S5 modality

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The Ontological Argument: Question Begging?

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.



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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