May 10, 2009
Omniscience and Actual Infinity
Hi Dr Craig
I have been contemplating omniscience of God and how this relates to infinity.
I am struggling to come to terms with an omniscient God and an infinite future. After reading Eric Sotnak’s “The Kalam Cosmological Argument and the Possibility of an Actually Infinite Future (1999)”. I am persuaded by his argument but this does not sit will with my theological view that God is all knowing.
The part that of his argument I found convincing was
(AL1) God’s intellect apprehends Peter’s afterlife as unending.
(AL2) If God’s intellect apprehends Peter’s afterlife as unending, then God’s intellect either apprehends Peter’s afterlife as potentially infinite or as actually infinite.
(AL3) If God’s intellect apprehends Peter’s afterlife as potentially infinite, then there will be days of Peter’s afterlife that will come to pass that are not included in God’s intuitive apprehension of it.
(AL4) There is nothing that will come to pass that is not included in God’s intuitive intellect.
(AL5) Therefore, God’s intuitive intellect apprehends Peter’s afterlife as actually infinite.
(AL6) If God’s intuitive intellect apprehends Peter’s afterlife as actually infinite, then Peter’s afterlife is actually infinite.
(AL7) Therefore Peter’s afterlife is actually infinite.
(AL8) If Peter’s afterlife is actually infinite, then an actual infinite is possible.
(AL9) Therefore, an actual infinite is possible.
being only of engineering background maybe some aspect of logic is missing which I can’t see.
Its the difficulty with a potential and actual infinity that confuses me. Such that It seems plausible that if God were able to comprehend everything then he must be able peter’s actual infinity. But this seems impossible as an infinity can be traversed. Does that then imply God does not know everything.
For those readers who are puzzled by the point of this argument, let me say that a key feature of the kalam cosmological argument for a Personal Creator of the universe based on the finitude of the past is the claim that an actually infinite number of things cannot exist. Objections of the above sort seek to show that an orthodox theist cannot endorse the kalam argument. These sorts of objections do not seek to refute the argument so much as to embarrass its proponents by forcing them to adopt theologically unorthodox views.
I notice with interest that Sotnak’s argument is cast in terms of God’s intuitive knowledge, which serves to differentiate his objection from arguments based on the assumption that God’s knowledge is propositional in its mode, which I discussed in Question of the Week 106. Sotnak wants to prove that even if God’s knowledge is an undivided intuition of reality, His omniscience generates a problem for the claim that an actually infinite number of things cannot exist.
In responding to Sotnak’s argument, David, it seems to me that one ought to deny (AL3). Given that future things and events do not really exist, that is to say, temporal becoming is an objective feature of the world, Peter’s afterlife is potentially infinite. Infinity in this sense is a mere limit concept, a limit which the days of Peter’s life endlessly approach but never achieve. It therefore follows that there simply are no days “beyond” this limit which remain unknown to God. (AL3) is thus completely wrong-headed.
Perhaps what Sotnak is implicitly assuming is that if Peter will live forever, then his afterlife will be actually infinite. But then he’s begging the question against Peter’s afterlife’s being potentially infinite. What is wanted is some argument for that assumption. Moreover, all the talk about omniscience becomes in that case just superfluous window-dressing. The argument should just be that immortality implies the existence of an actual infinite. Omniscience doesn’t even enter the picture. Whether immortality implies the existence of an actual infinite was a central issue in my dialogue with Wes Morriston on the kalam cosmological argument, which I commend to you. (see "Debate on the Kalam Argument" Reasonable Faith Podcast)