The Infinite, part I. What is finite?
January 12, 2010 1 Comment
I sort of threatened to discuss infinity some time ago. Why? Well, Joseph Smith delves deeply into the infinite, and in particular in funeral sermons, even though he does not engage it with rigor.
There are several ways Joseph finds a need for the infinite. Some of these became or were immediately controversial but most of them have not been carefully examined outside very narrow wedges of literature.
It may be easier to grapple with the infinite by first thinking a bit about its negation: the finite. As a descriptor, “finite” can be an equivalent to being fixed or determined. More often it suggests the idea of boundedness, being limited. Theologically it might refer to having an existence which is conditional, or, it might be used to suggest something is subject to limitation of some kind.
Much of theology has been devoted to the postulate that God is unlimited in every way. Such an assumption seemed to be the only way God could be distinguished from other beings. That idea leads naturally to the notion that God created everything else, from nothing. The postulate had and has many difficult consequences which remain puzzling to the thoughtful. Dealing with them has resulted in a very large literature and has included the option of simply shrugging the shoulders and giving up.
Time and its counterpart, timelessness, are closely related to the notions of finite and infinite.
Measurement is clearly related to at least some meanings of finite and measurement involves numbers in some form. For the sophisticated, the so-called counting numbers, 1, 2, 3, 4, . . . form the basis of measurement. Any collection of objects would be declared finite if it can be “counted” using some sufficiently large collection of numbers, 1, 2, 3, . . . K.
So far, I have hidden an important principle in the discussion. It may have seemed natural to most of you, but historically it is critical to the landscape of counting and theology. That principle is the so-called “law of excluded middle.” Briefly, it requires that every statement, where the assignment of truth value makes sense, is either “true” or “false.” False being the equivalent of “not true.” There is no other possible assignment to be made. “Middle” values, are altogether excluded. In the case of finite and infinite, infinite is simply the negation of finite. That which is not finite, is infinite. Indeed, that will be our working definition of infinite.
 This does not mean that creatio ex nihilo was first proposed as a distancing strategy between God and “not God.” That is almost certainly not true.