While we haven't recently discussed God's properties in class, this post is related to a claim that has always puzzled me and will also probably be featured in my R&R paper. I have never understood how God can be infinite in existence and yet the world and everything else can also exist. These two ideas seem inconsistent to me, and yet I think infinite existence is supported in Judeo-Christian religious tradition.
If something is infinite in its own kind, then it must include all things of its type. If something of its type were to exist independent of the set contained in infinite, then this would limit infinity and instead make it finite. Therefore, any other thing existing outside the infinite existence of God would seem to limit God's infinite existence. The world and its inhabitants are clearly imperfect and don't have many of the same qualities as God, so they must be different from God. But if the world exists and is independent of God, then it limits God's infinite existence.
Does anybody know if there is any justification for the religious claim? Am I misinterpreting infinity or the way religion considers existence? Are there two types of existence being referred to, and does this get religion out of the contradiction?