Monday, August 23, 2010

The Scotist-Anselmian argument for God?

Doug says the following argument is "just for kicks," but I think it has some fertile potential. Quote:

1. There is possibly a sound ontological argument [sOA].
2. Therefore, God exists. (From 1 and S5)

Now, if you don't know, "S5" refers to an axiom in modal logic that, "If possibly p, and p necessarily, then necessarily p."

According to the Wikipedia, "The axiom is given as either

Possibly P implies Necessarily Possibly p \Diamond p \to \Box\Diamond p
Possibly Necessarily P implies Necessarily p \Diamond\Box p \to \Box p

Both of these axioms are properly called axiom 5."

Briefly stated, St. Anselm's "ontological argument" OA for the existence of God is the following:

1. God is that than which none greater can be thought. (Axiom)

1a. The very definition of God is that being which transcends any conception of Him, and therefore God is that 'being' compared to which no other 'thing' can be thought.

2. To exist actually is greater than to exist merely notionally. (Premise)

2a. A real dollar is better than the mere idea of a dollar. (Postulate)

2aa. That which does not exist has no way of enjoying, or having ascribed to it, any value or predicates whatsoever, therefore only that which actually exists can enjoy greatness and predication.

2ab. An imaginary dollar would not be money and therefore would be inferior as money to a real dollar. (From 2a and 2aa)

3. For God to exist actually is greater than for God to exist merely notionally. Insofar as the actual God would possess a greater perfection than a purely notional God, only an actual God would be that than which none greater can be conceived. (From 1 and 2)

4. Therefore God actually exists. His essence (or 'definition') necessarily includes His existence. (From 2 and 4)

I know of two standard objections. First, "existence is not a predicate," i.e. X's existing adds no content to 'what' X is. Therefore 'what God is' is trivially but decisively distinct from the proposition 'that He is'. Since the definition of a thing does not include its existence, the essence of God does not include His existence. Second, while it may be true that God's essence includes/entails His existence, this is a fact unknowable to us and therefore the ontological argument is merely suppositional. Kant is the most famous advocate of the first objection and St Thomas Aquinas is the most notable objector (besides Gaulino himself!) to the OA. It is a truism that, while everybody agrees the OA, no one agrees on why it fails. As such, it remains a tantalizing project for theists and non-theists to perfect and bury, respectively.

In this post I will not present my own thoughts on the OA--aside from saying I think a reasonable case can be made that, in some cases, existence is a predicate--, but rather will stick to considering Doug's argument above. His point is that, if in some world W there is a sound form of the OA (sOA), and since sOA delivers a necessary conclusion (viz. God exists), therefore God necessarily exists, and thus exists in our actual world AW. Here's an expansion of his argument:

1. There is possibly a sound ontological argument [sOA].
1.1 A sOA proves the necessary existence of God.
1.2 The necessary existence of God is possible.
2. Therefore, God exists. (From 1 and S5)

As I read it, this seems very much like Duns Scotus' modal argument (MA) for the existence of God, about which I have written very briefly before. Here's the argument in brief:

1. An Uncaused Producer is logically possible. (Premise)

2. Anything logically possible is either actual or potential. (Axiom)

3. A potential Uncaused Producer can only be caused (i.e. is not 'uncaused'), but a caused Uncaused Causer is a contradiction. (Postulate)

4. Hence, no Uncaused Producer is merely potential. (From 2 and 3)

5. Therefore, an Uncaused Producer is actual. (From 2 and 4)

6. This actual Uncaused Producer we call God. (Premise)

7. Therefore, God actually exists. (From 5 and 6)

Doug has written about the MA before as well, and he adds an objection by William Rowe, which I believe was dispensed with in the combox there. But again, I won't go into great detail on the argument as such, instead preferring to note the strange link between the OA and the MA. For the OA is effectively saying that it's impossible for God to be God and not exist, while the MA is saying that a necessary being is not possible unless it exists, and a necessary being is certainly possible. Hence, I'm inclined to say the OA and the MA mutually entail each other. Consider:

1. There is possibly a sound Scotist modal argument [sMA].
2. Therefore, God exists. (From 1 and S5)

Since it is possible that a necessarily true formulation of the OA exists, and the OA necessarily entails that God exists, then necessarily God exists. Likewise, since it is possible that a necessarily true formulation of the MA exists, and the MA necessarily entails that God exists, then necessarily God exists.

I suppose the rejoinder to all this would be that, since it is possible sound refutations of the OA and the MA exist, therefore God cannot exist. But I don't think that will work, since the necessity of the refutations is notionally parasitic on the arguments themselves. The only way to refute them entirely is to deny the first premise of all philosophical theology, namely, that "it is possible that God exists." I don't see how this denial could ever actually be made, so the OA and MA seem asymmetrically immune to absolute refutation. After all, the very act of mounting a decisive refutation of God admits "God" as a coherent, and therefore possible, subject of debate.

1 comment:

Doug Benscoter said...

Good stuff, Codgitator. :)

As Plantinga has noted, the ontological argument is immune to Kant's objection once we distinguish necessary existence and contingent existence. The claim needn't be that existence is greater than non-existence (although something can be said for that as well), but that necessary existence is greater than contingent existence. If "God" is possible but not necessary, that would imply that God is contingent. So, God is not really God according to this conclusion, which is contradictory.

With that said, I think your connection between the ontological argument and Scotus is made very well.