As long as you don’t confuse sets with reality, that’s OK with me.
Confuse? No. Represent reality with sets? Yes, that is rather the point. For all your pretense to agreement, it is apparent that after all, you don’t agree.
(to my suggestion that wG = {G}.)
No. Not if {G} is different from God.
If you think there is something (that sets a set apart from its elements), you will have to show what it is.
Gladly.
en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
The contemporary standard
In standard, Zermelo–Fraenkel (ZF) set theory the natural numbers are defined recursively by 0 = {} (the empty set) and n + 1 = n ∪ {n}. Then n = {0, 1, …, n − 1} for each natural number n. The first few numbers defined this way are 0 = {}, 1 = {0} = {{}}, 2 = {0,1} = {{},{{}}}, 3 = {0,1,2} = {{},{{}},{{},{{}}}}.
(end wiki quote)
Consider the empty set, {} = 0. Consider the set, {{}} = 1. Clearly, 0 =/=1, so clearly, {} =/= {{}}. So clearly, the sole element of a singleton set is not the same as the set itself. Therefore, {G} =/= G, and, I would assert, although you unsupportably object, since G =/= {G}, consequently, wG =/= G.
Nonsense; Catholic doctrine has it that God is the creator of everything. If He does not create, there is only G and if {G} is different from G, then there is no {G}. Because you cannot account for the difference. G describeS the whole of reality.
G is God, and {G} is the world with God alone in it. I’m happy to see you’ve accepted set notation, if you are not yet prepared to accept set theory per se. I can at least treat wG as = {G} and wait for you to object.
Now, if you want to say that the world with God alone in it IS God, that’s Pantheism straight up. Making the world equal to God is Pantheism, whether or not there is anything else in the world. The Pantheos creates by transforming itself, by becoming the world. But that is not how God creates. God creates from nothing — ex nihilo. Not from Himself, but from nothing.
en.wikipedia.org/wiki/Axiom_of_regularity
Axiom of regularity
From Wikipedia, the free encyclopedia
In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo–Fraenkel set theory and was introduced by von Neumann (1925); it was adopted in a formulation closer to the one found in contemporary textbooks by Zermelo (1930). In first-order logic the axiom reads:
Code:
\forall A (\exists B (B \in A) \Rightarrow \exists B (B \in A \land \lnot \exist C (C \in A \land C \in B))).
Or in prose:
Code:
Every non-empty set A contains an element B which is disjoint from A.
[One of the] results which follow
from the axiom [is] that “no set is an element of itself.”
(end wiki quote)
But if G = {G}, then {G} is an element of itself.
The specific reason is that to exist and to not exist are contrary. So to ‘call’ something into existence is like shouting in a void.
Ah! I see your confusion on this point! You seem to think that, rather than create from nothing with His will, God commands nonexistent entities to come forth into existence. I can see how you think this absurd!
It is absurd, but not what I said. Perhaps I confused you by using the phrase, “called into existence from nothing by God.” No doubt, I was using as common metaphor. I should not suppose you are familiar with every metaphor. “Called into existence,” would be a metaphorical way of saying “created.” God created everything that is, from nothing. You say He can’t, but so far all you’ve got to back that up is a gross misunderstanding of set theory, and an imaginary world where God somehow painted Himself into a corner.