A partial order of angels and some other ideas

    The nine hierarchies of angels described by Dionysius the Areopagite is an inspiring concept.  The idea is that in addition to whatever duties an angel has individually, each angel is part one of nine larger classes and these are arranged hierarchically.  The nine classes, called choirs, in descending order are: Seraphim, Cherubim, Thrones, Dominions, Virtues, Powers, Principalities, Archangels, Angels.  Very few people who have ever lived have had primary knowledge about this subject and one who perhaps might have, Paul, said he was not permitted to speak about it.  Nevertheless, it is worth thinking about how to imagine these hierarchies.   

    

A picture from the Baptistry in Florence depicting seven of the nine choirs of angels

    Peter Kreeft, following Aquinas writes in his book Angels and Demons

    "Therefore, angels are arranged in a vertical hierarchy.  There is no equality among angels, no angels twins."

    Mortimer Adler expands on this some more in his book The Angels and Us.  The idea is that two angels, being incorporeal, can only differ from one another in the number and generality of their ideas, so one must have more ideas and more general ideas, while the other must have less general and less ideas.  This is what Aquinas believed, that angels are linearly ordered.  However, even if we accept the idea that angels can only differ in terms of their ideas, then why can there only be more or less ideas?  Why not some angels who have the same amount of ideas but simply different ideas?

    Adler also writes: 

"According to Bonaventure, physical matter or corporeality, or having a body is not the sole cause of individual differences.  He maintained therefore, contrary to Aquinas, that it is not impossible for two angels to differ as individual members of the same species, even though they are incorporeal substances."

    I agree with Bonaventure.  There is a concept from mathematics called a partial order, which is helpful to imagine how the angels may be arranged.  In a linear order (also known as a total order) given two objects, one is greater in the ordering and one is smaller.  In a partial order, given two objects, one may be greater than the other or they may be incomparable.  Partial orders can be represented by pictures called Hasse Diagrams.  Here is an example: 

    

    We can see that the partial order is sorted into levels, where elements in each level are directly above the level below.  So, 0000 is less than 0010 and 1001, but 0010 and 0001 are incomparable.  Also, elements on a different level can be incomparable.  For example, 0100 and 1101 are incomparable.

    Of course, this idea is not unique to mathematics; it is something that is used implicitly in many everyday situations.  For instance, whenever someone needs to rank things but considers some to be equivalent and some not.  The advantage of the mathematical concept is to abstract the essential aspects of a partial order from any particular situation in which it is used. 

    This kind of situation gives us a good model of how the angels might be arranged in the 9 choirs.  Within each choir, many angels may be incomparable.  They have different tasks and different capabilities, but none are above another.  While on the other hand those of a higher level would have greater capabilities.  Notice also that in the Hasse diagram shown, if a number contains more ones in the exact same entries than another, then the number with more ones is greater than the one with fewer.  For instance, 1101 is greater than 0001.  So, likewise, an angel in a higher choir could be more powerful than one in a lower choir while the one in a lower choir may still have capabilities which the higher angel does not have.  

    There could also be angels in a particular choir who have their own unique, unusual tasks that are not shared by others in their same level.  

    Here are some other ideas about angels that are not are not enough for their own post: 

    It may be that the function of some angels is to deal with the destiny of human beings on a grand, world-historical or societal scale.  If we were properly oriented to the spiritual, then we would be able to allow these angels to "plan for us."  If we were properly aligned with God and Creation, then we would be able to allow them to direct us and things would work out long-term even with no plans of our own.  But in our hubris, we have tried to usurp the function of these angels with grand schemes of social engineering.  Which are bound to fail because perhaps that was never the function of human beings in the first place.  

    Also, there is the famous and old notion of the Angel of Death who is permitted to kill human beings.  In the book The Boy and the Brothers, there is an interesting passage towards the end: 

    "It was then that I saw a tall form like a deep black shadow behind the bed on his left-hand side.  It was not a Brother as we had known them.  It did not flash in and out like the Brothers I had seen, and see, but was still and constant.  'Of course,' I mused as I worked, clearing up, with a strange quiet on me, 'there might be a Brother like that - the Shadow of Death - the Angel of Death?"

    And if there is an Angel of Death, then why not angels who do similar work as fungi, angels who are decomposers and who clean up in certain circumstances.  In The Last Battle, C.S. Lewis envisions something similar; there are creatures who destroy the land of Narnia after the end of that world. 

    Of course, any primary knowledge about such matters is far above my capability, but these things are sill worth thinking about. 

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