God and Infinity

I received a question about the Kalam Cosmological Argument.  As you may remember, in furthering the argument we will want to say that an actual infinity cannot exist.  It is for this reason that the universe cannot have an infinite past but must have had a beginning.

The question was why we cannot have an actual infinity with respect to the past but we can have an infinite being?

My response is below:

I believe part of your question is answered in question #248 on the Reasonable Faith website, and I would encourage you to read through it.  In that response Dr. Craig details why an infinite regress is impossible.  If you have any questions about the response, please let me know!

In short, it is important to note that when theologians talk about God being “infinite” they don’t mean it in the numerical sense.  They mean that God is not finite in any way.  God is not finite in his knowledge, power, goodness, etc.  In other words, the theologian is saying that God is without limits.  This is different than postulating the existence of an actually infinite number of things (such as would be the case in an infinite regress of causes).


Matt Bilyeu

6 thoughts on “God and Infinity

  1. Does God know every single Natural number? If so, God’s knowledge must be infinite in the numerical sense, by definition. If not, we have discovered a limit to God’s knowledge.


    1. I think you are conceiving of God’s knowledge as a collection of actual things. I am not sure this is appropriate.

      I wouldn’t say that God’s awareness of the number 5, for example, is itself a “thing”. For that reason I wouldn’t say that God’s knowledge amounts to an actual infinite number of things.


  2. I’m not sure I follow. Surely, knowledge is a thing. If so, it would follow that knowledge of a particular fact is a thing. Knowledge of each particular Natural number would therefore constitute an actually infinite set of things.

    What would it even mean for knowledge of a number to NOT be a thing? How could one differentiate it from the lack of such knowledge?


    1. I am not a realist when it comes to either knowledge or the content thereof. Rather I would say that knowledge is a state of affairs (namely that you are in the state of having warranted true belief regarding an issue).

      Spatial relations may be a good analogy. I would liken your knowledge of a statement to your spatial relationship to physical objects. You are in the spatial relation of being south of the north pole. This spatial relation is not a “thing” however, but rather a description of your relationship.

      In the same way, your knowledge of X is a statement of your relationship to X, namely that you have warranted true belief of X. In this way your knowledge of X isn’t a “thing” but a description of how you are related to X.


      1. Is a state of affairs a thing? If so, then knowledge, as a state of affairs, is a thing. If not, then what is a state of affairs?

        Similarly, even if we are describing a relationship by use of a phrase, that relationship is a thing, isn’t it? It has its own properties which differ from the properties of some other relationship.

        I’m still unsure how the knowledge of an actually infinite number of particular facts would not constitute an actually infinite set.


        1. I can see we disagree about this, but no I don’t think a state of affairs or a relation is itself a thing.

          You and the sun each have properties, but the spatial relation between you and the sun doesn’t itself have properties. The relation of being 98 million miles away doesn’t have properties, it is just a description of your spatial relationship.

          In the same way, when you have warranted true belief (knowledge) about something the mere fact that you have such knowledge has no independent existence.


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