Plantinga's "victorious" modal ontological argument

With fresh eyes, I revisited Plantinga's "victorious" modal ontological argument (hereafter, VMOA) yesterday.  Some summaries of the argument, including the one at IEP, has Plantinga defining the term 'maximally great being' (hereafter, MGB) to be such that if it's possible an MGB exists, then an MGB actually exists, and has the properties of omnipotence, omniscience, and moral perfection.  On the IEP's account, Plantinga's argument really only has one premise, and the conclusion follows immediately.

It turns out that IEP's summary is incorrect.  Plantinga's argument has a number of different premises, and he doesn't ever explicitly define anything.  His approach, instead, is to let the reader supply their own intuitive understandings of a given concept.  Sometimes he'll help this process along by giving examples, or brief conceptual sketches. In one case (as we shall see momentarily) he actually gives an analysis---although that's still not quite a definition.

For his VMOA, he introduces the concepts of 'greatness' and 'excellence'.  As usual, Plantinga declines to give explicit definitions, and instead expects us to have a kind of intuitive understanding of greatness.  And I suppose we do, although I'm not at all certain our intuitions here are sufficiently refined to be pressed into service in the way that he wants.  At any rate, he does have this to say about greatness and excellence:

"We might make a distinction here between greatness and excellence; we might say that the excellence of a being in a given world W depends only upon its (non world-indexed) properties in W, while its greatness in W depends not merely upon its excellence in W, but also upon its excellence in other worlds."

I think I can follow him here.  For instance, a person's greatness lies in part in his abilities, but then it also lies in part in the actions he actually performs.  I suppose it's vaguely intuitive to isolate, so to speak, the second component as a separate concept.  And I don't mind temporarily re-purposing the word 'excellence' to refer to it.

Before turning to Plantinga's VMOA, we also need the concept of an 'essence'.  Roughly, he takes this to be a property, or group of properties, that an object has essentially, and that is unique to that object.

Now Plantinga states his argument:

(1) The property 'has maximal greatness' entails the property 'has maximal excellence in every possible world'.

(2) 'Maximal excellence' entails omniscience, omnipotence, and moral perfection.

(3) 'Maximal greatness' is possibly exemplified.

(4) For any property P, if P is possibly exemplified, then there is a world W and an essence E such that E is exemplified [by an object existing] in W, and E entails 'has P in W'.

(5)  Every world-indexed property of an object is entailed by its essence.

(6)  A being [or object] has a property in a world W only if it exists in that world.

Therefore, Plantinga claims:

(7)  There actually exists a being that is omniscient, omnipotent, and morally perfect; and that exists and has these properties in every possible world.

In reasoning from premises (1)-(6) to the conclusion (7), Plantinga considers a possible world W and a proposition p, and decides that, were W actual, p would be necessarily true. He then concludes that p is in fact necessarily true.  These moves seem relatively safe, but they require two additional, unstated premises:

(8)  For any proposition p and possible world W, if p is true in W, then, were W actual, p would be true.

(9)  For any proposition p, if there's a possible world W such that, were W actual, p would be necessarily true, then p is in fact necessarily true.

Is there a way to avoid these premises?  Let's walk through Plantinga's reasoning and see if we can adjust it to make (8) and (9) unnecessary.

From (3) and (4), there is a world W* and an essence E* such that E* is exemplified by an object existing in W*, and such that E* entails 'has maximal greatness in W*'.  At this point, Plantinga invokes (8), and then a little later he invokes (9), too.  Can we avoid it?

By definition of 'essence,' there is an object x* that has essence E*.  Now, x* therefore has the property  'has maximal greatness in W*'.  This we shall take to mean simply that, at W*, the object x* has the property of 'maximal greatness'.  Does that interpretation count as an additional premise?  Let us suppose not.  By (1), the property 'maximal greatness' entails 'has maximal excellence in every possible world', which again we shall simply take to mean that, for any world W, x* has 'maximal excellence' at W.  In particular, x* has maximal excellence at the actual world.  By (6), x* exists in the actual world, which is just to say that x* exists simpliciter.  By (2), x* has the properties of omniscience, omnipotence, and moral perfection in every possible world.

So, not only have we avoided (8) and (9), we've also avoided (5).  But this comes at the cost of imposing a certain interpretation on the world-indexed properties mentioned above.

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