Two Arguments for the Impossibility of an Omniscient Being

An Impossible (or Penrose) Triangle

Source: OpenClipArt; License: CC 

Version #1

1. Either God can know what it is like not to know that p or God cannot know what it is like not to know that p. 
2. If God can know what it is like not to know that p, then God is not omniscient (since to know what it is like not to know that p, there must be some p that God does not know). 
3. If God cannot know what it is like not to know that p, then God is not omniscient (since there is some p—i.e., (L) or (L*)—that God cannot know). 
4. (Therefore) Either way, God is not omniscient. 

Version #2

1. Either God can know what it is like to be finite or God cannot know what it is like to be finite. 
2. If God can know what it is like to be finite, then God is not omniscient (since to know what it is like to be finite, God must be finite). 
3. If God cannot know what it is like to be finite, then God is not omniscient (since there is something that God cannot know, namely, what it is like to be finite). 
4. (Therefore) Either way, God is not omniscient.

Both versions of this argument belong to Moti Mizrahi. See:

Mizrahi, Moti (2013). "New Puzzles About Divine Attributes." European Journal for Philosophy of Religion 5 (2):147-157.