Is the ontological argument question begging? Short answer: some versions yes, others, no. For the long answer, read on:
Many versions of the ontological argument appear to beg the question. The Anselmian version of the argument seems invalid, but there are other formulations of it which avoid its invalidity (cf. Maydole’s chapter on the Ontological Argument in The Blackwell Companion to Natural Theology, eds. Craig + Moreland, 553ff). Then, Alvin Plantinga came along and introduced the modal ontological argument, which relies on S5 modal logic. I have discussed Plantinga’s argument elsewhere, as well as demonstrated its validity.
Therefore, we will focus on a new considerations. Consider the following very simple version of the modal ontological argument:
1) Possibly, God necessarily exists
2) Therefore, God necessarily exists
The argument seems, at first face, to be a very strange argument. However, the argument does not beg the question when viewed through modal logic. 1) does follow from 2) in a non-tautological way, but 1) must be established.
Symbolically, the argument is written as the following (Take “T” to be “God exists”):
1) ◊□T
2) □T
S5 modal logic is based upon this very axiom. Namely, ◊□x⊃□x or ◊□x iff □x (Hughes & Cressewell, A New Introduction to Modal Logic, 58). For in modal logic:
3) that which is “possible” exists in “some possible world.”
4) That which is necessary exists in all possible worlds
Therefore, if something is possibly necessary, then it must obtain in some possible world (3). however, if it is necessary, then it exists in all possible worlds (4). Therefore, if something is possibly (exists in some possible world) necessary (exists in all possible worlds), then it exists in all possible worlds.
Is this argument question begging? If it is, then it is not obviously so. Alexander Pruss has argued out that the argument is question begging only if it is directed at one who does not understand that 1) entails 2) (Pruss, The Principle of Sufficient Reason, 232). I’m not convinced that this is correct. Soundness of arguments don’t depend upon whether people understand them–they depend on whether they are valid or true. However, it seems Pruss has an intuitive point here, in that even if this argument isn’t question begging, it appears to be.
How might the theist respond? Well, Pruss argues that if the theist argues for the establishment of S5, then it is no longer question begging (232). Alvin Plantinga does just that in God, Freedom, and Evil, as Pruss points out. We’ve already established elsewhere that Plantinga’s argument doesn’t beg the question regardless (see here), but this symbolic proof is bolstered by providing an argument for S5.
Then, it seems to be the case that if S5 modality is valid, God necessarily exists.
Are there versions of the ontological argument that resist this reduction to the “simplistic” version offered here? Yes, there are. For example, Stephen Parrish’s ontological argument:
5) The concept of the GPB (Greatest Possible Being) is coherent (and thus broadly logically possible)
6) Necessarily, a being who is the GPB is necessarily existent, and would have (at least) omnipotence, omniscience, and moral perfection essentially.
7) If the concept of the GPB is coherent, then it exists in all possible worlds.
8 ) But if it exists in all possible worlds, then it exists in the actual world.
9) The GPB exists (Parrish, God and Necessity, 82)
This argument may initially seem to be susceptible to the same reduction, but it can avoid this reduction by lengthening it to:
10) the GPB is coherent (and logically possible)
11) the GPB’s coherence entails modal possibility
12) the GPB is necessary
13) modally, if something is possibly necessary, then it is necessary
14) the GPB exists necessarily
The key premise here is 10), because if it is true, then the rest of the argument follows necessarily. What reasons do we have for thinking 10) is true? Such a debate is beyond the scope of this post (good discussions can be found throughout theistic philosophy of religion–see, in particular, Craig and Moreland, Philosophical Foundations for a Christian Worldview and Swinburne, The Coherence of Theism; see also my brief discussion in the post on the argument here); but it seems to me that there is no incoherence in the concept. If that is the case, then I am justified in holding 14).
Therefore, it seems the modal ontological argument is not question begging, particularly if one argues first for the validity of S5 modality. Furthermore, there are other modal arguments which don’t rely on a reduction to a simple modal argument. For example, Parrish’s ontological argument relies instead upon the coherence of the GPB. Such arguments are successful if arguments against the GPB’s coherence are shown to be unsuccessful. In either case, God exists.
Ergo deus est.
SDG.
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.
Pruss, Alexander. The Principle of Sufficient Reason. Cambridge. 2006.
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J.W. Wartick - Reconstructing Faith 
I wonder — what about something like an AGPB, an Almost Greatest Possible Being? A being who is the greatest being in any world where it exists, but does not exist in all possible worlds, that is, is not a necessary being.
It seems that if an AGPB is possible (and I can’t see why it isn’t), then a GPB is impossible. And if a GPB is possible, than an AGPB isn’t.
But I can’t imagine why GPB is coherent and AGPB isn’t.
What do you think?
Posted by Cam | March 28, 2012, 5:00 PMBy definition the AGPB would not be compossible with the GPB. However, I think the logical priority would favor GPB, because it actually constitutes a simpler explanation (i.e. necessary existence as opposed to contingent greatness) and it fulfills the criteria of GPB better. For example, how is the AGPB actually analogous to the GPB? It does not exist in all possible worlds, and so there is a potentially greater possible being in any world in which the AGPB exists, which undermines the notion of the AGPB.
Posted by J.W. Wartick | March 29, 2012, 4:17 PMHi JW, the 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). In other words, they 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)
Posted by Aristotle341 | May 31, 2012, 10:34 AMI already showed symbolically that the argument does not beg the question in my other post on the topic.
Posted by J.W. Wartick | June 1, 2012, 1:01 PMYes, and have left posts there too. You cannot formally show that an argument begs the question because an argument-begging question is always deductively valid. In your symbolic argument, Premise [1] ◊(∃x)Ax begs the question. It doesn’t get more straightforward than that, does it?
Posted by Aristotle341 | June 6, 2012, 6:18 AMThe problem with this argument is that it is question begging since it relies on a semantic shift on the definition of God and appeals to possibility that equivocates between the two modes drawn. In the “Nature of Necessity”, Plantinga draws out the idea of a maximally excellent being (triomni) and then defines a maximally great being as a maximally excellent, necessary being.
In positing that a maximally great being is possible, Plantinga is asserting that maximal excellence being exemplified is possibly necessary and of course draws the conclusion that such a being is necessary and hence existent. But, stating that PNp is the same as asserting Np in S5; any combination of the possibility and necessity operators is equivalent to the last operator since per S5, the possibility and necessity modalities are accessible from each world.
So ultimately, Plantinga’s modal argument comes to little more than asserting that necessarily maximal excellent is exemplified; which is equivalent to stating that maximal greatness is exemplified. But that’s Plantinga’s conclusion to begin with, so his argument is hardly persuasive since it’s viciously circular. The purported innocuousness of his premiss that PNg comes from the semantic shift from God =df maximally excellent being to God =df maximally great.
Posted by AspiringPhil | June 15, 2012, 7:23 AMEven if the argument weren’t circular, the statement “it seems to be the case that if S5 modality is valid, God necessarily exists” is false.
This is because even if S5 is valid, there is room to dispute the first premise of the argument. I’ve not attempted it, but here is a sketch of an a posteriori approach: according to contemporary physics, there is no need to posit a God to explain anything of our universe; entities ought only be posited when their existence is necessary to explain something of the universe; therefore, we ought not posit the existence of a God in this world. This is equivalent to the provisional claim that there is no God in this universe, i.e., that this is a possible world in which God does not exist (and thus, God does not exist necessarily).
The point is, further argumentation is needed even after S5 is established, contrary to your claim that ‘S5->God exists necessarily.’
Posted by npapadakis | August 21, 2012, 8:55 PMThe first statement – “Possibly, God necessarily exists” can be re-worded as follows:
“It is possible that the existence of God is necessary.”
By substituting the following:
“Possible” means – “true in some possible worlds”.
“Necessary” means – “true in all possible worlds”.
“It is true in some possible worlds that the existence of God is true in all possible worlds.”
Posted by ignor | October 18, 2016, 5:28 AM