June 23, 2013
The Concept of God
Firstly, I would like to say that, despite the fact that I'm agnostic, you are one of my heroes. In all of the debates that I've watched, you've been the sole provider clarity and rigor to the discussion.
My question regards whether or not your definition of "God" is a proper definite description. Among other things, he's posited as a being which is omnipotent and omniscient. However, is there good reason to think that there are upper-bounds on power and knowledge, so as to allow this to be feasible?
Let's look at one area in which any being's abilities and knowledge is necessarily finite and incomplete. For example, it is obvious that there's no greatest natural number, as this set is an infinite one. Now, we know that no possible being can know all of the elements of this set, since it's uncountable. We can also say that if one being knows or can know more natural numbers than another, then that being is more knowledgeable or capable, respectively, in this area. This means that since the set of natural numbers is infinite, there cannot, in general, be a single greatest-possible being, because we can always conceive of a being with greater cognitive capabilities or knowledge (i.e, the ability to know n + 1 elements of the set). Since there are certain areas pertaining to knowledge and power which do not have an upper-bound, it is necessarily the case that any possible being's net knowledge and capabilities are limited and imperfect. Hence, there cannot be a being possessing the properties that are ascribed to God.
I appreciate your kind remarks, Ian.
As I read your question, I think that you’re not really asking about the definition of the word “God.” There are standard dictionary definitions of this word in English, and the meaning may vary from context to context. What you’re really asking about, I think, is the concept of God. Why do theists usually think of God as omnipotent and omniscient?
There are two guidelines for doing Christian theology: Scripture and perfect being theology. We Christians believe that God has revealed Himself in the Bible; that is to say, He has furnished us with propositional truth about His existence and nature. Scriptural teaching is, however, underdeterminative with respect to many divine attributes. For example, Scripture teaches that God is all-mighty but does not provide a philosophical analysis of what it is to be all-mighty. Indeed, Scripture says that there are things that God cannot do, e.g., sin.
So in addition to Scripture we appeal to perfect being theology to fill out our concept of God. According to this approach, God is the greatest conceivable being. This presupposition seems to be necessarily true, since nothing can be greater than God. So in line with perfect being theology, we construe Scriptural teaching on God’s nature in such a way as to augment God’s greatness to the maximal extent possible. Omnipotence and omniscience seem to be properties which do have an intrinsic maximum: roughly, to be able to actualize any possible state of affairs and to know every truth. You can’t get any more powerful or knowledgeable than that!
You quite properly ask whether knowledge and power do have upper bounds. You want to give an example showing that “any being's abilities and knowledge is necessarily finite and incomplete.” If successful, your argument would show that any being necessarily has some finite degree of the property and that it is always possible to have a higher degree. So there would be no highest degree of power or knowledge that God might have.
So far so good; now let’s look at your example: the set of natural numbers, which has an actually infinite number of members. You assert, “we know that no possible being can know all of the elements of this set, since it's uncountable.” This inference is mistaken, Ian. First, the set of natural numbers is countable! It’s what mathematicians call a denumerably infinite collection. For an example of a non-denumerable collection, you should have picked, e.g., the set of real numbers, which is so numerous that it can’t even be counted.
Never mind that minor point, however. Why can’t someone know all the real numbers? There’s nothing incoherent about the universally quantified claim that for any person S and any number n, if n is a real number, then n is known by S. Certainly, we may agree that “if one being knows or can know more natural numbers than another, then that being is more knowledgeable or capable, respectively, in this area.” It follows that a being who knew all the real numbers would be maximally knowledgeable or capable in that area because there aren’t any more real numbers than that. So this is a nice illustration of maximal greatness in this respect.
I think your confusion is that you’re conflating something’s having no upper bound with a property’s not having a maximal degree. Hence, you say, “Since there are certain areas pertaining to knowledge and power which do not have an upper-bound, it is necessarily the case that any possible being's net knowledge and capabilities are limited and imperfect.” As we’ve seen, that doesn’t follow. A property can have a highest degree, e.g., knowing all the natural numbers, even though there is no highest number.