Ontological Arguments Part Three: The Flip

Back to Stoebenau (I don't have any references on who he is apart from the website - The Ontological Argument: an assessment):


From there we read (again):

Anselm first gave what has become known as the ontological argument in his Prosologion. He used the definition that God is that being than which no greater can be conceived. Using this, he gave a reductio ad absurdum, that if one claimed that this being did not exist, then there exists a being which is greater than the being which no greater can be conceived. A major assumption of Anselm’s was that whatever exists in both the mind and in reality is greater than that which exists only in the mind. However, it is tough to see why one should accept this premise as sound. Is five dollars actually being in my pocket greater than 100 dollars existing in my mind? Can we even make such a comparison? This does not seem likely. One cannot claim that an old worn down coin is greater than a hypothetical brand new one of the same date, just because it exists. Furthermore, the premise that if one denies the existence of God, that there is a being greater than the being which no greater can be conceived, presupposes the actual existence of that being, so the argument runs in a circle. Hence, Anselm’s original argument fails.

Anselm is not, as Stoebenau claims, presupposing the actual existence of God, but that if God exists, by definition, He is "that being than which no greater can be conceived."  That is not a presupposition, but the premise of who God would be by definition.  Again, it's important to understand the reasoning behind the use of a reductio ad absurdum.  He's attempting to show, based on scripture from Psalm 14:1 "The fool says in his heart 'There is no God'" as a valid assessment of the logic of the whole statement and the illogic of the internal statement: "There is no God;" while in the process, he's able to show that such a statement is illusory not because a person cannot know that there is no God, but because there is in fact a God.  It is not presupposition that states God's existence, but the argument itself, starting with the premise that God would be by definition "that being than which no greater can be conceived."  And again, as Plantinga has pointed out, it's a problem of the properties of existence and between what can be conceived of and what we already know exists(from the Ontological Argument section of the Kindle version of God, Freedom, and Evil - page numbers do not correspond to the hard copy version).  Everything that we already know exists contains properties that are not contradictory in the sense of a square circle: Cats are cats, and are not also dogs, and we define things according to their recognizable properties, not according to any contrary properties.  The properties that we can conceive about God (by definition) are not contradictory.

Allow me to illustrate a point: Recent Cosmologists have proposed a multiverse as either a finite number of other universes outside our own, or an infinite number of universes outside our own.  The concept of a finite number does not immediately conjure up a problem with logical conception.  There do not immediately appear to be any contradictory properties of such a conception.  However when one considers an infinite number of universes outside our own, there's an immediate absurdity based on what we understand about actual infinite numbers of things, and based on what we understand about our own universe as existing in a finite space.

The issue with God is not in the 2nd example; an absurd infinite number of universes: no contradictory properties come to mind when one conceives of God.  God does not represent an infinite number that is absurd; rather, we understand God as one immaterial being who is eternal.  Eternal is not in the sense of possessing an infinite number of years or other units of time, but actually the condition of being timeless or outside of time.  Time is only meaningful in reference to space and motion.  By definition God is not within the limits of space, time and motion.  So a conception of God is closer to a conception of a finite number of universes, our first example; as in not immediately contradictory.  Now while I believe for other reasons that the concept of a finite multiverse is problematic, it can be conceived without the immediate absurdity of an actually infinite set.  The idea of other universes, finite or otherwise in my understanding, is that it contradicts the definition of a universe as being all that physically or metaphysically exists, with the exception of that which caused all that exists; getting back to Cosmological Arguments.

So Stoebenau's disagreement is not with the logic of the argument, but with Anselm's insistence on the definition of God; as he sees it, to define God is to presuppose God.  That is not the case.  We could not work out the reductio without knowing what we are attempting to refute.  The fool says "there is no God," so we must begin with what or who God is.  We are not attempting to show that "the fool says in his heart 'there is no something that we cannot and must not define.'"  That in itself would be illusory.  No argument could deal with that.  I find it interesting that Stoebenau recognizes the argument as a reductio ad absurdum,  "a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence," but does not allow it to be so.

I want to leave off with some things to ponder:


If we go back to Hartshorne's Modal Cosmological Argument, and then approach Plantinga's own Modal Cosmological Argument, Stoebenau has a few things to say, which I would like to examine in my next post:

Hartshorne’s ontological argument is based on Anselm’s second argument and claims that God’s existence is logically necessary. Hartshorne’s argument is given here, where ▯A means it is logically necessary that A, ~A means it is not the case that A, → is strict implication, ∨ means or, and g means God exists:

1. g → ▯g

2. ▯g ∨ ~▯g

3. ~▯g → ▯(~▯g)

4. ▯g ∨ ▯(~▯g)

5. ▯(~▯g) → ▯(~g)

6. ▯g ∨ ▯(~g)

7. ~▯(~g)

8, ▯g

9. ▯g → g

10. g

This argument is valid. Furthermore, given an Anselmian conception of God, premises one and five are sound. Premise two is just the law of the excluded middle, and premise three is a law of the modal logic S5. Premise nine is obviously sound, so this leaves premise seven as the only premise to question. Premise seven says that it is logically possible that God exists. If you were to change it to:

7′. It is possible that God does not exist.

Then using premise one, and 7′, one gets this conclusion:

10′. God does not exist.

That's the flip. Thinking that we can simply flip the elements of the argument around by using contrary premises we can arrive at a contrary conclusion. It all seems quite sound; but is it? It ought to be from the structure of the argument; but is the premise "It is possible that God does not exist" quite the same as the premise "It is possible that God exists?" Is the argument designed to deal with the premise: "it is possible that God exists," but not with "it is possible that God does not exist?" Apparently it is, but is there any logical reason why it should be different for the two opposing premises given the other elements of the argument?  This is something that I've been grappling with and I'm not certain that I'm quite done with it.  Stay tuned.

Concepts:

Law of the excluded middle

Modal Axiom S5