(September 25, 2018 at 9:01 am)SteveII Wrote:
(September 24, 2018 at 7:51 am)polymath257 Wrote: You do, however, need a partial order that has a largest element. The problem is that 'greater' isn't well defined. Even if it were, there is no reason to think there is a greatest element.Nope. Concerning God, the concept of 'greatest' does not require us to know what is actually the greatest. You are confusing ontology with epistemology.
So, at the very least, you need a consistent definition of 'greater'. Since there is more than one variable on which you want to measure (power, goodness, knowledge, etc), you have to find a consistent way to guarantee a maximum on each variable at the same time. This is usually impossible, even when each individual variable has a largest element.
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.