An Intro to the Philosophy of Religion, Ch. 5 Part 1 (Ontological arguments)

Religious experience might justify belief in the absence of propositional evidence and undercutting defeaters; however, not all persons have religious experiences.  In addition, some religious experiences may be defeated, or else propositional evidence (the problem of evil, divine hiddenness) outweighs experience.  Therefore, regardless of a reformed epistemology, good theistic arguments are indispensable.

Ontological Arguments
Anselm's starting point is that God is the being than which none greater can be conceived.  The argument goes as follows:

1. God is the greatest conceivable being.
2. God exists in the understanding.
3. To exist in reality is better than merely to exist in understanding.
4. Thus, if God exists merely in the understanding, then we can conceive of something greater than God, namely a being just like God, but who also exists.
5. But it is impossible to conceive of a being that is greater than the greatest conceivable being.
6. Thus it is impossible that God exists merely in the understanding.
7. Thus God exists in reality as well as in the understanding.
8. Thus God exists.

One popular objection to this argument is that other greatest conceivable things could be plugged into this argument.  For example, the Lost Island is the greatest conceivable island and thus exists.  But not so fast, how would an island be the greatest of its kind?  How many miles of beach would it have, potentially infinite?  Certain types of perfection do not have an instrinsic maximal value, and thus not just any old greatest conceivable thing can be plugged into this argument.  But this objection might cut both ways, since some of God's alleged great-making properties don't seem to admit of instrinsic maxima (eg., perfectly loving).  In other words, some intrinsic great-making properties may be problematic for this argument.

But is existence a property at all, much less a great-making property?  Kant answered in the negative.  To ascribe properties to something presupposes its existence.[1]  Murray and Rea point out that Kant is assuming that a precondition (for ascribing other properties) can't itself be a property.   "Taking up space" is a precondition for having the property of "being red", but "taking up space" is also itself a property.  Likewise with existence, except that existence the precondition for all properties (or so Kant argues).  Perhaps it is, but this still doesn't show that existence can't be a property.  On the other hand, Rea and Murray don't give any arguments in favor of predicating existence either (my guess is this gets deep under the hood of language).  So, I'm not sure about Kant's objection.

Some maintain that the ontological argument begs the question.  The first premise would need to be modified to be conditional. "[5.1**] For anything to count as God, that thing would have to be the greatest conceivable being."  But now the conclusion only says "Thus anything that counts as God would have to exist."

Recent work in the area of philosophy known as modal logic has produced a new rendition of this argument.  Modal logic deals with claims/inferences that are about/from possibility and necessity.   Rea and Murray define a possible world as "a comprehensive description of the way the universe might be...the maximally comprehensive description of our universe is the actual world."  Next, they define a necessary being and necessary property possession.  A necessary being is one that would exist in all possible worlds.  A being possesses a property necessarily if it has that property in all possible worlds.  For example, Arnold Schwarzenegger is 6 feet tall ascribes a property to Arnold, but Arnold could be 5 feet tall in some possible world.  On the other hand, Arnold Schwarzenegger is a person ascribes a property to Arnold that holds in all possible worlds.  Hmm, but what about Kant's objection?  Arnold can only hold a necessary property in the worlds that he exists in, right?  Consider the proposition Arnold is an existent.  Is existence a property or not?  Not sure what Plantinga says on this issue, but here is the modal argument:

5.20 God is the greatest possible being
5.21 The greatest possible being is one that possesses all perfections necessarily
5.22 Necessary existence is a perfection
5.23 It is possible that the greatest possible being exists
5.24 If it is possible that the greatest possible being exists, then that being exists necessarily
5.25 God exists necessarily
5.26 God exists

Premise 5.23 is susceptible to refutation.  For instance, some philosophical theologians think that the concept of a greatest possible being entails a contradiction.  Thus, it is not possible that the greatest possible being exists.  In other words, if a perfect being is shown to be conceptually impossible, this argument fails.  A more modest critic might just insist that we withhold judgement on this argument until we have resolved all the apparent contradictions in philosophical theology.  But a powerful rebuttal can be given to both critics here.  Since premise 5.23 asserts the possibility that the greatest possible being exists, then the response to conceptual impossibility is to adjust our concept accordingly to be in line with what is possible. Does omnipotence and impeccability entail a contradiction?  No problem, just adjust the concept.  The point here is that some philosophical concepts are hard to pin down and declare impossible.  The concept of the greatest possible being, by its very nature, is damn near impossible to deem impossible.

But someone can still object that necessary existence is impossible.  After all, the being must exist (or possess existence?) in all possible worlds for this argument to work.  Rea and Murray don't think that any convincing arguments have been offered in this direction.  A few references would have been nice.  But regardless, it looks like "its possible until shown impossible" isn't exactly a compelling reason to accept 5.23 either.  But, compelling reasons are hard to come by in these types of arguments (or so it seems to me at least).

[1] Alvin Plantinga, in God, Freedom and Evil (1977), proceeds meticulously through the details of Kant's objections in a section entitled "The Irrelevance of Kant's Objection."