This paradox can be expressed thus:
(1) God believes that (1) is false.
If (1) is true, then God believes that (1) is false and so is mistaken. If (1) is false, then God doesn’t believe that (1) is false and so fails to know a truth. Either way, there is a problem for divine omniscience.
Consider the standard Liar Paradox:
(2) This sentence is false.
Let me suggest a solution by quoting from my book.
(2) is neither true nor false, because there is no truth-bearer; there is no thing that might be considered true or false. “This sentence is false.” What is false? This sentence. But the sentence affirms nothing other than that it is false. A contentless no-proposition may very well be neither true nor false. We can even call it meaningless. It is meaningless not as “abracadabra” or “square circle” is meaningless, but as silence or an empty string “” is meaningless: nothing whatever is asserted by “This sentence is false.”
That something is asserted is an illusion foisted on us by the fact that the sentence is grammatical like “This sentence is in English.”
Ask, when you read (2), do you learn anything about the world? Not at all; you learn nothing. Suppose that you already knew reliably that (2) was false, though not what exactly was false. When you actually read the sentence, do you find that out? Of course not.
A proposition is a real state of affairs or slice of the real world being proposed, and proposing something is thinking about it as holding or failing to hold. But (2) does nor deserve to be called a proposition.
Grim further evaluates the Strengthened Divine Liar paradox:
(3) God doesn’t believe that (3) is true.
Again, either God fails to know something true or believes a falsehood. But a similar analysis saves divine omniscience. Suppose that (3) is true. God doesn’t believe it. What exactly is it that He does not believe? That (3) is true. What is (3)? “God doesn’t believe that (3) is true.” So, God doesn’t believe that (God doesn’t believe that (3) is true) is true. That pesky (3) doesn’t want to go away! Maybe if we replaced it again:
(3′) God doesn’t believe that God doesn’t believe that God doesn’t believe that (3) is true is true is true.
It’s still there. In general, then, what God doesn’t believe is that
(3″) God doesn’t believe that God doesn’t believe that… (ad infinitum) is true is true… (ad infinitum).
That’s not a proposition whose truth value anyone would want to evaluate. This is because it doesn’t have a truth value. Grim’s proof therefore fails.
This concludes my blogging of The Impossibility of God.