Thinking about Infinity

The radical thinking God asked for has really been beyond my intellectual reach.  I tried to think about infinity, for example.  It is certainly a daunting concept.  Every philosopher is aware of such puzzles as Zeno’s paradoxes and Immanuel Kant’s antinomies.

The Greek philosopher Zeno argued that, if the tortoise has a head start, Achilles can never overtake him.  Once he catches up with the tortoise’s previous position, the tortoise will have moved forward.  Achilles will now have to reach the tortoise’s new position but, by the time he does so, the tortoise will have moved forward again, even if only a little way, and Achilles will have to catch up to that position, by which time the tortoise will have inched forward yet again, and so on.  Since there are an infinite number of points between the tortoise and the goal post, and an infinite number of points can never be transversed in finite time, Achilles can never catch the tortoise.  Of course, in real life, he could.  That’s why it is a paradox.

Kant’s antinomies are more metaphysical than mathematical but also have to do with infinity.  For example, either the world had a beginning or it did not (these alternatives are the antinomies or contradictories).  If it did, one wonders what happened before that?  And if it did not, there would have to be an infinite number of moments in the past, and is that really conceivable?

There were world-class physicists at a conference I attended.  One reported that mathematicians had now proved you can have an infinite space within a sphere—within a ball, in effect.  He said it made no sense to him but, since mathematicians had proved it, he had to accept it.  A great deal of contemporary science doesn’t “make sense.”  While I was balking at giving up my categories for understanding the nature of God, I saw what scientists have to believe when they do quantum mechanics.  They have to believe that some subatomic particles do not actually have a location prior to being observed.  They have to believe that a certain change in one particle is always followed by the opposite change in another particle even though there is no contact between them and no way for the second particle to “know” which way the first particle changed.  If tough-minded physicists could be that flexible, surely I could too.

I did try to think about infinity.  One of the basic paradoxes in the philosophical tradition concerns whether it makes sense to have an actual or completed infinity.  No matter how large the number, you can always add “plus one.”  So it seems that the number series simply goes on forever and can never be completed.  If so, infinity is more a process term than the description of an actuality.  It expresses the possibility of a larger number, not the actuality of an infinite quantity.  But that seems to mean that no thing or being could actually be infinite.  The number series can always go on, but each number is the end point of a finite series of numbers.  That means that God could not actually be infinite.

I wondered if that was adequate.  I tried to think of a completed infinite.  In our home, we have two mirrors that face each other.  Each one mirrors the other, and mirrors the other mirroring the other, and so on, with the result that one sees an infinite series of mirrorings in each mirror.  And they all exist fully and in the present, not just as a series running into the future.  Maybe, I thought, this was an actual or complete infinite.  But, no, the mirror images get smaller and smaller but at some point they are presumably too small to be mirrored, so there are a finite number of reflected images after all.  Moreover, although the images seem to us to all exist at the present moment, in fact light takes time to go back and forth, and that means there is really a series of images.  Even if the series could go on forever, it would never be completed.

Perhaps I was on the wrong track.  What is meant when people say that God is infinite?  Do they mean some kind of actual or completed infinite?  Or is it another way to say that nothing is missing.  That is a less puzzling idea.  In a perfect painting, nothing is missing.  There is nothing to be added.  Perhaps that is a thought in the right direction.

Then I remembered:  I had already asked God, Are You infinite?  The answer was “I am boundless.”  It is not clear what “boundless” means.  Literally, it would mean “without bounds or limits.”  But the next two answers may be relevant here.  I had asked about omniscience, in effect, infinite knowledge, and was told, “I know everything that is important.”  And I had asked about omnipotence—infinite power—and was told, “I can do everything I want (care) to do.”  That sounds more like the perfect painting.