Here is an ontological argument that I haven’t seen:
Possibly, it is approximately true that God exists.
Necessarily, if it is approximately true that God exists, then it true that God exists.
If possibly God exists, then God exists.
So, possibly, it is true that God exists. (1 and 2)
So, God exists. (3 and 4)
Premise 1 is an interesting weakening of the familiar possibility premise from modal ontological arguments.
Premise 3 is also familiar, going back at least to Mersenne. We can say that God is the sort of being that couldn’t exist merely contingently: he either exists necessarily or he can’t exist at all—there is no room for mere possibilities in the case of God’s existence.
The thought behind 2 is rather similar to that behind 3: God is a kind of infinity that cannot be approximated. It is not possible for there to be a state of affairs merely approximating the existence of God.
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Are there good examples of existence claims which are approximately true but not true?
If there is someone who is 182 cm tall, but no one who is 181 cm tall, then "There is someone who is 181 cm tall" is approximately true.
The key phrase in understanding these kinds of modal arguments is this:
"there is no room for mere possibilities in the case of God’s existence."
That means there is no room for premise 1 in the case of God's existence.
IOW because saying that God possibly exists is the same as saying God exists, premise 1 does not provide one with a shortcut to proving God's existence, rather premise 1 can only be stated if it is certain that God exists, or, more correctly, if God's necessity has already been established. But if that were the case, the argument would be redundant.
So, these kinds of modal arguments do not contribute anything of interesting to the debate on God's existence.
This sounds to me rather like this objection: "The premises logically imply the conclusion." Whenever we give a valid argument, the premises leave no room for the denial of the conclusion.
Here's an interesting thing about the argument. The classic S5 ontological argument faces a parallel argument for atheism:
1a. Possibly, it's not the case that God exists.
2a. God possibly exists iff God necessarily exists.
3a. So, God doesn't exist.
But there is no parallel in the approximation version:
1b. Possibly, it's approximately not the case that God exists.
2b. God possibly approximately exists iff God necessarily exists.
3b. So, God doesn't exist.
But this argument is invalid. In fact, while the theist cannot embrace 1a, the theist can embrace 1b, and say that "God does not exist" is precisely false but approximately true. In fact, many mystics and theologians have explicitly said that "God does not exist". Strictly speaking, what they said isn't true---but it gets at something close to the truth.
Dr Pruss, you said, "This sounds to me rather like this objection: "The premises logically imply the conclusion.""
My objection is not that the premises entail the conclusion. My objection is that at least one of the premises is based on the conclusion. Denying God's necessity entails denying premise 1 because if God is not necessary, He is not possible and his existences is not possibly true.
Moreover, if is not possible for there to be a state of affairs merely approximating the existence of God, premise 1 is necessarily false. It cannot be approximately true that God exists.
In any case, since I am convinced that God doesn't exist, I am well withing my rights to deny premise 1.
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