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.
J.W. Wartick - Reconstructing Faith 
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 PMWhat on earth does the phrase “near infinite” mean?? Either a series is infinite – i.e. is unending – or it is not. How can it be “near unending”?
Posted by Allistair Graham | November 6, 2016, 11:06 AMHi 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 AMABSOLUTELY wrong. JW says: “A valid argument cannot beg the question.” A FORMALLY valid argument can beg the question. As any logic textbook will state: A strong deductive argument must be valid AND avoid question-begging, ambiguity etc.If an argument is question-begging then it assumes the truth of its conclusion in a premise (and hence has no cogency) but can still be formally valid. Validity is the minimal requirement of a deductive argument.
Posted by Aristotle341 | May 31, 2012, 10:49 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 PMNo you should not concede, Mateo, because I believe you are entirely correct. Plantinga’s argument is question-begging because in modal logic MNp (it is possible that it is necessary that p) is logically equivalent to Np (it is necessary that p), which was your original insight. In other words, they say the same thing. Indeed, Rod Girle (Possible Worlds, p46) has this to say: “In fact, in S5 any uninterrupted sequence of modal operators is equivalent to just the last in the sequence. This means that there are really only three modalities in S5. They are no modality, possibility and necessity.” This means that (1) entails (2) ONLY in the trivial sense of claiming p entails p (i.e. being a Texan entails being a Texan) but not in the non-trivial sense of asserting p entails q (i.e. being a Texan entails being an American). Hence, Premise (1) says the same thing as Premise (2), in which case you can do away with (1) and just have (2), which is the thing that needs to be shown (as deriving p from Np I take as axiomatically true). Even though the argument if FORMALLY valid, it is informally invalid, as you pointed out.
Posted by Aristotle341 | May 31, 2012, 11:31 AMI think you are confused , the ontological argument states that a certain statement is possible,viz., a maximally great being exists. It doesn’t say “it is possible that it is necessary that a maximally great being exists.
Posted by Christopher | June 17, 2012, 8:34 AMAristotle, I think you are confused. The ontological arguments states that a certain statement is possible, viz., “That a maximally great being exists” it is not “It is possible that it is necessary that a maximally great being exists. A fortiori, William Lane Craig has pointed out this flaw, it confuses logical equivalence with synonymity. Those two statements are logically equivalent, but do not MEAN the same thing as the meaning is relevant to epistemic status. So you can’t mistake “Possibly necessary” being equivalent to “necessary” if you say they MEAN the same thing. And it is a matter of deduction, the nature of a deductive argument is that the conclusion is implicit and makes a presence to the conclusion. So, I don’t think its logically circular, don’t know if it is epistemically circular either. Say that an argument is epistemically circular if for any cognizer C, such an argument has as its conclusion a statement about the reliability of C’s source of beliefs.
Posted by philosophiachristi | June 17, 2012, 8:55 AMIn Response, to PhilosophiaCristi below: No I’m not confused, as Platinga states that a maximally great being is a maximally excellent being in all possible worlds. So if it is possible that a maximally great being exists it is stating that it is possible that it is necessary that a maximally excellent being exists. And the fact that they are logically equivalent means its is logically question begging. The “morning star” and “evening star” do not mean the same thing (in terms of sense) but they have the same reference and hence are logically equivalent. It is the latter we are interested in.
Posted by Aristotle341 | July 16, 2012, 5:27 AMI think you are assuming this argument does more than it is suppose to. The whole point of the argument is to show that if God is even metaphysically possible then God necessarily exists. In fact, the point of the argument is to show that the first premise is logically equivalent to its conclusion. But by your logic, the argument begs the question on purpose, but there are problems with thinking that. First off, begging the question is starting with a premise and offering no knew information in order to persuade for or prove your premise. The ontological argument doesn’t do that. It provides more information about the ontology of God in order to show that if God is metaphysically possible then God necessarily exists. Observing the first premise (◊G) doesn’t give anyone the clue that it also means (God exists). Therefore, the argument informs (not persuades) us more about the ontology and properties of God to show that the possibility of God (◊G) is equivalent to the existence of God. This is, in fact, circular in a sense, since the ontological argument shows us that premise 1 and the conclusion are equivalent. However, it doesn’t beg the question. As Aristotle pointed out circular reasoning and begging the question do not mean the same thing. An argument is still valid if it is circular as long as it offers to inform us. This is precisely what the ontological argument does. It informs us that saying, “God is possible” is equal to saying “God exists”. That is the entire purpose of it. It doesn’t beg the question by informing us two statements are equivalent. If the argument didn’t inform us of anything knew then it would be begging the question and be pointless.
Furthermore, Plantinga warns us against using this argument as irrefutable proof that God exists. It actually just shows God’s existence is rational to believe in. So I don’t think the conclusion proves God exists in reality beyond a shadow of doubt, it just shows it is rational to accept.
Overall though, the argument does, in fact, show that the possibility of God’s existence is equivalent to God’s existence. That is the whole point. Pointing out this obvious fact and assuming it begs the question it misunderstanding the argument’s intentions and structure.
Posted by IP | November 19, 2012, 12:03 PMIn REPLY TO IP (NOV 19 2012).
I agree that Plantinga warns against claiming that his OA is a proof – he explicitly denies that it is so (see P 112, God Freedom and Evil). He also explicitly states that the premise “Maximal Greatness is possibly exemplified” is contentious and may be rationally rejected (see Nature of Necessity). The reason it may be rationally rejected is because it can be considered as begging the question. Plantinga certainly attempts to defend it from this criticism but he fails, in my view. Remember, he wants to show maximal excellence in OUR world. Maximal greatness entails maximal excellence in EVERY world (and hence in OUR world). BUT maximal greatness is assumed as a premise. and hence it assumes what it seeks to prove. As an analogy: we want to know whether there is a marble in a particular urn X out of a dozen urns before us. We cannot look into any urn, including X, to verify there is a marble there. So, we have to use argument. We assume (P) that EVERY urn has a marble in it. Therefore, X must have an marble in it. The conclusion is valid but question begging. Certainly, you would not consider it persuasive unless there is an independent argument to accept P. But there isn’t. This is the same problem with Plantinga’s argument.
Posted by Aristotle341 | February 6, 2013, 2:09 PMTwo things can entail without begging the question, as that is the nature of a circular argument. Something doesn’t automatically beg the question if two things are logically equivalent.
You are once again assuming this is not already none. The point of the argument is to show that P1 (maximal greatness) is equivalent to the conclusion(maximal excellence in every possible world). Every time one says it is possible God exists that automatically means they are saying God exists. This is not question begging though because it operates as an informing argument and because the argument is not merely 2 premises. The least it could be is 3.
P1: if it is possible God exists then God exists.
P2: It is possible God exists
C: Therefore God exists.
If the OA begged the question it could only rely on 1 premise, as that is what is means to beg the question. However, P2 could either be – It is possible God exists or It is not possible God exists. So the OA doesn’t beg the question, as it has to draw from the ontological claim in P1 and the possibility of God’s existence in P2. We know P1 is the case because of the independent reason of the ontology of God. He is either impossible or necessary. So if it possible He exists then He exists, as there is no contingent middle ground. P2 also has independent reasons as we can draw a pessimistic inference from the repeated failures to show God is incoherent or an abductive inference from natural theology.
Again you have an odd definition of begging the question. For an argument to beg the question it cannot just show logical equivalence, it can only draw support from one single premise. The OA clearly doesn’t do that. It is circular, no doubt. But in an informative way so it cannot be question begging or invalid.
Posted by IP | February 9, 2013, 5:05 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 AMGodlessons states: “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.” As stated this is actually incorrect, as JWW points out. You need to re-state your case as: “When using S5 modal logic, saying ‘something is possibly necessary’ is logically equivalent (have identical truth values in any situation) to saying ‘something is necessary’.” This does not mean there is a contradiction in the premises, but rather, the argument begs the question (because the OA aims to show that something, i.e. God, is logically necessary). Therefore, the argument provides no support for its conclusion.
Posted by Aristotle341 | May 31, 2012, 1:41 PMSomeone 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 PMJWW, to deny premise (1) is to ASSUME that atheism is logically impossible. It would be the theist who begs the question here. Of course, one could use the theistic OA to conclude God exists and therefore deduce that Premise (1) of the atheistic OA is false, but then the atheist can do the opposite. It should be noted that Plantinga gives an inverted version of his OA similar to this and concludes that his OA is NOT a successful piece of natural theology because rational persons can reject its premises. I would go further, and say although valid, Plantinga’s OA begs the question, and therefore provides no rational support for its conclusion at all.
Posted by Aristotle341 | May 31, 2012, 1:58 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 AMHi Mr. Wartick – The Goldbach’s Conjecture parody is very interesting and your post helped me to see why it doesn’t work, but I think your comment here beats around the bush a little. I don’t think you need to say that we’re “on uneven ground” regarding the truth or falsity of GF (though that may be what you think for independent reasons). See what you think. Take two propositions:
GT = Goldbach’s Conjecture is true
GF = Goldbach’s Conjecture is false
It seems to me that the parody gets its oomph from (I think this is an elaboration on what you say) the readers’ uneasiness that the parody could be run on either claim, and we could thus prove either GT or GF. That would be nasty.
One of these propositions is logically (necessarily) true and the other is logically (necessarily) false. That means that one of them is logically coherent and the other isn’t. If at some time in the future we discover which of them it is, it will be because we have discovered a theorem for one of them. Presumably at that time we’ll understand why the other is logically incoherent.
So whichever one is true – GT or GF, the other is logically incoherent. Then, on Parrish’s version, we get a sound argument for the true one, but the false one cannot fund a parody since there would be a false premise. So in fact, we cannot run the parody on both of them: it’s just that we don’t at present know which one the parody works with and which it doesn’t.
Posted by Luke Kallberg | September 12, 2018, 10:50 PMI 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 PMIs there any account of the ontological argument that actually describes the frame being used, and what it means by saying that the idea is “coherent”? I think it’d be very difficult to find anybody who understands the argument who believes it to be impossible to construct an S5-type frame in which Premise 1 and 2 hold (which is how I interpret the suggestion that it is “coherent”), and that the rest follows from there. However, the argument should be about whether or not this frame contains the actual world; without proof that the negations of Premise 1 and 2 are inconsistent, we should have two disjoint models, only one which could contain the actual world.
It would appear that the frame being used in the argument is somehow the superframe of superframes; the S5 frame to which every other frame would be a subframe. The question then is: Is this necessarily existent God – on top of being coherent with some S5 model – would be consistent with a model defined over this all-encompassing frame, using an accessibility relation which interconnects every member of the frame to every other member.
Being that I’ve seen no proof that either Ω (“It is possible that a maximally being exists, and exists necessarily”) or ~Ω (“It is NOT possible that […]”) is S5-incoherent (in the sense that you can’t construct a logically consistent S5-frame in which the statement holds), my position – when looking at the hypothesized superframe of superframes – remains that (◇Ω OR ~◇Ω) [and equivalent statements such as (□Ω OR □~Ω)]; going beyond that would require further proof.
Posted by tesseraktik | May 8, 2012, 5:25 AMSorry it has taken me so long to get back to you.
I’m not sure what your last paragraph draws out other than a tautology. To say we can’t go beyond that seems to undercut the possibility of even drawing inferences about the existence of God. Of course, perhaps what you mean is that we can’t know that God necessarily exists, but that would confuse epistemology with ontology. Perhaps you could tell me what you mean to draw out there.
Regarding the first part of the post and the analysis of frames. It is necessarily the case that if something exists necessarily, it exists in every possible world, so I’m not sure how one could say that it isn’t about the actual world already.
Posted by J.W. Wartick | May 18, 2012, 8:38 PMHi there!
Indeed, the statement (◇Ω OR ~◇Ω) isn’t terribly informative. The point is more that one doesn’t have to choose between (◇Ω) or (~◇Ω); until further information is provided, it makes more sense to stick to (◇Ω OR ~◇Ω).
The reason I point this out is that some like to use the ontological argument to shift the burden of proof, whereas I feel it does no such thing.
“Regarding the first part of the post and the analysis of frames. It is necessarily the case that if something exists necessarily, it exists in every possible world, so I’m not sure how one could say that it isn’t about the actual world already.”
However, every claim of possibility and necessity must take two things into account:
1) the set of frames
2) the accessibility relation between them
To me, all the ontological argument really does is divide the set of all possible worlds in which Ω is well-formed into two subframes: One where Ω in every PW, and one where ~Ω in every PW. It then states that we must be in either one subset or the other (which is about as informative as the statement (◇Ω OR ~◇Ω)).
To use the ontological argument, you’d need the S5-model which is a supermodel to all other S5-models: One where every possible world which is free from contradictions in any S5-model is connected to every other such world by an S5-type relation, even possible worlds containing statements about other possible worlds. I am doubtful that such a model can be constructed. If it did, we’d be getting world where □Ω connected to worlds with □~Ω, resulting in a contradiction.
Either that, or you need to show that out of the two subframes (one where Ω in all worlds, one where ~Ω in all worlds), we must necessarily be in the one where Ω in all worlds, thus making Ω a matter of epistemology.
Posted by tesseraktik | May 29, 2012, 9:42 AMThanks for coming back and continuing our discussion! I appreciate your valuable comments, a lot.
One thing I’m not sure I follow is why you think that “To use the ontological argument, you’d need the S5-model which is a supermodel to all other S5-models: One where every possible world which is free from contradictions in any S5-model is connected to every other such world by an S5-type relation, even possible worlds containing statements about other possible worlds.”
Simply put, if something necessarily exists, then it exists in every possible world. There doesn’t need to be a superstructure. Could you explain why you think there would have to be?
Posted by J.W. Wartick | May 29, 2012, 10:32 AM“Thanks for coming back and continuing our discussion! I appreciate your valuable comments, a lot.”
…and to you, as well 🙂
“Simply put, if something necessarily exists, then it exists in every possible world. There doesn’t need to be a superstructure. Could you explain why you think there would have to be?”
I very much disagree with this: If you’re using modal logic, then the claim “X is necessarily true” is basically an abbreviation of the statement “X is necessarily true in the possible world W in the frame F with respect to the accessibility relation R”.
This is why when you switch models, strictly “local” logical statements remain unchanged, whereas modal statements (that is, ones that make statements about other possible worlds) must be reevaluated.
To illustrate this, take a very simple S5-type model, m: A single world w which is accessible to itself.
In this model, every statement that is true at w is NECESSARILY true at w in the model M.
Now, take the S5-type model m’: A single world w’ which is accessible to itself.
Every statement that is true at w’ is NECESSARILY true at w’ in the model m’.
Now, take the compound model M, consisting of the worlds w and w’, both accessible both to themselves and to each other.
Now, the local statements remain unchanged, but all necessity claims must be re-evaluated: If A was true in w in m, then □A was true in w in m. Likewise, if ~A was true in w’ in m’, then □~A was true in w’ in m’.
However, □A is not true in w in M, nor is □~A true in w’ in M. Instead, (A & ◇A & ◇~A) is true in w, and (~A & ◇A & ◇~A) is true in w’.
Modal claims are model-dependant, which is why I feel that I can’t draw any conclusions from the modal ontological argument without a clear definition of the model being used.
Specifically, until I know the criteria for inclusion in this model, I can’t see why I should grant Ω over ~Ω, nor can I say whether or not the real world is in this model.
In fact, even if S5 modal logic is free from contradictions (which I’m assuming here), I can’t say for certain that the model you’re using is.
Posted by tesseraktik | May 29, 2012, 11:57 AMI think you’re wrong on this. One of the fundamental axioms of S5 modal logic is ◊□x⊃□x or ◊□x iff □x (Hughes & Cressewell, A New Introduction to Modal Logic, 58). Furthermore, necessary existence is the existence in every possible world (Plantinga, “The Nature of Necessity”, 55).
So I’m not sure where this objection is coming from. If something exists necessarily, it exists in all possible worlds. Our own world is a possible world, so if □x, then x in our world.
Posted by J.W. Wartick | May 29, 2012, 12:27 PM“Furthermore, necessary existence is the existence in every possible world (Plantinga, “The Nature of Necessity”, 55). ”
…necessary existence in world w in the model M is existence in every world accessible to w in M.
“I think you’re wrong on this. One of the fundamental axioms of S5 modal logic is ◊□x⊃□x or ◊□x iff □x (Hughes & Cressewell, A New Introduction to Modal Logic, 58).”
Yes, possible necessity in S5 is equivalent to necessity. However, those claims are still made within a single model.
In the metaphor adopted by Hughes and Cresswell, consider a set S of people with pieces of paper, each of which has a number of letters written on it.
If the model is S5, it means that:
a) Every person in S can see him-/herself. We write this as xRx ∀x∈S (Reflexive)
b) Let a,b be persons inS. Then, if a can see b, b can also see a. We can write this as aRb → bRa ∀a,b∈S. (Symmetric)
c) If a, b and c are persons in S, then if a and b can both see c, a can also see b. We write this as aRc & bRc → aRb. We write this as ∀a,b,c∈S. (Euclidean)
[From this you can also deduce the Transistive property: aRb & bRc → aRc ∀a,b,c∈S. This means that an S5-type accessibility relation is in fact an equivalence relation, since it’s Reflexive, Symmetric and Transitive.]
In this metaphor, when somebody calls out a letter, say “A!”, you raise your hand if A is on your sheet of paper, and otherwise leave it down.
If somebody shouts the negation of a letter, say “~A!”, you raise it if you left it down for “A!”
[In this metaphor, you may only shout “~A!” if you’ve already shouted “A!”.]
If somebody shouts a possibility claim, such as “◇A!”, you raise it if an only if at least one person you could see (including yourself) raised their hand when “A!” was shouted.
[You may only shout “◇A!” if you’ve already shouted “A!”.]
Similarly for “◇~A!”.
If somebody shouts a necessity claim, such as “□A!”, you raise your hand iff ALL of the people you can see (including yourself) raised theirs when “A!” was shouted.
[You may only shout “□A!” if you’ve already shouted “A!”.]
Similarly for “□~A!”.
By expanding this, you can also have statements like “◇□A!”. You raise your hand for this iff at least one person you could see raised their hand for “□A!”.
Now, because this system is S5, every person you can see can see exactly the same people as you, so if you saw one of them raise their hand for “□A!”, it means that everybody you could see raised their hand for “A!”, and therefore, you too must raise your hand for “□A!”.
That is: ◇□A ⊃ □A
Now, let’s assume that it really was the case that you raised your hand for “□A!”, because everybody you could see raised it for “A!”, and likewise for “◇□A!”.
However, now something happens. Another person enters the room, and he/she has their own piece of paper. Furthermore, he/she can see exactly the same people as you (including yourself), and all of them can see him/her, so the system remains S5.
However, there’s a catch: This new person doesn’t have the letter A on their paper, so if “A!” is called again, and then “□A!”, you’ll still raise your hand for the first call, but keep it DOWN for the latter.
Have you contradicted yourself? No: The first time “□A!” was called, it was with respect to a different seating arrangement. It was really an abbreviation of “□A with the current seating arrangement!”
When a new person entered the room, you got a new seating arrangement and therefore had to reevaluate all of your necessity claims.
Likewise, if a person had left the room, or if your vision had been obscured, you would have had to reevaluate all of your possibility claims.
Another illustration:
Consider two consecutive coin tosses, and the following statements:
H1: The first coin has been tossed, and it landed on HEADS.
T1: The first coin has been tossed, and it landed on TAILS.
H2: The second coin has been tossed, and it landed on HEADS.
T2: The second coin has been tossed, and it landed on TAILS.
As we have four boolean variables, there are a total of 2^4 = 16 different combinations of values; sixteen possible worlds. I’ve illustrated them here: http://imageshack.us/photo/my-images/560/cointosses.png/
[Here, I use V to mean “OR”, since the font didn’t support the wedge symbol.]
Now, I’d like you to first look at the left-hand side, where I have mapped out the seven “realistic” possibilities. For the time being, this is our FRAME; our set of possible worlds. I’ll call it G (for “Green”). The complement – the 9 “unrealistic” possibilities – I shall call U (for “Unrealistic”). The union of these two sets – the frame containing all 16 worlds – I shall call S (for “Superframe”).
Taking G (green circles), I then define an accesibility relation, R:
(i) Every green circle is accessible to itself. (R is reflexive; xRx ∀x∈G)
(ii) If an arrow begins at circle a and ends at circle b, then a can access b (aRb).
(iii) aRb & bRc → aRc ∀a,b,c∈G (R is transitive)
(iv) If a can’t access b by any of the criteria above, then ~(aRb).
What we have here is an S4-type accessibility relation (because it’s reflexive and transitive). We can interpret it as “If we are at a and aRb, then b might happen at some point in the future.” What we have is a very basic epistemic model.
Now let’s look at some of the claims we can make using this model:
(1) In the world furthest to the left, before any coin tosses have been made, we can say ◇H1 & ◇T1. However, we can’t say ◇(H1 & T1).
(2) In the bottom world in the middle column, we can say ~◇H1, or – equivalently – □~H1. We can also say □T1. We can also say (◇H2 & ◇T2), but not ◇(H2 & T2).
(3) In all of these worlds, we can say (H1 ⊃ ~T1 & T1 ⊃ ~H1). We can interpret this as “The first coin toss can result in either heads or tails, but not both.” We can make the same claim for the second coin toss.
(4) In all of these worlds, we can say ~(H1 V T1) ⊃ ~(H2 V T2). We can interpret this as “You have to do the first coin toss before you do the second.”
(5) The column furthest to the right consists of worlds where a⊃□a and ~a⊃□~a for any well-formed statement a. In the bottom world in the right-most column, we can say that because T2 is true, □T2 is true, and since ((T1 & T2) V (T1 & H1)) is true, □((T1 & T2) V (T1 & H1)) is also true.
Okay, so that’s what we get from the accessibility relation R. Now, I’ll define the accessibility R’.
It’s the same as R, except you modify (ii) so that the arrows go both ways; R’, unlike R, is symmetic. It’s now a model not just of what’s happened and what might happen, but a model of what’s happened, what might happen and what COULD have happened.
Using R’, aRb ∀x∈G; they’re all interconnected. If follows that it’s euclidean (aRc & bRc → aRb and vice versa), and therefore R’ is S5.
Now, let’s reexamine our statements (1)-(5):
(1) Remains unchanged.
(2) We can no longer say that ~◇H1; since all the worlds are not accessible to each other, this world can access worlds where H1 is true, and therefore ◇H1, or – equivalently – ~□~H1. We also can’t say □T1. However, we can still say (◇H2 & ◇T2), but not ◇(H2 & T2).
(3)-(4) Remain unchanged. [In fact, G is precisely the set of worlds in S such that (3) & (4) hold true. Using both R and R’, it’s possible to add □ to the beginning of these statements; they are necessary truths.]
(5) Here, a no longer implies □a. T2 is still true in the bottom right world, but not □T2. Likewise, the last claim of (5) now seems quite ridiculous: “Either both coin tosses land on tails, or the first lands on both heads and tails.”
Now, at last, I’d like to point your attention to the superframe, S, consisting of both realistic and unrealistic possible worlds. The stars mark cases where a coin toss results in both heads and tails. The blue markers mark cases where the first coin toss comes after the second. What’s more, I’d like to define the accessibility relation Q, which is defined thusly:
(i) aQb ∀a,b∈S
That is, all worlds of S are accessible to one another through Q. It follows that Q has all the criteria for S5.
This is not an inconsistent model in terms of modal logic. There’s nothing wrong with the statement (H1 & H2). (3) and (4) in the previous section were precepts of reality, not consequences of the axioms of modal logic; due to the properties of consecutive coin tosses, we chose to consider models excluding heads-and-tails results, and cases where the second coin toss precedes the first. However, if we were to interpret H1 as “Hillary’s first child is a boy” and T1 as “Ted’s first child is a boy”, we’d probably prefer to work with a model where (H1&T1) is treated as a “realistic” alternative.
Note that the interpretation of H1, H2, T1 and T2 are not aspects of our models, which is just the frame (such as G or S), accessibility relation (such as R, R’ or Q) and the local truth value operator (which hasn’t been discussed, but it’s what we’re using when we say “statement x is true at world w”). The fact that Hillary and Ted can both have a male firstborn child doesn’t impede our ability to consider models where they can’t.
Also, note that the interpretation of H1, H2, T1 and T2 are not aspects of modal logic, which is just the set of rules we use to say “Given a model M, and the statements A and B, what other statements can we make?” Modal logic in fact allows us to consider statements which seem nonsensical to us: We can have worlds full of married bachelors, square circles, talking unicorns and inspiring dialogue on “2½ Men”.
A change of interpretation is just that: A change of interpretation.
Now, let’s look at statements (1)-(5), again, using the frame S and accessibility relation Q:
(1) (◇H1 & ◇T1) remains true [in all worlds, in fact]. However, unlike in the previous models, we can now also say ◇(H1 & T1) [again, in all worlds]. It violates our precepts of reality if we take this to be a coin toss, but we’re not violating modal logic.
(2) Same as in the model with R’, except we can now say ◇(H2 & T2).
(3)-(4) As has been mentioned, we’ve thrown out these two statements.
(5) As with R’, a no longer implies □a.
Notice how when we changed from one S5 model to a larger one, several modal statements have changed. Most interestingly, some necessity statements broke down. In the first two models, we could have said □~(H2 & T2), and □(H1⊃~T1), and □(H2 ⊃ (H1 V T1). However, modal statements are model-dependent.
Now, consider this question: Is there an S5-type model where H1 ⊃ □H1?
It’s not true in any of the models we’ve considered, but it’s easy to construct them. Even if we disclude the empty model (a model with the empty set as its frame; it’s S5, but kind of boring) and models containing “islands” (for example, a model over any subframe F⊆S with the accessibility relation T : xTy if and only if x=y; it’s S5, but it’s kind of pointless to do modal logic over), I can still come up with several. In total, I believe there are 512 such models, just using subframes of S (but, of course, without that restriction, I could take it to infinity).
In 256 of those, H1 is both true and necessarily true; in the other half, H1 is untrue and necessarily untrue.
So, my point – and I am sorry it’s taken me this long to get to it – is this:
When you tell me “I have an S5-type model where God exists, and does so necessarily!”, my reaction is “Okay, cool; I have 256 different S5-type models where a particular coin toss lands on heads, and does so necessarily.”
My reaction would be the same if somebody told me “I have an S5-type model where God DOESN’T exist, and non-exists necessarily.”
Now, when you come with the statement “I have an S5-type model where God exists, and does so necessarily, and in a world accessible from the ACTUAL world!”, my reaction instead is “Really? Define it for me!”
Meanwhile, if some other guy comes in and says “I have an S5-type model where God DOESN’T exist, and non-exists necessarily, and in a world accessible from the ACTUAL world!”, my reaction would still be “Really? Define it for me!”
In short: I don’t doubt that you can have S5-models where □Ω. What I’ll need proof to accept is that you can have an S5-model where ◇□Ω (or ◇□~Ω) is true in the actual world.
Now, if I were given rigorous criteria for inclusion in the frame being considered, and a rigorous definition of the accessibility relation, then I could move on to consider whether or not it’s a consistent model.
I realize that that may be asking for a bit much, and I’m willing to work with less, such as a rigorous but incomplete model, which would allow me to check what consequences substituting Ω with ~Ω would have, or interpreting Ω not as “GOD exists” but as “The first coin turns up heads”. However, thus far I haven’t seen anything that even allows me to approach the matter.
Anyhow, sorry for the long post; let me know if you want me to clarify anything!
Posted by tesseraktik | May 29, 2012, 6:23 PMOkay, there is no way for me to fairly take the time needed to respond to this lengthy critique. My main point is that I still don’t see why you’re taking necessity as model-relative. A necessary truth just is a necessary truth. I don’t think your examples show that accessibility can change necessity. In fact, I think that is incorrect. I would need to see a much better argument to convince me otherwise.
Posted by J.W. Wartick | June 1, 2012, 1:04 PM[Sorry if I double-posted this; not sure if the previous one got through.}
“My main point is that I still don’t see why you’re taking necessity as model-relative.”
…because modal statements are dependent on the model.
“A necessary truth just is a necessary truth.”
…and how can I check if Ω is a necessary truth in the actual world without a well-defined model?
“I don’t think your examples show that accessibility can change necessity.”
“Necessarily true in world w” in modal logic is defined as “True in every world accessible from w”. My model has multiple submodels where the outcome of the first coin toss is necessarily heads. Expanding the frame to include a world where it isn’t heads and making all the worlds mutually accessible changes it to a contingent truth.
Let’s put it simply:
You have an S5 model Ω in every possible world.
I have an S5 model where ~Ω in every possible world.
Show me why the actual world must be in your model, or why it can’t possibly be in mine.
Posted by tesseraktik | June 1, 2012, 1:20 PMThe possibility discussed is not just “possible from a perspective” but logical possibility. Are you suggesting logic changes from world to world?
Posted by J.W. Wartick | June 6, 2012, 9:14 AMThe propositional calculus remains the same from world to world, and the axioms and construction rules of modal logic remain the same from world to world and model to model. What varies is what theorems are true:
Theorems that only concern the local world are dependent on what world you’re in, but independent of the model.
Modal statements are dependent both on the chosen world and the chosen model.
Without a model, I have no reason to take your claim that God is in any way “possible” seriously. Your statement may not be internally inconsistent, in the sense that you can construct a model where it’s true, but it says nothing of wheter or not it’s actually true in any S5 model containing the actual world.
That’s why my question from the beginning has been if you can actually account for the model you’re using to claim that your Ω is possible.
Posted by tesseraktik | June 6, 2012, 9:55 AMIn Reply to JWW’s comment on May 29 in this thread to Tesseraktik: “Simply put, if something necessarily exists, then it exists in every possible world. There doesn’t need to be a superstructure. Could you explain why you think there would have to be?”
There DOES need to be a superstructure in Plantinga’s ontological argument because Plantinga states that It is possible that it is necessary that there is a being with omnipotence etc. (This is because a maximally great being is a maximally excellent being that exists in ALL possible worlds).
In terms of possible world semantics, a necessary statement is one that is true in ALL possible worlds (of that setup). A possible statement is on that is true in A possible world. So how can there be A possible world in which a statement is true in ALL possible worlds unless there is a superstructure (i.e. a world which has all possible worlds as sub-worlds within it). In S5 the accessibility relation is equivalence between logical worlds, not sub-worlds. This is why is S5 “It is possible that it is necessary that” is logically equivalent to “it is necessary that” (as you yourself acknowledge). This equivalence would NOT hold if in S5 there could be sub-worlds (see proof below*) – and Plantinga’s argument clearly requires sub-worlds.
Hence, as I keep on saying on this thread: Plantinga’s argument is logically question-begging.
* Such a position is self-referential for if a possible world w contains all possible worlds as sub-worlds, w must also contain w as a sub-world, and this sub-world w would contain all all possible words as sub-sub-worlds and so on infinitum.
Posted by Aristotle341 | July 16, 2012, 6:25 AMHello sir,
I was hoping you could help me with another question. Why is God necessary? It seems like this is just assumed.
I have been contemplating this for a while and I think I figured it out, but I thought I should check with you on this as well. Is God necessary because of His properties – Omnipotence, omniscience, moral perfection?
For example, since God is omnipotent He must be necessarily in all possible worlds because if a possible world exists without God then His power is limited to only some worlds, meaning God is not all powerful. Therefore, God must be in all possible worlds if He is omnipotent.
Is this why God is necessary?
Posted by Mac Johnson | June 20, 2012, 8:05 PMI think your argument from omnipotence to necessity is very interesting.
A simpler answer can also be provided: God is defined as the greatest possible being. As such, God exists necessarily.
Posted by J.W. Wartick | June 21, 2012, 3:26 AMBut doesn’t that beg the question? Defining God as maximally great is the same as saying God is necessary, which is saying God exist because I said He necessarily must?
What am I missing? Please Help?
Posted by Mac Johnson | June 21, 2012, 7:29 PMIt doesn’t beg the question because one could say “If God exists, God exists necessarily.” The question, of course, is whether God does exist.
Posted by J.W. Wartick | June 22, 2012, 6:39 AMThe traditional understanding of omnipotence is that God can only affect logical possible outcomes. Since God affecting or actualizing worlds at which He does not exist is logically impossible, there is nothing about omnipotence that entails necessity.
Posted by rayndeon | June 23, 2012, 2:45 PMI think this is a misunderstanding of modality.
Posted by J.W. Wartick | June 23, 2012, 5:52 PMCould you please elaborate?
Posted by rayndeon | June 23, 2012, 5:55 PMOmnipotence is the ability to do anything logically possible. Thus, unless it is impossible for a being to exist in all possible worlds (a claim which would need serious argument), then it seems omnipotence would have to be instantiated in all possible worlds. You’ve reversed the modality.
Posted by J.W. Wartick | June 24, 2012, 5:22 AMMy reply had nothing to do with the possibility or impossibility of necessary concrete objects. It had to do with that, if an omnipotent being existed at some world, it obviously cannot actualize worlds at which it fails to exist. So, omnipotence doesn’t entail necessity. You’ll need additional properties (in this case, maximal greatness) in order to make the argument that omnipotence is compossible with necessary existence, not merely the definition of omnipotence alone.
Posted by rayndeon | June 24, 2012, 12:11 PMIt’s not clear how omnipotence would be omnipotence if only instantiated in certain possible worlds. For example, a conceivably “more omnipotent being” could exist in one more world, and then the first being would not actually be omnipotent.
Posted by J.W. Wartick | June 24, 2012, 3:53 PMI don’t see how you can be “more” omnipotent than another. Being unable to actualize a world at which you fail to exist isn’t, according to most analyses of omnnipotence, a lacking in power. Possible worlds don’t really “exist” per se as flesh and blood entities (unless you entertain modal realism), so I can’t see how it could possibly threaten an all-powerful being’s power. If you’re omnipotent, then you’re every bit as omnipotent as some other omnipotent entity that happens to exist in some abstract possible world w.
Posted by rayndeon | June 24, 2012, 3:58 PMYou’re actually restricting the definition beyond the restrictions of classical theology. Classical theology holds that omnipotence is the capacity to do whatever is logically possible. Thus, unless it is logically impossible for a being to exist in a certain world, then omnipotence would entail its existence in that world.
Posted by J.W. Wartick | June 24, 2012, 4:01 PMIn other words, I think your definition of omnipotence is incorrect.
Posted by J.W. Wartick | June 24, 2012, 4:01 PMThat doesn’t follow from that an omnipotent being can do whatever is logically possible. If some omnipotent being exists at some world w and fails to exist at w*, the being cannot obviously actualize worlds like w*. But, since it is impossible for an omnipotent being to fail to exist at w*, “actualizing w*” is a logically impossible state of affairs and is not exemplified at any possible world, and hence, not within the purview of power of the omnipotent being. Since an omnipotent being can only do the logically possible, being unable to actualize worlds at which some contingent omnipotent being did not exist does not make said being non-omnipotent.
Indeed, Plantinga makes this very argument when constructing his FWD in the same book he makes the MOA. There are metaphysically possible worlds at which all beings do good, but not possible for God to actualize, given contingent counterfactuals of freedom. This doesn’t threaten said being’s omnipotence at all. Likewise, being unable to actualize or “hold power” over worlds at which said being doesn’t exist likewise poses no threat for an omnipotent being’s power. Hence, that omnipotence entails necessary existence is simply false.
Posted by rayndeon | June 24, 2012, 5:24 PMOk, hopefully I’ll get it the more I think about it. By the way, this argument from omnipotence to necessity isn’t mine. I took it from a comment by a youtube user named InspiringPhilosophy. In fact, one of his videos is how I found your blog. He has links to your articles in the information section of some of his videos.
Thanks again
Posted by Mac Johnson | June 22, 2012, 5:47 PMThis is the maximally worst argument for God’s existence. All you’re saying, and this really is all you’re saying, is that if we can conceive of a necessary being’s existence, then that being necessarily exists. Why even try to make it into a fancy looking syllogism at all? I could make this argument for a maximally evil being, or a maximally funny being, surely a being that exists in all possible worlds is funnier than one who only exists in one. I could argue for a maximally bright being, or annoying, or place any adjective between the words ‘maximally’ and ‘being,’ and conclude by your logic that this being exists. All I have to do is say: the Maximally Stupid Being (MSB) necessarily exists by definition, without explaining why this should be the case, and if you want to hold on to the ontological argument, you’ll have to grant that such a being necessarily exists right alongside the maximally great being.
Posted by iblis22 | December 30, 2013, 2:22 PMThank you for your comment. I think you raise what is perhaps the most common objection to the ontological argument. The thing which is missing from your reductio is that the Most Stupid Being would not have necessity as part of its being for any reason whatsoever other than as an ad hoc objection to the ontological argument.
Posted by J.W. Wartick | December 31, 2013, 4:57 PMBut your definition of the MGB is also ad hoc, so my objection stands.
Posted by iblis22 | December 31, 2013, 5:53 PMFeel free to demonstrate your claims.
Posted by J.W. Wartick | December 31, 2013, 5:58 PMIn order to prove the existence of the dumbest possible being (DPB), I have defined the DPB as necessary. This is an ad hoc definition constructed to prove the existence of the DPB by Parrish’s logic. If this is ad hoc then it is also ad hoc to define the GPB as necessary.
I’m assuming that you claim that a necessary being is greater than a contingent being, but I don’t see how there is a direct connection between greatness and necessity. It makes just as much sense to claim that a being who exists necessarily is dumber than a being who exists contingently. The DPB which exists contingently can have equally dumb characteristics as the DPB which exists contingently. And the GPB which exists contingently can have the omni characteristics which define greatness. Therefore, it seems that to define the GPB as necessary is an ad hoc definition to make the argument work.
Posted by iblis22 | December 31, 2013, 6:59 PM“Dumbness” is a concept relative to those defining the term. You’ve taken a concept which is on a sliding scale and confused it with logical necessity.
Posted by J.W. Wartick | December 31, 2013, 7:00 PM“Greatness” is a concept relative to those defining the term. You’ve taken a concept which is on a sliding scale and confused it with logical necessity.
Posted by iblis22 | December 31, 2013, 7:36 PMI admit I set a trap there. My point was that some concepts depend upon the definition of persons, while some do not. Maximal greatness is in the latter category. In particular, the concept that maximal greatness entails necessity is firmly in the latter camp.
You began this discussion, in part, with the notion that you don’t see any reason for thinking that necessity is greater than contingency. Perhaps that is true, and you simply do not grasp how contingency would be lesser than necessity. I admit I find that hard to believe, but I’ll grant you the benefit of the doubt. I would ask you: in what way could it be otherwise? If there were a being which existed in every possible world and–this is important–could not fail to exist; then in what way would that being be equivalent to or less than a being which both did not exist in every possible world and could fail to exist in the worlds in which that being did exist? Of course, part of your confusion may stem from viewing each property abstractly, which is decidedly not what Anselm, Plantinga, or Parrish would do. For them–particularly for Parrish, a friend of mine–I can tell you that the concept of a necessary being is not to be abstracted from the other properties of greatness.
Of course, you may persist in denying that such a concept is necessary. At that point I would say we are indeed at an impasse. I think the argument is convincing and irrefutable, simply supposing someone grants such a being is possible. You seem to think that opens the ontological floodgates. I would ask you to justify this concern; that is, to show that your attempts at reductio are in fact analogous.
Posted by J.W. Wartick | December 31, 2013, 7:45 PMI agree this seems to be an impasse. But I think we’re viewing necessity differently. If a being necessarily exists, that means it had to exist, and couldn’t have not existed. But an Almighty Being could currently exist even though it didn’t necessarily have to exist. That doesn’t mean it will fail to exist, or that anything could be powerful enough to bring it out of existence. And this being could still be as great, with respect to omnipotence, omnipresence, and omniscience, as the being would be if it necessarily existed. It doesn’t matter that a contingent being could be imagined to not exist in a possible world, because possible worlds are just ideas. We’re discussing the actual world, reality. Assuming that God exists, whether God necessarily exists or not, God is still the greatest possible being. But if we disagree here, then there is no point arguing about the question of necessity. I think there are other arguments that show that God necessarily exists, anyway, but I don’t like the Ontological one.
I can raise an additional objection to Parrish’s formulation. I’m very confused at why there is some kind of cumulative greatness that arises when we add possible worlds in which the great being could exist. Let’s say we have two possible worlds, and a greatest being exists in one but not the other. Now if we add a third possible world, where a greatest possible being exists, then how does that effect the greatness of the other being? These worlds are completely separate imaginary constructs, so how can an imagined change in one effect the other?
Posted by iblis22 | December 31, 2013, 9:12 PMLet me restate that last paragraph.
I can raise an additional objection to Parrish’s formulation. I’m very confused at why there is some kind of cumulative greatness that arises when we add possible worlds in which the great being could exist. Let’s say we have one possible world where the greatest possible being exists. Now if we add an additional possible world, where a greatest possible being exists, then how does that effect the greatness of the other being? These worlds are completely separate imaginary constructs, so how can an imagined change in one effect the other?
Posted by iblis22 | December 31, 2013, 9:14 PMReblogged this on Jesus Cares and commented:
Ontological Argument
Posted by Jesus' Princess | February 23, 2014, 2:43 AMI know this is all old stuff, I see some posts from as far back as 2010.
Is it allowed that a person put “The concept of all GPB’s are coherent (and thus broadly logically possible)?
or “The concept of no GPB is coherent….” or “The concept of no GPB’s are coherent…”?
Thx.
Posted by Josh | March 22, 2014, 11:16 PMWhat do you mean by “Is it allowed that a person put”? I’m just not entirely sure what you’re asking.
Posted by J.W. Wartick | March 23, 2014, 10:27 AMI’m not a trained individual of debating, proofs or argument creations. I just was wondering if a person who reads a theory or I guess an argument? Are you allowed to modify it? Or is it illegal? I mean, that it is published stuff?
The reason why I asked was because I see the direction the argument takes but why is it one god? What if you were Hindu and believed in many gods? Or a follower of Norse beliefs? And for that matter, what if you were an atheist, could you put “no greater being”? Could it be that humans, as we know it, are the highest level of a being?
Posted by Josh | March 23, 2014, 7:01 PMThe notion of a greatest possible being would imply, I would think, that we are certainly not it. I would guess that few people would agree that nothing could improve upon humanity.
Regarding any system with a pantheon (Norse/Hindu, for example), it is unclear how they could be the “greatest possible” being because each would have shared attributes with others. Regarding “no” greatest possible being; the assertion would essentially be to declare that it is impossible for a GPB to exist, and that would need support. That’s why I think this argument is successful.
Posted by J.W. Wartick | March 23, 2014, 9:48 PMI can totally respect your opinion on this equation. It works for you, but you are a monotheistic person. So was the people who came up with this argument and proof. It is a monotheistic equation custom designed for only one god.
Yes, the logic is correct, but anyone can say, “A=B, B=C, therefore C=A”. Once you start throwing around terms like “god-like” and “god” that is when I find fault in the argument.
Again, it is an argument designed for one god, by people who believe in one god.
On another note, there could be multiple gods, all with the same exact power and abilities but be totally independent of each other, with their own free will. I don’t expect you to be able to rationalize this because your faith is what it is, one god.
In closing. I always find it amusing when people of faith try to define or prove their god. Where is the faith in that?
Thanks for the blog. It was nice communicating with you about this subject.
Posted by Josh | March 24, 2014, 10:01 PMYour comment is an example of the fallacy known as the “genetic fallacy.” Simply because an argument comes from monotheists does not make it any less valid. Indeed, if you say the logic is correct, then you must either affirm the conclusion or remain in irrationality.
Posted by J.W. Wartick | March 24, 2014, 10:10 PMJosh,
One can’t have multiple greatest conceivable beings because the greatmaking properties of these beings would come into conflict. E.g., omnipotence. Each being would not have the power to do countless things (perhaps a near infinite number of things); namely, whatever the other beings decided to accomplish. This is a case like the “stone so big” argument often used against a single omnipotent being. In the case of a single omnipotent being the objection fails because we run into a contradiction with a single agent, a single power being able to do and not do the same thing. But if you introduce multiple omnipotent beings the logical contradiction disappears and the “stone so big” objection seems to go through.
Posted by Remington | March 25, 2014, 7:44 AMIf this argument does not allow a pantheon to exist, then how can it allow a trinity to exist? What is a logical reason for the impossibility of a million GPBs that does not also prove the impossibility of three GPBs?
Posted by iblis22 | March 25, 2014, 2:35 PMTheir oneness
Posted by Remington | March 25, 2014, 3:55 PMThe trinity would not be three GPBs but rather one. The Godhead is one being.
Posted by J.W. Wartick | March 25, 2014, 4:44 PMId add that this might be a problem for strong versions of social trinitarianism, but not for more traditional models that have a stronger view of God as a single being.
Posted by Remington | March 25, 2014, 4:51 PMBut I could as easily say, well there are 99 gods but they form one Panhead, and if you try to say it doesn’t make sense I’ll say it’s either above your head or deeply mysterious.
Posted by iblis22 | March 25, 2014, 5:09 PMWell you certainly could say that but you’d be talking nonsense. Christianity doesn’t say there are three gods which form one Godhead. Rather, there is one God in three persons. One substance.
Posted by J.W. Wartick | March 25, 2014, 6:47 PMWhat J.W. said. And if you said “Well what about a quadrinity?” Or something like that, fine. I can concede that such a concept isn’t subject to the “so big objection” but then a quadrinity wasn’t what Josh was talking about (or something anyone believes). I was addressing myself to Josh’s multiple gods suggestion.
Posted by Remington | March 25, 2014, 6:53 PMThis discussion has been going on for a long time! It just looks invalid to me. Look at the original premises:
3) If the concept of the GPB is coherent, then it exists in all possible worlds.
I don’t think so; the CONCEPT is of something which exists in all possible worlds. That doesn’t entail that it does in fact exist in all possible worlds.
4) But if it exists in all possible worlds, then it exists in the actual world.
It is the concept of something which exists in this world.
5) The GPB exists (Parrish, 82)
It is the concept of something which exists.
The fact that it exists in a possible world is being mishandled, in my opinion. If you think of something that exists in a possible world as ‘something that might have existed’, it becomes clearer.
3′ If the concept of the GPB is coherent, then it is the concept of something that exists in all possible worlds.
3a If it exists in some possible world, then it might have existed.
3b If it might have existed, it might have existed in all possible worlds
4′ But if it might have existed in all possible worlds, it might have existed in this world.
5′ The GPB might have existed.
Posted by Brian C | April 15, 2014, 2:39 AM