April 26, 2009

Is God Actually Infinite?

Question 1:

Dear Mr. Craig,

As I am always debating and defending the Kalam, I am always refuting the possibility of a past-eternal universe, by simple explaining the difference between actual and potential infinites. Now it's quite simple to "disprove" an actual infinite, but the question always pops up "how is God infinite if actual infinites cannot exist?". I do my best to answer, but it never seems to get the job done the way I want it to. I usually say that actual infinites don't exist in the physical universe; God is actually infinite but transcends the physical universe and is not bound there-in or there-by. Any respone would be greatly appreciated.


Question 2:

If actual infinites do not exist as you argue, do you not agree that God knows an infinite amount of things?

Clearly there are an immeasurable but finite number of things in the universe for him to know, but what about his own thoughts? Are there not an infinite amount of thoughts in his own mind within the trinity?


Question 3:

I don't have a question; I am reporting a typo. In the most recent submission of WLC's work regarding Carrier, he states:

"It's just to say that one needn't establish a document's general reliability before establishing that that document reliably records some specific event."

You should now notice that there are two instances of the word "that".

God bless


I would answer your question differently, Russ. Whether something is physical or not seems to me irrelevant to the question of its quantity so long as the things can be numbered or counted. Thus, it is, for example, perfectly intelligible to ask whether there are an actually infinite number of angels or an actually infinite number of souls. Things don't have to be physical in order to be countable. (Mathematically, there are also non-denumerable infinites, but these don't come into the picture here.)

Rather the key to your question is to understand that the mathematical notion of an actual infinite is a quantitative concept. It concerns a collection of definite and discrete elements that are members of the collection. But when theologians speak of the infinity of God, they are not using the word in a mathematical sense to refer to an aggregate of an infinite number of elements. God's infinity is, as it were, qualitative, not quantitative. It means that God is metaphysically necessary, morally perfect, omnipotent, omniscient, eternal, and so on.

Really "infinity" is just a sort of umbrella term used to cover all of God's superlative attributes. If you abstract away all of those attributes, there really isn't any distinct attribute called "infinity" left over. But none of those attributes need involve an infinite number of things. To take your example, Alan, omniscience need not entail knowing an infinite number of, say, propositions, much less having an infinite number of thoughts; nor need we think of omnipotence as entailing the ability to do an infinite number of actions.1 When we define omniscience as knowledge of only and all true propositions, we are expressing the extent of God's knowledge, not its mode. The mode of God's knowledge has traditionally been taken to be non-propositional in nature. God has a single undivided intuition of reality, which we finite knowers break up into individual bits of information called propositions. Thus, the number of propositions is at best potentially infinite. Similarly, omnipotence is not defined in terms of quanta of power possessed by God or number of actions God can perform but in terms of His ability to actualize states of affairs. As such it involves no commitment to an actual infinity of things. Therefore, there's no reason to think that God is susceptible to the sort of quantitative analysis imagined by the objection.

Thus, denying that God is actually infinite in the quantitative sense in no way implies that God is finite. This inference does not follow, since the quantitative sense of infinity may be simply inapplicable to God.

Finally, I couldn't resist taking your question, Michael, because it reminds me of a story I once heard. A student teacher grading high school English papers corrected a student's use of the word "that" five times in a row in his theme essay. The student complained to his regular teacher, who, after looking at the paper, reversed the student teacher's correction, remarking, "Although the chances are a million to one that this usage would ever occur, we've got to admit that that "that" that that student used is correct!"

Similarly, in my sentence the first "that" is a conjunction and the second "that" is a demonstrative pronoun—good English grammar!


1 See William Alston, “Does God Have Beliefs?” Religious Studies 22 (1986): 287-306; Thomas P. Flint and Alfred J. Freddoso, “Maximal Power,” in The Existence and Nature of God, ed. Alfred J. Freddoso (Notre Dame: University of Notre Dame Press, 1983), pp. 81-113.