Suppose I agree with theists that "God exists" is a necessary proposition, and so is either a tautology or contradiction. That seems to indicate that the probability of "God exists" is either 1 or 0. Suppose also that I don't know which it is, but I find the evidential argument from evil convincing, and so rate the probability of "God exists" at, say, 0.2. But if the probability of "God exists" is either 1 or 0, then it can't be 0.2 - that would be like saying that "God exists" is a contingent proposition, which I've accepted it isn't. How then can I apply probabilistic reasoning to "God exists" at all? If I can, then how should I explain the apparent conflict?

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If "God exists" is necessary, then the probability that God exists is 1. Full stop. It is not either 1 or 0, it is simply 1. It is also not 0.2 or any other number.

Nothing like begging the question big-time, eh?

On the other hand, I can't see why anyone serious about the question of God's existence (even theists, who would like the answer to be affirmative, but presumably not on foolish grounds) would accept the claim that "God exists" is necessary. If that were true than the could be no possible world (=a world that can be described without contradiction) in which God did not exist. But it seems obvious that there can be such a world. Consider this description:

World W = a world in which only a single pencil exists.

It's hard to spot the contradiction in that simple world! It would be a pretty boring place to be...but wait! If anyone were to be there, it would be a different world! Whew!

I'd like to offer a rather different take on this than my co-panelist. Many theists don't think that "God exists" is a necessary proposition. However, some famously do. St. Anselm is the most well-known example, but he's not the only one. The contemporary philosopher Alvin Plantinga apparently does as well.

Now we can grant that it's not obviously a contradiction to say that the world contains only a single pencil, but people who think God exists necessarily may not think that metaphysical necessity is the same as logical necessity. If I understand Plantinga correctly, he doesn't think it's a contradiction to say "God doesn't exist," though he does think that God's existence is metaphysically necessary.

All of that is throat-clearing. We could make a similar point in a different way. Mathematical truths are necessary if true at all, or at least so we'll suppose. But it's famously hard to argue that mathematical truth is the same as logical truth. So the more interesting question is this: suppose X is a proposition that, if true, is a necessary truth. I may still find myself inclined to make probabilistic claims. For example: Jones offers a mathematical conjecture. I realize that if it's true, it's necessarily true. But I'm not sure if it's true. I might say things like "I think it's probable that Jones's conjecture is true." Indeed, I believe that mathematicians really do talk and think this way sometimes.

Superficially, it's not hard to see what we should say here. We can make a distinction between "objective" probability -- which has to do with the things themselves, to to speak, and epistemic or subjective probability, which has to do with our degrees of belief. Something might have an objective probability of one, but I might not know this, and so my degree of belief might be less than one. In particular, if God actually exists, and exists necessarily, or if Jones's conjecture really is true and necessarily so, I might still have doubts, and so my degree of belief would be less than 1.

All of this is fine, though there are some remaining puzzles. Subjective probabilities are supposed to conform to the rules of the probability calculus. If the necessary truth is a logical truth, then we have a problem: logical truths have to get probability one, but there seem to be plenty of cases where we aren't sure whether something is a logical truth.

However that problem gets sorted out (and there are various possible strategies) it's not directly an issue for the case of God. We've conceded that "God exists" isn't a logical truth, but allowed that it might nonetheless be metaphysically necessary. And that means there is no straightforward conflict with the rules of probability. Whether there are subtler issues about assigning subjective probabilities of less than one to metaphysically necessary propositions is something I'll leave to people who have thought about it more than I have.

I confess I don't understand the notion of "metaphysical necessity," if it does not entail that that there is no possible world in which the "metaphysically necessary" being does not exist. But only a pencil exists in world W. So I really don't see what is gained (or why the very question of God's existence is not simply begged) by the claim that God is a (metaphysically) necessary being.

Interesting points. I take it that the most reasonable reply for a defender of the ontological argument to make is to claim that Prefoessor Smith's world is not in fact possible. If one can make a case for abstracta (properties or propositions necessarily existing) then there cannot be a world where only a single pencil exists. For a good case for such a Platonic position, see Roderick Chisholm's Person and Object. R.M. Adams also has a good discussion of the difficulty of imagining / conceiving of God's non-existence. I take this up in a modest book: Philosophy of Religion: A Beginner's Guide (Oneworld Press, Oxford) or in more detail in a discussion of Hume and necessity in Evidence and Faith: Philosophy and religion since the seventeenth century (Cambridge University Press).

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