Is there also a Premise (0) that goes unstated, namely that being "great" has a partial ordering (a necessary condition for a being-none-greater to be a coheren

Is there also a Premise (0) that goes unstated, namely that being "great" has a partial ordering (a necessary condition for a being-none-greater to be a coherent formulation), or does Anselm address this? I find it difficult to judge, for example, whether this cup of tea is greater than that palm tree, or whether this composer is greater than that wristwatch; yet Anselm seems to consider it obvious that I could conceive of a being or thing strictly "greater" than all of them. I don't know what that would even mean!