The situation as regards an appeal to global properties is, in short, as follows.  An advocate of the argument from evil points to various events, such as the rape and murder of Sue, and claims that no matter how carefully one considers the case, one’s conclusion is that the known wrongmaking properties of not preventing that occurrence outweigh any rightmaking properties that not preventing the occurrence is known to have had.  In response, the possibility of a relevant, morally significant global property is introduced.  But this is a mere possibility, since there is no relevant morally significant global property of which one has knowledge, let alone which one has good reason to believe is present in the case in question.  So the possibility of a relevant global property is simply that: a mere possibility, and as such it gets dealt with in the way that all unknown morally significant properties, both rightmaking and wrongmaking, and both local and global, are dealt with in, for example, the logical probability version of the evidential argument from evil set out above in section 3.5.