A Meta Version of a Modal Ontological Argument

[Update again: Revised version of the argument is here]

[Update 7/19/2012: On further reflection on this argument, I’ve discovered that it does not succeed.  The second level of symmetry does permit identity between the two entities described in each argument.  I hope to continue to work on this argument in the future and develop a version that is immune.  For now, I cannot see how to get this argument off the ground]

It’s been quite a while since I last posted on this blog. My program has been keeping me busily preparing for my comprehensive exams.  But I wanted to air an argument that I am working on.  This is by no means a finished draft.  It’s just an argument that I’ve been thinking for some time.  I call it a “Meta Version of a Modal Ontological Argument”.

In the latter half of the twentieth century, the ontological argument enjoyed a remarkable revival.  This was due, primarily, to the work of Norman Malcolm, Charles Hartshorne, and Alvin Plantinga.  Perhaps the best known is Plantinga’s “A Victorious Modal Version” which Robert Maydole (2009, 573) succinctly reconstructs as:

P1 The property of being maximally great is exemplified in some possible world.

P2 The property of being maximally great is equivalent, by definition, to the property of being maximally excellent in every possible world.

P3 The property of being maximally excellent entails the properties of omniscience, omnipotence, and moral perfection.

P4 A universal property is one that is exemplified in every possible world or none.

P5 Any property that is equivalent to some property that holds in every possible world is a universal property.

Therefore,

P6 There exists a being that is essentially omniscient, omnipotent, and morally perfect (God).

Much ink has been spilled in defending an critiquing the soundness of this argument, and its sister versions developed by Malcolm and Hartshorne.  Maydole remarks,

And what should we think about the first premise of each of these arguments, which effectively says in each case that it is possible for God to exist? None of the authors of these respective arguments is particularly sanguine about proving this. Hartshorne merely suggests that we might “employ one or more of the other theistic proofs . . . to demonstrate that perfection must at least be conceivable” (1962, p. 52). Plantinga treats the possibility premise as a philosophical hypothesis, which he says it is rational to accept because otherwise “we should fi nd ourselves with a pretty slim and pretty dull philosophy” (1974, p. 221). (Hardly the highest standard for what counts as rational!) And Malcolm says that he does “not know how to demonstrate the concept of God . . . is not self-contradictory” (1967, p. 318). Yet he assumes that it is not self contradictory because it has “a place in the thinking and lives of human beings” (1967, p. 318).

In other words, the force of these arguments hangs and, unfortunately, falls on the key possibility premise that is difficult, if not impossible to defend.  At best, then, these modal ontological arguments demonstrate the reasonableness of believing in God, granting that God is at least possible.

There are further problems with these arguments, namely, that they are easily parodied.  Maydole (2009, 573-574) explains:

For example, one might easily validly argue contra Hartshorne that Anselm’s Principle, and the premise that it is possible that a supremely perfect being does not exist, jointly entail that a supremely perfect being does not exist. If we were merely to postulate that, possibly, a supremely perfect being exists, then we could also rightfully postulate that, possibly, a supremely perfect does not exist. But then the parody would refute Hartshorne’s argument because we should not be able to rightfully claim that the premises of the parody are less justifiable than those of Hartshorne’s argument.

In other words, one could run a symmetrical version of the ontological argument that seeks to prove God’s non-existence.  All that such an argument would require is a parallel possibility premise–one that suggests that, for instance:

P7 The property of being maximally great is not exemplified in some possible world.

But since being maximally great is defined as being maximally excellent in every possible world, it would follow from P7 and P4 that maximal greatness is a universal property only insofar as it holds in no possible world, thus refuting God’s existence or:

P8 There does not exist a being that is essentially omniscient, omnipotent, and morally perfect (God).

Trent Dougherty has offered some helpful insights into the problem of the possibility premise.  And much of his discussion will be crucial for understanding the meta argument that will be developed here.  However, I do not think Dougherty’s argument ultimately succeeds in rescuing modal arguments of the Malcolm-Hartshorne-Plantinga variety.

Dougherty explains that the possibility premise has its origins in Leibniz, who argued that there was a gap in Anselm’s original formulation of the argument.  That is, God’s existence could not be inferred, unless it is established that God could at least possibly exist.  But Leibniz also notes that possibility can be safely assumed unless there is proof to the contrary.  Dougherty sums this doctrine up as the benefit of the doubt or BOD, and contrasts it with actuality claims which bear a burden of proof (Dougherty n.d. 4-5). In effect, I am permitted to assume the logical possibility of God, broadly construed, unless and until it can be shown that the concept of God is logically impossible.  But the benefit of the doubt is a benefit short lived for those who are hopeful for a sound modal ontological argument, for if BOD is granted to the possibility of God, or a maximally great being, then fair is fair and BOD must also be granted to the possibility of ~God, or there not being a maximally great being.  Dougherty (n.d. 6) refers to this as the symmetry problem.  To break the deadlock, he suggests an asymmetry that gives the possibility of God a certain kind of edge over the possibility of there not being a God.  What is this advantage?  Dougherty invokes a conceivability principle.  According to this principle (ibid.):

P9 For any sentence S and agent A, if A can conceive ~S, then A can conceive S.

Dougherty holds that supposing ◊~G, where G is God–the key premise to the atheologian’s parody, requires via P9, that ◊G has prima facie support.  And if ◊G has prima facie support, we can infer via the ontological argument that □G, or ~◊~G, which serves as a defeater for ◊~G.

I find Dougherty’s asymmetry argument to be rather weak in that it is not apparent to me why the atheologian might restore symmetry by offering a parody of the conceivability principle that:

P10 For any sentence S and agent A, if A conceive S, then A can conceive ~S.

Thus, if the theologian supposes ◊G, then by P10 ◊~G has prima facie support.  With symmetry restored, it seems there is no reason to prefer the ontological argument to the atheologian’s parody version.

What I would like to offer is a version of a modal ontological argument that is immune to parody by generously granting possibilities, come what may.  What we will see, is that even if parody is attempted, possibility granted, and the balance of symmetry achieved, the conclusion that God exists cannot be avoided.  It is in embracing the perceived shortcomings of previous versions of the ontological argument, that I hope to produce a truly victorious version.  To achieve this end, my possibility premise will be drawn from the arch-critic of ontological arguments, Graham Oppy.  Summarizing some of the primary objections to ontological arguments Oppy (2011) then goes on to say:

Even if the forgoing analyses are correct, it is important to note that no argument has been given for the conclusion that no ontological argument can be successful. Even if all of the kinds of arguments produced to date are pretty clearly unsuccessful—i.e., not such as ought to give non-theists reason to accept the conclusion that God exists—it remains an open question whether there is some other kind of hitherto undiscovered ontological argument which does succeed.

This stunning admission has led me to generate the following meta version of a modal ontological argument:

P11 Possibly, a sound version of the ontological argument is discoverable that is impervious to parody.

P12 If possibly a sound version of the ontological argument is discoverable that is impervious to parody, then possibly there is a true concluding proposition to an argument such that necessarily there is some being x that is omnipotent, omniscient, and morally perfect.

The plausibility of P12 is in the very fact that premises imply their conclusions.  So if there is a sound ontological argument, it certainly would establish the necessary existence of the being it purports to prove.

P13 If possibly there is a true concluding proposition such that necessarily, there is some being x that is omnipotent, omniscient, and morally perfect, then it is possibly necessary that there is some being x that is omnipotent, omniscient, and morally perfect.

P14 It is possibly necessary that there is some being x that is omnipotent, omniscient, and morally perfect (From P11-13)

P15 Necessarily there is some being x that is omnipotent, omniscient, and morally perfect (P14, S5 axiom).

P16 There is a being x that is omnipotent, omniscient, and morally perfect (P15, NE).

Note that the possibility premise of this argument is with regard to an argument, rather than God.  Thus, we are able to grant the possibility of the symmetrical proposition,

P17 Possibly, there is not a sound version of the ontological argument is discoverable and is impervious to parody.

Of course P17 is perfectly compatible with P16, for God’s necessary or actual existence does not necessitate there being a sound ontological argument that cannot be parodied.  Perhaps, for instance, God’s existence simply cannot be demonstrated a priori.  Or maybe God’s existence could be demonstrated a priori, but there are possible worlds where no such argument is ever discovered.  Or perhaps any sound ontological argument, will nonetheless always be subject to parody.  Of course one possibility is that God, in fact, does not exist.  But so long as these other possibilities remain, P17 remains compatible with the rest of the argument.  So the symmetry of P17 with P11 does not generate a parody.  But couldn’t there be a deeper symmetry by which a parody would be generated?  I have my doubts that another level of symmetry would generate a parody.  But, let us take this up in form of an argument.  Let us suppose, for a moment the following argument:

P18 Possibly, a sound version of an anti-ontological argument is discoverable that is impervious to parody.

P19 If possibly a sound version of the anti-ontological argument is discoverable is impervious to parody, then possibly there is a true concluding proposition to an argument such that necessarily there is not some being y that is omnipotent, omniscient, and morally perfect.

P20 If possibly there is a true concluding proposition such that necessarily, there is not some being y that is omnipotent, omniscient, and morally perfect, then it is possibly necessary that there is not some being y that is omnipotent, omniscient, and morally perfect.

P21 It is possibly necessary that there is not some being y that is omnipotent, omniscient, and morally perfect (P18-20).

P22 Necessarily there is not some being y that is omnipotent, omniscient, and morally  perfect (P21, S5 axiom).

P23  There is not a being y that is omnipotent, omniscient, and morally perfect (P22, NE).

Incidentally, we would also grant that that there is a symmetrical possibility premise:

P24 Possibly, there is not a sound version of an anti-ontological argument is  discoverable that cannot be parodied.

Likewise, there are a wide variety of disjunctive possibilities that might account for the compatibility of P23 and P24, i.e. that no such argument is possible, that there are possible worlds where no such arguments might be discovered, etc.  The pressing question is whether P16 and P23 are contradictory.  If they are, then this symmetry would result in a parody that would once again push off our discovery of a sound ontological argument, since there would be no good reason to prefer one contradictory over the other.  But P16 and P23 are not contradictory, at least not explicitly.  For the atheologian to succeed in parody, she would have to prove,

P25 x = y

That is, she would have to prove that whatever being is proved to exist in P11-16 is identical with the being proved not to exist in P18-23.  But what arguments might the atheologian provide to prove this identity relationship?

For one thing, the atheologian might try to establish the identity between x and y through their shared properties, i.e. omniscience, omnipotence, and moral perfection.  Of course neither argument argued that such properties were exhaustive of the essential, or even accidental, natures of the entities established in each. So the atheologian could not make use of the identity of indiscernibles to establish the identity claim.

Might the atheologian establish identity because symmetry simply demands it?  I counter that such a demand is question-begging.  Furthermore, if P11 is granted by the benefit of doubt, then it is granted that it is possible that there is a sound ontological argument that is not parodied.  This is granted to the symmetrical claim in P18 that there is a sound anti-ontological argument that is also parody proof.  Therefore, whatever possible argument is invoked in P11-16, it is not going to be related to the argument invoked in P18-23 by way of parody.  So, if the same entity that is established to exist in P16 is identical to the being established not to exist in P23, then the fact that these two propositions are contradictories could not be relied upon by invoking the possibility that there are parallel premises and deductive steps in the possible ontological/anti-ontological arguments.  In other words, an identity between x and y would require two entirely independent sound ontological arguments reaching contradictory conclusions.  This is far more than a coincidence!  It is to affirm the existence of the grossest kinds of contradiction actually do obtain.

So while I have been overly generous in granting the possibilities of symmetrical premises for the atheologian, I will not grant an identity between x and y without an adequate argument.  And I have provided two reasons to think the atheologian will not succeed in this task.  If my argument is indeed successful, then it would be actually be the kind of argument that is supposed possible by the argument.  That is, the argument appears to be valid, with true premises.  And despite attempts at symmetrical parody refutations, it has shown to be impervious.  Of course this is not to say that the existence of this argument can serve as evidence in support of P11, as that would be question-begging.  Nonetheless, I think the existence of God, or a being with God-like attributes, can be demonstrated.

References:

Dougherty, T.  N.D. “Conceivability, Defeasibility, and Possibility: A Defense of the Modal Ontological Argument” URL =< http://apollos.squarespace.com/ontological-argument/A%20Defense%20of%20the%20Modal%20Ontological%20Argument.pdf>

Maydole, R. 2009. “The Ontological Argument” in The Blackwell Companion to Natural Theology. Ed. J.P. Morland & W.L. Craig. Malden, MA: Wiley-Blackwell.

Oppy, G. 2011. “Ontological Arguments” in The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.), URL =<http://plato.stanford.edu/archives/fall2011/entries/ontological arguments/>.

Posted on June 2, 2012, in Arguments for God and tagged , . Bookmark the permalink. 6 Comments.

  1. Hey Daniel,

    Glad to see that you’re back. I have a question about the identity relationship between x and y. In the original symmetry that was proposed (P6 & P7-8), it is symmetrical because both P6 and P8 propose a claim about the existence of “a being that is essentially omniscient, omnipotent, and morally perfect (God)”. Why can we not replace the language of x and y with the same language in the former premises, or use “x” in both instances?

    Like

    • Hi Matt,

      Thanks for the question! I’m back, at least in a limited way for now. I’m preparing for my comprehensive exam this August, so I’m spending most of my days studying in the library.

      As for your question, there are a few points that I would like to make. The first is to draw a distinction between the symmetry fount in P6 &P7-8 and the latter attempt at symmetry between P11-16 & P18-23. The relevant difference is that in the earlier argument, Plantinga’s argument, the possibility premise regarding God’s existence is made explicit. We know where it occurs, and at which step. I would describe this as an un-nested possibility premise. Consequently, the atheologian can justify a parody possibility premise regarding that very entity, God, on something like the Humean dictum that anything that conceivably exists can also be thought not to exist (like my P10). There is, at the very least, some justification and parallel for saying that the argument, and the parallel possibility premise reference identical entities.

      In my meta argument, the explicit possibility premise is with regard to the argument itself. Any possibility premise with regard to God, or a being with God-like attributes, is nested within the argument and goes unseen. By the time we reach P16, we have an existential claim that could be instantiated with a particular pseudonym, say “u”, rather than variable. So we could, in theory, adopt the same variable “x”, going forward in the argument from P18-23 as you suggest, but we could not existentially instantiate that x with the same name “u” when we reach the conclusion at P23. We’d have to assign it a new name, say “v”, and then parody would only be achieved by successfully arguing that “u” is identical to “v”. We cannot assume identity between the two without violating the EI rule by introducing the same quasi-variable that was introduced on a previous line. And we cannot appeal to parody and parallel, or Humean principles, as we did with Plantinga, because the possible ontological arguments themselves are completely nested within the argument, i.e. we don’t see the steps, premises, deductions, and which possibilities are actually assumed. Assuming that the entity that falls out of P11-16 is identical to the entity that falls out of P18-23 through sheer stipulation begs the question that a parody exists within the nested arguments, or that similar possibilities are being assumed, or there is some parallel between the possible arguments that one can appeal to (by possible arguments, I mean the possible sound arguments supposed in P11 and P18). We just don’t know that. It is through not knowing what the possible arguments say that this meta-argument gains its strength.

      Let me know what you think!

      Dan

      Like

      • Updated this comment for clarity.

        Like

      • I’ve recently returned to this argument and have discovered that I did not achieve what I had hoped. P18-P20 is not an existential claim and so an identity can be established between the two. Parody is achieved. So Matt, you are correct that we can substitute x for both. I put the argument into symbolic form and it revealed that I did not successfully nest away what I thought I had done. Perhaps I’ll return to this argument in the future, but for now I am abandoning it.

        Like

  1. Pingback: An argument for the Possibility Premise from Epistemic prudence | Third Millennial Templar

  2. Pingback: Revised Meta Modal Ontological Argument in QML « vexing questions

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: