 This enhanced version, if it’s distinct from PAP, will not appear in what follows. But the discussion below could be relevant to PAP-ultimate. In particular, it’s likely that PAP entails PAP-ultimate, so that arguments considered below for the former  (§2)  could be brought in favor of the latter. What’s less clear is whether PAP-ultimate entails PAP. If it doesn’t, then objections to the latter  (§3)  needn’t damage the former.