(September 25, 2018 at 10:44 am)SteveII Wrote:(September 25, 2018 at 9:16 am)polymath257 Wrote: Yep. Without a definite concept of 'greater', there is nothing else that can be concluded. For example, does your version of 'greater' actually have a 'greatest' element? Not all partial orders do. Some have maximal elements (none greater) that are not 'greatest' (all lesser). That depends on whether you have a linear order. But it is very far from clear that there is a well defined linear order that merges all the characteristics you seem to want to lump into a deity.
You want to claim the existence of a greatest. But a greatest need not exist for most partial orders. Even for linear orders there may not be a greatest.
So, you are just ducking the central issue: what does it mean to be greater in this context? How do you know there must be a greatest in that definition of greater? How do you know there isn't more than one 'maximal'? All of these are very relevant questions that need to be addressed *first*, before any claims of existence can be demonstrated.
What are you talking about?
When talking about characteristics of a conscious being, there are definitely 'greater than' determinations that can be made.
It is greater to be all-powerful or limited?
Is it greater to be eternal or finite?
Is it greater to be all knowing or limited in knowledge?
Is it greater to be Good or Evil?
Loving or hateful?
Creative or destructive?
Just or unjust?
Holy or unholy?
Immutable or fickle?
Keep promised or break them?
Merciful or unmerciful?
In case it isn't clear to you, it is clear in the Bible that the former is greater than the latter in this list. Therefore a biblically-informed Perfect Being Theology is entirely coherent, rational, and not particularly hard to understand. The fact you can dream up a mathematical set that has no greatest member is sooooo irrelevant.
You have given several distinct notions of 'greater'. In no way have you shown that they are part of a consistently defined partial order. Nor have you shown that there is a greatest in any of them, let alone a single greatest for all of them.