I do not understand why you posted this under Christianity since it seems to belong in Philosophy. Nevertheless, thank you for a good topic. I was starting to get bored. Be that as it may, I do not find any of the Kalam-style demonstrations compelling and highly doubt that Kalam enthusiasts have thought very much about actual/potential infinities.
I see resolution of the apparent paradox in Aristotle’s distinction between two modes of existence: actuality and potentially. The number of actual infinities would be finite whereas the number of potential infinities is infinite (but not unlimited).
I have always maintained that God’s knowledge consists only of that which it is possible to know and that this position satisfies the definition of all-knowing, as in knowing all there is to know. From there I say that there is nothing to know about things that do not exist either in actuality or could not possibly be. For example, an oak may currently exist as an actual acorn and simultaneously be said to exist as a potential sapling. Thus God knows everything it is possible to know about what the acorn is (now) and what it could potentially become (later). However, God does not and cannot know what the acorn will actually become since that is in the future and the future does not yet exist. What potential will be actualized could be contingent upon the decisions of freely acting beings (humans). These people could prevent the acorn from being planted or start a forest fire.
One thing that continues to puzzle me is the ontological status of the past since technically the past does not exist anymore; it is a current memory or embodied history. That also strikes at the heart of Kalam-style demonstrations. Not only could there not be an actual infinite regress into the past, there cannot be any temporal regress at all! The passage of time is, as it were, a kind of illusion within an eternal present.
I see resolution of the apparent paradox in Aristotle’s distinction between two modes of existence: actuality and potentially. The number of actual infinities would be finite whereas the number of potential infinities is infinite (but not unlimited).
I have always maintained that God’s knowledge consists only of that which it is possible to know and that this position satisfies the definition of all-knowing, as in knowing all there is to know. From there I say that there is nothing to know about things that do not exist either in actuality or could not possibly be. For example, an oak may currently exist as an actual acorn and simultaneously be said to exist as a potential sapling. Thus God knows everything it is possible to know about what the acorn is (now) and what it could potentially become (later). However, God does not and cannot know what the acorn will actually become since that is in the future and the future does not yet exist. What potential will be actualized could be contingent upon the decisions of freely acting beings (humans). These people could prevent the acorn from being planted or start a forest fire.
One thing that continues to puzzle me is the ontological status of the past since technically the past does not exist anymore; it is a current memory or embodied history. That also strikes at the heart of Kalam-style demonstrations. Not only could there not be an actual infinite regress into the past, there cannot be any temporal regress at all! The passage of time is, as it were, a kind of illusion within an eternal present.
