Omniscience is supposed to be knowledge that is maximal or complete. Perhaps knowledge of all truths, as (D1) puts it, captures that idea. But there are other features that might be included in such maximal knowledge when it is had by a perfect being. For example, perhaps a perfect being does not merely believe all true propositions but, in addition, could not possibly be mistaken. Perhaps, in other words, such a being is infallible, that is, necessarily such that any proposition it believes is true. Van Inwagen (2006: 26) adds to his variant of (D1) that it is impossible that there is a proposition q such that S believes q and q is false, which is equivalent to requiring that necessarily if S believes p then p is true. (See also van Inwagen 2002: 221.) It is conceivable that a being might satisfy (D1) by knowing all truths without its being such that it could not possibly hold a false belief. In that case infallibility adds an additional component to the standard account given by (D1).