But what of omniscience? It is often said that God is all-knowing. Can such a concept as being all-knowing have a similar logical contradiction at the heart of it? I'd argue that it does. The argument goes as follows:
Suppose a being can hold all the knowledge about everything. But to hold knowledge about everything creates a new fact, that there is a set of knowledge that contains everything. And that in itself creates a new fact, that there is a set of knowledge that contains the set of knowledge that contains everything. And so on. So no matter how one wants to encompass all the facts, doing so creates new facts. Thus absolute knowledge can never be reached. Thus omniscience is impossible. Q.E.D.
From this we should be able to reject the possibility of any being claimed to be omniscient a priori.