A being X is omniscient iff:So for fun….
(i) for every true proposition p, X knows p, and
(ii) there exists no proposition p such that X believes p and p is false.
1. Let p be the proposition: “God does not know p.”That is, p is a self-referential proposition.
To put this into words, for those who are less inclined toward reading logic, the original definition of omniscience is, in language form: “An omniscient being knows all true statements, and does not know any false statements.” Now, orthodox Christians believe God is omniscient, so we can examine a specific statement, the statement: “God does not know this statement.”
2. Suppose p is true.
3. Therefore, p is known by God, per (i).
4. If p is known by God, then p is false.
5. Therefore, if p is known by God, (ii) is false.
6. Suppose p is false.
7. Therefore, p is not known by God, per (ii).
8. If p is not known by God, then p is true.
9. Therefore, if p is not known by God, (i) is false.
Typically, we would say the statement, “God does not know this statement” is either a true or false statement. If it is true, then God does not know the statement “God does not know this statement.” The result is that there is a true statement that God does not know. But the definition of omniscience includes in it the fact that “An omniscient being knows all true statements.”
On the other hand, if the statement is false, then we are saying God does know the statement “God does not know this statement.” But that means that God knows a false statement, which violates the second part of the definition: “An omniscient being…does not know any false statements.”
As I said, typically we would say the statement, “God does not know this statement” is either a true or false statement, but now we realize that the statement is neither true nor false; or rather, the truth value of the statement is in a constant state of flux. If it is true, then it is false; but if it is false, then it is true. So does God know these types of statements? The above definition of omniscience cannot tell us.
The result is that, at best, the above definition of omniscience is incomplete—it does not take into account statements that have variable truth-value. In other words, this definition of omniscience didn’t take Gödel into account.