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Ontological Argument for the Existence of ... Objective Truth?

I have just returned from Spring Break, during which time I made a strange realization. I'm sure someone must have discovered this before, but did you know that by using the same logic employed in the modal version of the ontological argument for the existence of God, one can pull a reductio ad absurdum on the thesis of relativism (which is to say, reduce it to a contradiction)? The reasoning isn't much different than when a person is told that there is no such thing as absolute truth and responds with the question, "Is that absolutely true?" but this version sounds much more... well... impressive. Check it out:

First, some definitions. An ontological argument for the existence of God is one which claims that the concept of God is such that to say that such a being does not exist involves a logical contradiction. Modal logic is reasoning involving "possible worlds". There is (conceptually, not actually) one possible world for every way things might possibly be, and one possible world is the actual world. The modal logic ontological argument goes something like this:

1. God is (by definition) a Being with all perfections
   
2. It is possible that God exists (i.e. God exists in at least one possible world)
   
3. Necessary existence is a perfection
   
4. Beings which exist necessarily in one possible world exist in all possible worlds (by the definition of necessary existence)
   
5. The actual world is one possible world
   ----
   
6. :. God exists in the actual world

Now, ever since the first ontological argument (which was very different in form) was proposed by St. Anselm philosophers have been looking at it and saying "There is something wrong with this, but we don't know what it is." This is probably the best version of the ontological argument, but there is still something troubling about it. However, I don't think that this effects the logic of the argument I intend to put forth against relativism, so on with the definitions.

For a proposition (statement) to be objectively true means that if it is true for one person it is true for everyone. The thesis of relativism is that whatever I believe is true for me and whatever you believe is true for you (which obviously implies that there is no objective truth). Now, watch this:

1. Whatever a person believes is true for that person (the thesis of relativism)
   
2. If a proposition is objectively true and it is true for one person then it is true for everyone (definition of objective truth)
   
3. Person A believes that proposition P is objectively true
   
4. :. P is objectively true for person A (from 1 and 3)
   
5. :. P is true for all people, including person B (from 2 and 3)
   
6. Person B believes that proposition P is false
   
7. :. P is false for person B (from 1 and 6)
   ----
   
8. :. P is both true and false for person B (from 5 and 7)

Since 8 is a contradiction, that means that the thesis of relativism and the empirically true proposition that there exists some person (say, me) who believes that some propostion (say, "God exists") is objectively true together imply a contradiction: one or the other must be false. Which do you pick? Incidentally, some relativists respond by rejecting the idea that it is impossible for a proposition to be both true and false for the same person, which is to say that they deny that logic works at all, even from a sort of relativistic ("true for me, true for you") point of view. And just think, they claim to be the mature, cosmopolitan, rational, scientific thinkers, and we're supposed to be backwoods rednecks stuck in the past. Is logic really outdated? No, on the contrary, postmodernism is dead or dying, and the reason for this is that something had to give, relativism or logic, and it wasn't going to be logic.