Afternoon with Borges

Things I wonder about while at the INS.
  July 9, 2002

I went to the Immigration Service today and spent six hours sitting in an uncomfortable chair, waiting to hear my number called out, and reading Borges to pass the time.  He always gives me new ideas, or at least teaches me about old ones that I didn’t know.  This time was no exception.  His essay Avatars of the Tortoise, for example, turned out to be an excellent overview of the historic development (and mutations) of Zeno’s idea of infinite multiplication of elements (or regressus in infinitum, as Borges calls it).  Zeno cast his thinking in the form of aporias, or paradoxes, one of which is the famous story of Achilles and the tortoise.  I think everybody knows it so I won’t bother repeating it.

What caught my eye in Borges’s essay was his description of Aristotle’s use of Zeno’s logic to refute a doctrine of Plato’s.  (Borges borrowed from Aristotle who borrowed from Zeno who borrowed from ... I don’t know who.  I cheerfully plunder them all.  Is it conceivable that one of us actually had original thoughts?)  Plato’s doctrine “tries to demonstrate that two individuals who have common attributes (for example, two men) are mere temporal appearances of an eternal archetype.”  The important thing is, this archetype is supposed to be independent and comprehensive; it exists on its own and it contains all.  Aristotle gives a verbal refutation which I found a bit confusing until Borges illustrated it symbolically in this manner:

Let us postulate two individuals, a and b, who make up the generic type c.  We would then have:

a + b = c

But also, according to Aristotle:

a + b + c = d
a + b + c + d = e
a + b + c + d + e = f . . .

You get the picture.  As long as c is a separate entity, it can’t be all-inclusive.  Sure, it includes everything else.  It does not, however, include itself along with everything else.  Just so a mirror in a room reflects everything contained there—except for the mirror that reflects the room.  If the mirror is c in the example above, then the room with the mirror included would be d.  But d also is just a vision existing in the eye of a beholder outside of d, an eye that in sum with d we may call e; etc., ad infinitum.

This leads us to the exciting part and out of Zeno’s territory.  What’s stopping us, one may ask, from putting another mirror opposite the first one and letting them reflect each other and everything in between—all-inclusively and, as we know, infinitely.

The answer is, nothing.  In fact, this idea has been put forth by philosophers and imbeciles alike (which means I’m comfortable with it any day of the week).  Skip to Borges’s another essay, Partial Magic in the Quixote, and you’ll find the followng quote from Josiah Royce’s The World and the Individual:

Let us imagine that a portion of the soil of England has been levelled off perfectly and that on it a cartographer traces a map of England.  The job is perfect; there is no detail of the soil of England, no matter how minute, that is not registered on the map; everything has there its correspondence.  This map, in such a case, should contain a map of the map, which should contain a map of the map of the map, and so on to infinity."

Alternatively, one can adduce this immortal exchange from Beavis and Butt-head:

Butt-head: If I could get a tattoo, I’d get one in the shape of a butt that has a tattoo of a butt with a butt-shaped tattoo on it.

Beavis: Huh huh huh ... yeah!  And I’d get it right on my butt!!

(I miss that show.)

This has been a lengthy but necessary introduction to my ideas.  The ideas themselves will take scarcely half this much space to expound.

In March, I wrote a sketch regarding the nature of Truth.  In my comments to that post, I toyed with the idea that perfect Truth is a complete description of the world, something which contains the world and yet is not it.  Such features make Truth an all-inclusive yet separate entity akin to Plato’s eternal archetype.  Just like the archetype, my concept falls prey to Aristotle’s refutation: Truth that is truly complete must include in itself complete Truth that includes complete Truth, etc.  Grasping it will require grasping the act of grasping it and also grasping the act of grasping the act of grasping it, until one can’t grasp any longer.  A finite being can catch up to the absolute Truth no more than Achilles in Zeno’s aporia can catch up to the tortoise.

I presume that any human (or superhuman, for humans are too feeble) who is out to learn every detail of the universe will be satisfied to leave his own knowledge out of the final account and thus avoid the trap of regressus in infinitum.  While imperfect, his knowledge will be as complete as is finitely possible.

One can postulate, however, a theoretical being that possesses the stupendous faculties required to know the whole Truth in all its endless repetitions.  I suppose this entity is what theologians would label “god.”

This, I realized with surprise and delight, touches obliquely on yet another favorite preoccupation of Borges’s, the illusory nature of reality.  He caught the idealist bug from the musty tomes of Berkeley, and so from Berkeley we shall quote next:

Some truths there are so near and obvious to the mind, that a man need only open his eyes to see them.  Such I take this important one to be, to wit, that all the choir of heaven and furniture of the earth, in a word all those bodies which compose the mighty frame of the world, have not any substance without a mind, that their being is to be perceived or known; that consequently so long as they are not actually perceived by me, or do not exist in any mind or that of any other created spirit, they must either have no existence at all, or else subsist in the mind of some eternal spirit ..."

(Principles of Human Knowledge, quoted in Borges, A New Refutation of Time.)

An eternal spirit who holds in its mind our entire universe, its minutest details, the Truth in all its vertiginous infinity, and solely by such an act keeps everything in existence, — what a magnificent abstraction!  Sometimes I regret I am an atheist.

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