The Christian Perspective

Complete sets with members that are unending in quantity do exist.

A sample set would be the set of all possible configurations of the letters ABC, where duplication of characters is permitted. We would have: ABC, ACB, BAC, BCA, CAB, CBA, AABC, AACB, ABAC, ABCA, ACAB, ACBA, BABC, etc.

In fact, the quantity of complete sets with members that are unending in quantity are themselves unending in quantity (the set of all infinite sets is an infinite set).

However, it is true that the possibility of iterating all the way through an infinite set is logically incoherent.

In other words, while infinite sets exist, it is not possible to completely iterate through each item in an infinite set -- you cannot list them all one-by-one. If it were possible to iterate through the set, to list them all one-by-one, then the set would necessarily have both a beginning and an ending, and therefore it would not be infinite, but finite, by definition.

Having said this, when God is spoken of by Christians as being infinite, the meaning of the statement is not intended to be taken mathematically, since "God" is never understood to be an unending set of anything. Such a statement is either intended as a poetic or metaphorical statement, basically meaning something along the lines of "God is bigger and more powerful and more important than anything you can imagine", or else it is not referring to God directly but rather to some property of God, or quality of God, such as His knowledge, meaning perhaps "If God were to tell you every piece of information He knows one-by-one, He could never finish telling you it".

Clearly, neither of these meanings claim that God is a completed iteration through an infinite set (which, as we have seen above, is logically incoherent), since God Himself isn't an iteration through anything anyway.

To rephrase the second part of your question, "could God be construed as a potential infinitely omnipotent being", God can only do that which He will do. He cannot do anything else. His capabilities are indivisibly tied to His will, such that if He does not will to do something, then He cannot do it, for He cannot deny Himself (2 Timothy 2:13). If, on the other hand, He does will to do something, then He does do it. In my mind, this ultimately leaves no room for potentiality, or possibility. Humans only speak of potentiality or possibility in this sense due to our own lack of knowledge or lack of certainty, neither of which plague our God.

In other words, while I would be comfortable saying that Christ could "potentially" return at any moment (for example), that is only the case from my own subjective perspective, since I do not know when He will actually return. In the ultimate and objective sense (from God's perspective), Christ cannot "potentially" return at any moment. He can only return when God has decided He will return. There is no other "potential" option.

If, for example, God has decided that Christ will return in 2073, then there is absolutely no potentiality for Him to return in 2052. I, of course, do not know when God has decided that Christ will return, therefore, as far as I am concerned in my ignorance, His return could potentially occur at any moment.

All this is to say that since God has perfect knowledge, and since whatever He plans comes to pass exactly as planned, it doesn't seem coherent to me to speak of God as "a potential infinitely omnipotent being". He is already perfect and complete; potentiality and possibility refers to a lack of completion.

The Christian worldview is in fact the only worldview that is not logically contradictory.

God bless you as you work to think God's thoughts after Him.

The Impossibility of the Contrary