise is not question begging, an argument can be. So here also your objection fails.
(And before I delve into the symbolic logic, I’d like to note that you instantly dropped the “we can’t know things about God” argument… are you conceding my point? I hope so, because if not then, as I said, you’d have to hold to the dubious phrase “We know [about God] that we can’t know things about God”.)
I claim it is deductively valid, but I can back it up symbolically:
“Let
Ax=df x is maximally great
Bx=df x is maximally excellent
W (Y) =df Y is a universal property
Ox = df x is omniscient, omnipotent, and morally perfect
1) ◊ (∃x)Ax pr
2) □(x)(Ax iff □Bx) pr
3) □(x)(Bx⊃Ox) pr
4) (Y)[W(Y) iff (□(∃x)Yx ∨ (□~(∃x)Yx)] pr
5) (Y)[(∃Z)□(x)(Yx iff □Zx)⊃ W(Y)] pr
6) (∃Z)□(x)(Ax iff □Zx) 2, Existential Generalization
7) [(∃Z)□(x)(Ax iff □Zx)⊃W(A)] 5, Universal Instantiation
8 ) W(A) iff (□(∃x)Ax ∨ (□~(∃x)Ax) 4, Universal Instantiation
9) W (A) 6, 7 Modus Ponens
10) W(A)⊃ (□(∃x)Ax ∨ (□~(∃x)Ax) 8, Equivalence, Simplification
11) □(∃x)Ax (□~(∃x)Ax) 9, 10 Modus Ponens
12) ~◊~~(∃x)Ax ∨ (□(∃x)Ax) 11, Communication, Modal Equivalence
13) ◊(∃x)Ax ⊃ □(∃x)Ax Double Negation, Impl
14) □(∃x)Ax 1, 13 Modus Ponens
15) □(x)(Ax iff □Bx) ⊃ (□(∃x)Ax ⊃ □(∃x)□Bx) theorem
16) □(∃x)□Bx 14, 15 Modus Ponens (twice)
17) □(x)(Bx ⊃ Ox) ⊃ (□(∃x)□Bx ⊃ □(∃x)□Ox theorem
18) □(∃x)□Bx 16, 17 Modus Ponens (twice)
19) (∃x)□Bx 18, Necessity Elimination
(taken directly from Maydole, as quoted in the post above)”
Posted by J.W. Wartick | February 23, 2010, 12:11 AM“screeeeeeeeeeech” , *crashes into wall of text*. I don’t know why I do this to myself. I forget you do this for a living. I definitly do not concide, but you have taken it from a servicable level of discussion to what ever that was. It’s my fault for being ignorant towards your response but it’s not very nice or respectful to add barbs into many of your responses like “obviously”. Wether its obvious to you is besides the point; it has no place in discourse. Your better than that
Posted by Mateo | February 23, 2010, 4:37 PMI wasn’t trying to add barbs there. Perhaps I should leave adjectives/adverbs out of my responses. Point taken. I do think that A = A can be demonstrated to be a tautology, however. And (trying to be concise) you don’t need to concede anything, except that the argument is valid (and thus not question begging). It’s all a matter of whether it is sound or not at this point. I believe that it is.
Posted by J.W. Wartick | February 23, 2010, 6:04 PMPremise 1 is misleading in both situations. When using modal logic, saying something is possible not what we normally consider possible to mean. It is the same as saying that something is necessary. Saying something is necessary means that in any conceivable world it could not possibly not exist. So saying that it is possible has a burden to get over. It must be proven that it is not possible in all possible realities. This means that there is actually a contradiction in the premise.
All that is necessary to disprove premise 1 is to ask the question, “Is it possible that GPB does not exist?” If it is possible to imagine some possible reality where GPB does not exist, suddenly we have a problem with your premises. Now, ask yourself, is there some possible reality where GPB does not exist? No? What about a reality where nothing exists? Uh oh, you just thought of something that refutes your first premise.
Now, some people have argued that a world where nothing exists is not a possible world. While I would argue with that, I could also say to imagine a world where only a single hydrogen atom exists. By saying only a single hydrogen atom exists, that would be a world where GPB is necessary, thus also proving the point.
Posted by Godlessons | March 1, 2010, 10:40 AM“It is the same as saying that something is necessary.”
Absolutely not. Possibility in modal logic is not the same as necessity. This is completely false, which means the rest of this falls apart.
“What about a reality where nothing exists? Uh oh, you just thought of something that refutes your first premise.”
There is no such thing as nothing “existing”. Nothing is just that, nothing. So, no, this is no problem.
“By saying only a single hydrogen atom exists, that would be a world where GPB is necessary, thus also proving the point”
Such a world could not exist if the GPB does exist, however. It would be logically contradictory for there to be a possible world without the GPB. Of course, one could imagine that there is a world with a single hydrogen atom, but it doesn’t seem at all clear that such a world is possible… and again, if the GPB is possible, such a world would be logically impossible.
But, for the sake of argument, I can actually grant you this point. Still, one cannot argue against the ontological argument construed in this fashion by arguing that we can think of worlds without the GPB, because in the second version I presented, the premise is not whether the GPB exists in some possible world, no, the premise is that the GPB has no logical contradiction in itself. More specifically, it argues that the concept of the GPB is coherent. Thus, it does not rely on possibility in the modal sense, only broadly logical possibility, and this second argument then avoids every single counter you have presented. Further, I don’t think any of your counters really adds up to anything, as I outlined above, for if the GPB is possible (here moving back a level to Plantinga’s “victorious modal” argument), then there would be no such thing as a possible world without the GPB. In order to argue against Plantinga’s version of the argument, one has to somehow show not that we can conceive of worlds without the a maximally great being, but that such a being is impossible, for if the being is possible, it exists in all possible worlds.
Thus, the arguments stand undefeated.
Posted by J.W. Wartick | March 1, 2010, 11:36 AMSomeone I was speaking with tried to debunk the ontological argument by doing the opposite, Like this:
Premise 1: It is possible that God does not exist.
Premise 2: If it is possible that God does not exist, then God doesn’t exist in some possible worlds.
Premise 3: If God doesn’t exist in some possible worlds, then God doesn’t exist in all possible worlds.
Premise 4: If God doesn’t exist in all possible worlds, then God doesn’t exist in the actual world.
Premise 5: If God doesn’t exist in the actual world, then God doesn’t exist.
Please help, how do you refute this argument?
Posted by Mac Johnson | January 10, 2012, 4:09 AMFirst, it’s a neat coincidence that William Lane Craig’s latest podcast gets this exact question answered check it out: “Nothingness, Origins, and Handling Objections”: here.
Second, I would respond the same way he does–denying premise 1. Premise 1 is essentially the same as saying classical theism is false. Why? Classical theism holds God is necessary and therefore would exist in all possible worlds. To start the argument by saying “it is possible that God does not exist” therefore is equivalent to saying “Classical theism is false.” The argument therefore begs the question.
The theistic ontological argument, some have pressed, also begs the question–because once one says God is possible, one must agree God exists. The difference here is the theist can hold P1 of their ontological argument based upon argumentation. Those who wish to press that it is possible that God doesn’t exist (i.e. that theism is impossible) must justify their own premise.
Posted by J.W. Wartick | January 10, 2012, 7:40 PMEvery true arithmetic statement is true in all possible worlds (They are necessarily true)
If Goldbach’s conjecture is true in one possible world, it is true in all possible worlds.
It’s possible that Goldbach’s conjecture is true.
Therefore Goldbach’s conjecture is true in a minimum of one possible world.
Therefore Goldbach’s conjecture is true in all possible worlds.
So… Goldbach’s conjecture is true. (right?)
If so, then it seems you can’t “prove” arithmetic proofs (or God) through modal logic.
Posted by Fred Simmons | January 20, 2012, 1:24 AMThe problem with using this to try to parody the ontological argument is that you’re relying on an epistemic limit of human knowledge. It is true that we can’t prove Goldbach’s conjecture in that no one can ever go through every single even number to test it. Now what does that mean about Goldbach’s conjecture? It means that we are indeed on an uneven ground epistemically regarding this mathematical problem.
Is that analogous to the case of God? The only reason to deny that God is possibly necessary is to argue that there is a contradiction in His being. If there is not, then God is necessarily existent. The onus of proof is upon those who say “there is a contradiction” to show that there is one. Do we need to appeal to epistemic mystery and say we have no idea here? No. God is not composed of an infinite set which we can never go through and test. Rather, God’s attributes have been delineated within analytic theology for quite some time. There are varied versions of this set of attributes, but again, the onus is upon those who say “there is a contradiction” to show where the contradiction(s) are entailed.
Now, to revist the argument for Goldbach’s conjecture. Your parody states “It’s possible that Goldbach’s conjecture is true”–this is of course a parody of the premise “God possibly exists.” Now, again, to show that this premise is false, one would have to say “There is a contradiction in the nature of God.” Similarly, for Goldbach’s conjecture, one would have to say that there is a contradiction in Goldbach’s conjecture to say that it is not possibly true. Is there? It seems highly unlikely. Is the epistemic uncertainty there enough to discredit the argument? I don’t really think so. It seems that one could be epistemically justified in holding that Goldbach’s conjecture is indeed necessarily true. It has been verified up to extremely high numbers and one can work out probabilistic distributions such that one can fairly infer the conjecture is indeed necessarily true.
Really, the core of the parody revealed here–and indeed some people’s uneasiness with the ontological argument–is that people are uneasy about getting a result like “God exists” or “Goldbach’s conjecture is true” if we can’t go out and show it to their own satisfaction. This is, of course, not a logical problem with the arguments, but rather people’s own bias against certainty. Because they hold that we should have uncertainty about everything that we can’t just show via method (x), they deny that arguments from S5 modality work. But of course if S5 modality is true, then these arguments do in fact work, because they are simply based upon axioms of S5. Is it extraordinary that S5 can show with certainty that some truths are necessarily true? Yes, it definitely is extraordinary. Does that mean that we should discredit modal proofs? Certainly not. With the case of Goldbach’s conjecture, it seems we have probabilistic and empirical reasons for justification that it is indeed true, and so the S5 argument would make it necessarily true. In the case of God, it seems that philosophically, the concept of God is indeed coherent, so the S5 argument means God necessarily exists. Unless and until someone challenges the coherence of God or the whole system of S5 modality, the argument stands.
Posted by J.W. Wartick | January 20, 2012, 10:31 AMI have been wondering about the Ontological Argument and think I have come up with a solution:
I don’t understand how God has to be in every possible world, because I can imagine a world without God, making God not possible in every possible world. But then I thought that it might be impossible to imagine a possible world without a necessary being, because any world you imagine is dependent on your existence and, therefore, not existing on its own. So in a way, you become the necessary being for that specific world’s existence. Therefore, every possible world needs a necessary being to exist, and since our world is a possible world, it logically follows that our world needs a necessary being as well, who is God. Is this idea logical or am I just blowing smoke? Can a world exist on its own without a necessary being or is it true that every time you imagine a possible world, that possible world is depend on your existence, making you a necessary being for that world alone?
What are you thoughts?
Posted by Mac Johnson | January 31, 2012, 6:47 PMSorry it took me a while to get back to you.
I think your argument is very interesting. It relies upon a semantics of possible worlds which is controversial, however. You wrote, “any world you imagine is dependent on your existence and, therefore, not existing on its own.” Now for the sake of clarity, we’re talking about modal logic here, so worlds we imagine are not necessarily possible worlds. For example, I could “imagine” a world in which square circles exist [granting it is possible to think about the logically impossible--and I'm not convinced it is]. But if that’s the case, then the set of possible worlds is not identical to the set of imaginable worlds. Now this reveals that the argument you’ve made seems to conflate “possible worlds” with “imagined worlds.” Possible worlds, according to most semantics of possibility, are one of the following: 1) necessarily existing abstract objects [realism]; 2) real, instantiated worlds [extreme realism]; 3) concepts used only for the sake of clarification [fictionalism]. Now, your argument seems like it would work based upon fictionalism, but if one is a realist or an extreme realist, one would deny that possible worlds are the same as imagined worlds and therefore they would deny that the set of possible worlds rely upon our existence.
So I think your argument works, but only if one uses a fictionalist account of possible worlds. I, personally, am more of a realist, so I’m sympathetic to the argument but not convinced.
It could be worth developing if you take into account the nuances of fictionalism, include an argument for that position, and establish the necessary link between existence and possibility.
Now regarding the latter part of your post: you asked if “every time you imagine a possible world, that possible world is depend[ent] on your existence, making you a necessary being for that world alone?”
I would answer by saying this clearly does conflate possible worlds with imagined worlds. I’m not convinced at all that the set of possible worlds just is the set of imagined worlds, so I do not think that I am a necessary being for imagined worlds/possible worlds. Further, it seems one would have to clarify what is meant by “imagined world” because it is definitely being used here with a different sense than that of “possible world.”
Thanks for the interesting comment!
Posted by J.W. Wartick | February 4, 2012, 5:52 PMThen how do you show that God exists in all possible worlds if I think I can picture a possible world existing on its own? Can I not metaphysically think of a world existing without God? This is the part I do not get.
Posted by Mac Johnson | February 5, 2012, 11:46 AMAgain, this would seem to conflate imagined worlds with possible worlds. Just because I can imagine things doesn’t meant they are actually possible. Possible worlds are a restrictive set: they include only those worlds which are actually possible. If God is logically necessary, then any world we imagine in which there is no God is, strictly speaking, impossible. Of course we imagine impossible things all the time. I think you’re very loosely using the term “picture” or “imagine” and making it use the same sense as “possible” which it definitely is not.
Posted by J.W. Wartick | February 5, 2012, 4:28 PM