THE PROBLEM WITH INFINITY

When a person who gives serious thought to things states a reasonable belief contrary to my own, I often pause to reflect upon it.  After all, I can’t correct my mistakes, if I never entertain the possibility of error.  Such an opportunity for reflection arose in a recent discussion I had with Regi Firehammer, a student of Objectivism, about the existence of God.  I stated my belief that God existed as the creator of our universe.  An important basis for that belief is my observation that the universe is finite.  Regi firmly disagreed:  The universe is infinite.

Is it?  Well, I also had thought it was infinite for a long time.  Why did I think that?  I realized that my belief in an infinite universe had been predicated upon a confusion between infinity and very large numbers.  However, Regi is a careful thinker with an enviable precision in the concepts he expresses.  He wasn’t making the blunder I had in my callow youth.  So I began to mull over what would constitute a reasonable basis for the belief that the universe is infinite.

To my surprise (and to my satisfaction), this wasn’t easy.

First of all, the attribute of infinity is not one any of us has experienced.  No one has ever perceived either the boundless or the eternal.  And this is not just a function of our own finite nature that blinds our perception of infinity.  We experience boundaries and duration in all things, either directly or indirectly (with one profound exception discussed below).  Everything we have observed is finite – including the universe.  The discovery of a pervasive cosmic background of microwave radiation indicates both a size and an age for the universe, at least in its present form.  We are unable to peer beyond this cosmic wall and science presently offers no prospect that we ever will.

Thus, knowledge of an infinite universe is not empirical.  Indeed, our exploration of the universe itself reveals boundaries in both space and time.  But are these the boundaries of the universe, the realm of all that has existed, does exist, and will ever exist?  Are they instead the boundaries of only that portion of the universe we occupy, either spatially or temporally?  If that cosmic wall of microwave radiation only partitions the here and the now from the boundless and the eternal universe, how does anyone obtain true knowledge of that infinity?

Through reason?  A common argument for an infinite universe is that very existence of a boundary assumes the existence of time (in the case of an origin) or space (in the case of a cosmic wall) external to it that must logically lead to the conclusion of either an infinite progression of boundaries or an unimpeded infinite expanse.  The fallacy here is the reification of time and space.  These are relationships between existents, nothing more.  If nothing existed before the origin of the universe or if nothing exists beyond the cosmic wall, there exists no time or space to fill.  In other words, there are no temporal or spatial relationships to connect something – i.e., the universe – to nothing.  So the argument of infinite progression fails as proof that the universe cannot be finite.

But the failure of that argument does not settle the issue in favor of a finite universe.  The law of conservation appears to run contrary to it, at least in terms of time.  We know of no process that can either create or destroy the fundamental physical constituents of the universe.  However, there are any number of processes by which matter changes to energy and vice versa, and by which the entropy of matter and energy in a system increases or decreases.  In short, form can be created or destroyed, but not substance.  So if the law of conservation is inviolable, how can there be a creation event?  Nonetheless, the law of conversation does not imply an infinite universe.

It should be obvious that conservation can be true of a finite amount of matter and energy.  Any finite number of entities has a finite number and magnitude of spatial relationships.  Therefore, a spatially infinite universe cannot be concluded from the law of conservation.  But what about an eternal universe, one that is temporally infinite?  What does it mean to say that an entity, or group of entities, has always existed in relationship to itself?  How can this self-referential temporal relationship be identified?  The law of identity requires a difference between one existent and another, but where is the difference that permits the identity of the attribute of eternal existence for each and every quantum component of the physical universe?  The conclusion of an eternal universe requires conservation to trump identity.

Let’s say that is the case when it comes to the fundamental physical constituents of the universe.  The law of conservation remains inapplicable to the durability of any particular form the universe takes.  Even if the physical quanta of the universe have existed forever, conservation does not drive the conclusion that the present physics and structure of the universe are eternal.  There is still the finitude of form, even on the grandest scales, that is entirely consistent with everything we actually experience about and within the universe.

A finite universe accords with experience and reason.   A spatially infinite universe is not presently supported by scientific observation and would lead to the same breakdown in the law of identity as a temporally infinite universe does, except that there is no rationale – e.g., the conservation of matter and energy – to salvage a reasonable belief in unbounded space.  If the law of conservation does supplant temporal, if not spatial, identity and the universe is eternal, none of that requires the conclusion that its present form is eternal.  (Nor does it foreclose upon the possibility of a closed loop in time.)  At the end of the day, we must reckon with a universe in the here and now that empirically and rationally appears to be finite.

Existence exists is axiomatic, but it does no more than require the acknowledgment that an entity or any collection of entities occupies a certain amount of time and space.  It does not demand a belief in the infinity of all existence.  But what if it does permit the belief despite the empirical and rational objections I have raised?  What if the universe were infinite in time and space?  What are the implications?  What cannot happen in an infinitely capacious universe unbounded by either time or space?  What could not develop from such unlimited resources?  How many bountiful oases like Planet Earth would there be?  How many times could intelligent beings spring from these unnumbered gardens of life?  Can it be certain that from the multitude of intelligent beings birthed by an infinite universe, none in turn planted his own garden?

In short, how does a belief in an infinite universe logically preclude for the atheist the existence of God as the creator of man?

Such are the problems with infinity.