G: God, an omnipotent, omniscient, perfectly good and necessarily existing being, exists.
With this definition we get for free a number of trivial truths such as; if God exists then he is omnipotent, if he exists then he is omniscient, and most interestingly, if God exists then he exists necessarily. We can use this last truth along with the modal logic system S5 to prove that, if God's existence is even just possible, then he actually exists:
◊G → ◊□G → □G → G
This is the most popular version of the modal ontological argument for God. But what proponents of this argument don't want you to know is that atheists can parody their case with an argument of their own:
◊¬G → ¬□G → ¬◊G → □¬G → ¬G
And so if God possibly does not exist (if atheism is possibly true), then he in fact does not exist (atheism is in fact true). Now the question is, which is more plausible: ◊¬G or ◊G? Well clearly the theist, being a theist, thinks that theism is possible. And of course the atheist, being an atheist, thinks that atheism is possible. And so we have a standoff in which, if either the atheist or the theist is possibly correct in their theological view, then they're in fact correct. Once noticing this, the atheist would literally have to presuppose that atheism is impossible before he could be convinced by the ontological argument for God. Of course no one trying to prove that God exists using the ontological argument would mention this symmetry, and so unfortunately many people don't realize that a case can be made both ways. But now notice that we can open up the ontological argument to include other facts. Any fact that entails God exists, on atheism, must be necessarily false. And any fact that entails God doesn't exist, on theism, must be necessarily false. Are there any facts that might entail that God exists? I honestly can't think of any. Surely instances of apparent design are evidence for God, but they certainly do not entail theism. What about facts that entail God's nonexistence? Immediately gratuitous evil comes to mind, being the sort of evil that God has no good reason to permit. It's not very controversial that, if God were to exist then, by his divine providence, gratuitous evil (E) and suffering would not. And so we have another derivation:
◊E → ◊¬G → ¬G
And so if it's possible for gratuitous evil to exist, then it's also possible that God does not. And this, like I showed before, entails that God in fact does not exist. So the prior question can be posed again: Is it more plausible that either ◊E or ◊¬G, or that ◊G? While atheism and theism alone butting heads might seem to draw a tie, once we mention gratuitous evil the win should go to atheism.
Because the definition of God contains a nested modal operator, by claiming that God is possible we're making a statement about all of modal reality. In other words, we're saying that there's a possible world in which an entity that exists in all possible worlds, exists. But saying gratuitous evil exists requires us to make a statement about merely one possible world. In fact we can construct such a world very easily by supposing the greater good justification for some actual evil didn't exist. This is exactly the sort of modal reasoning we employ every day (e.g. If I had run that red light, I would have been hit by a truck). If we can't trust our modal intuitions on something as simple and obvious as gratuitous evil, then how can we trust our modal intuitions enough to confidently claim that God's existence, something that requires an infinitely greater scope, is possible? And so the necessity of God can actually be turned against theism, and be used to show that atheism is much better supported by it.
An objection the theist may have to my argument is that, when I speak of possibility, I'm really talking about epistemic possibility and not metaphysical possibility. That for all I know gratuitous evil might exist, but I don't actually know that there is a metaphysically possible world in which gratuitous evil exists. But that response would undermine the ontological argument for God as well, as the atheist is entitled to saying the same thing. For all the theist knows God might exist, but the theist doesn't actually know there's some metaphysically possible world in which God exists. And so it seems that the necessity of God either provides atheists stronger reason to reject God's existence than it provides theists reason to accept his existence, or it offers nothing at all to either party.
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