The Ontological Argument for the Existence of God

[God of Mr. Hanky]

Begging the question

Richard M. Gale, a metaphysician from the University of Pittsburgh, claims that the possibility premise begs the question. Basically, one is not justified in an epistemic sense to accept the possibility premise unless one also understands the nested modal operators in system S5. Within the modal system S5, “possibly necessary” means the same as “necessarily”. Since the concept of a being with “maximal excellence” entails this being’s necessary existence in a possible world, the possibility premise (3) contains nested modal operator “possibly necessary”. Since “possibly necessary” is equivalent to “necessarily” (within the system S5 that Plantinga needs for his argument to even get off the ground), the argument begs the question in the possibility premise (3), since the premise contains the conclusion within itself.

Metaphysical vs epistemic possibility

The modal ontological argument, in some presentations, relies on an equivocation between metaphysical and epistemic possibility. It may very well be that the existence of a maximally great being is epistemically possible (i.e. we don't know that it's false) but not metaphysically possible (i.e. non-contradictory). If the concept of a maximally great being is not self-consistent, then it is not metaphysically possible for such a being to exist. Compare: we don't know whether the twin prime conjecture is true or not. Suppose it is false but we don't yet know it; it follows that it is (metaphysically) necessarily false. We might nevertheless agree that it might be true because we don't know its truth value.

The issue with the metaphysical possibility as it relates to the first three premises can be clearly shown with a competing version of the argument:

1. It is possible that a maximally great being (God) does not exist.
   
2. If it is possible that a maximally great being does not exist, then there is some possible world where a maximally great being does not exist.
   
3. If a maximally great being exists in some possible world, then it exists in every possible world.
   
4. A maximally great being does not exist in every possible world (from 2).
   
5. Therefore, a maximally great being (God) does not exist.
   

This further highlights that the argument has two likely sources of error: with the construction of the argument in general (in which case the argument is not useful for proving anything) or a problem specific to the first premise (in which case the possibility of the existence or non-existence of the character God must be defended with further arguments). Of course it is also entirely possibly the problem lies in both areas, and it is neither possible to prove an actuality from a mere possibility or accept a possibility without supporting empirical evidence.

RationalWiki | Ontological argument

I'm not schooled in modal systems, I just google S5 and it isn't playing well with the eggnogg I just had.   But I am curious to know what would it say (not my being a little tipsy at the moment) of non-metaphysical possibilities? For example, I don't think it can be ruled out that on another planet somewhere there could have evolved some type of non-metaphysical pink unicorn (pink horse with a narwal-like horn). If it's possible, and the idea isn't metaphysical, then is it necessarily true?

EDIT: Keeping in mind the universe is finite!