omniscience_cantorian.pdf |

4.4 Omniscience and Cardinality: Patrick Grim (1988) has objected to the possibility of omniscience on the basis of an argument that concludes that there is no set of all truths. The argument (by

--Summary of the debate taken from SEP entry on Omniscience

*reductio*) that there is no set**T**of all truths goes by way of Cantor's Theorem. Suppose there were such a set. Then consider its power set, ℘(**T**), that is, the set of all subsets of**T**. Now take some some truth*t*1. For each member of ℘(**T**), either*t*1 is a member of that set or it is not. There will thus correspond to each member of ℘(**T**) a further truth, specifying whether*t*1 is or is not a member of that set. Accordingly, there are at least as many truths as there are members of ℘(**T**). But Cantor's Theorem tells us that there must be more members of ℘(**T**) than there are of**T**. So**T**is not the set of all truths, after all. The assumption that it is leads to the conclusion that it is not. Now Grim thinks that this is a problem for omniscience because he thinks that a being could know all truths only if there were a set of all truths. In reply, Plantinga (Grim and Plantinga, 1993) holds that knowledge of all truths does not require the existence of a set of all truths. He notes that a parallel argument shows that there is no set of all propositions, yet it is intelligible to say, for example, that every proposition is either true or false. A more technical reply in terms of levels of sets has been given by Simmons (1993), but it goes beyond the scope of this entry. See also (Wainwright 2010, 50–51).--Summary of the debate taken from SEP entry on Omniscience

I think another solution can be found here:

http://www.reasonablefaith.org/does-god-know-an-actually-infinite-number-of-things

http://www.reasonablefaith.org/does-god-know-an-actually-infinite-number-of-things