Gnostic cosmology and Cantor's paradise

[Ripheus27]

So in the gnosis.org summary of the Valentinian Christian movement it reads:

According to Marcus, each of the thirty Aeons contain further Aeons and each of these further Aeons contain further Aeons to form an inifinite number of Aeons. To illustrate this he makes use of the metaphor of the Aeons as letters of the Name. The Name consists of "thirty letters, while each of these letters, again, contains other letters in itself, by means of which the name of the letter is expressed. And thus, again, others are named by other letters, and others still by others, so that the multitude of letters swells out into infinitude" (Against Heresies 1:14:2). Using the Greek letter delta as an example, it can be written by means of five letters (d, e, l, t, a). Each of these letters is expressed by further letters, to infinity. The Fullness of Aeons corresponds to the Platonic world of ideas.​

If you've ever read The Mathematical Traveler, you might remember the chapter on transfinite numbers. "Discovered," if you will, by mathematician Georg Cantor, their domain was to some known as "Cantor's paradise." Now Cantor himself reportedly thought his theory was inspired by God, and the idea works like this (correct me if I'm wrong):

Try to count all the numbers on the real number line only using natural numbers.
When you figure out that you can't, you'll have realized that the infinity of the real numbers is greater than the infinity of the natural numbers.
But you can count the relation of greater than more times than just this one. You can count it to infinity itself, wherefore there are an infinite number of greater and greater infinities. The kinds of numbers these would contain--things as exotic compared to quaternions as quaternions are compared to whole numbers--would be concrete realities, but except for by way of Cantor's ladder inaccessible to our minds.
Even this is not the end. There are more intricate mathematical operations that can be done with the basic concept of the aleph numbers (as they may in fact be named) to construct abstract intuitions about types of numbers even more transcendent in a myriad escalating ways than even something as majestic as aleph-249,298,473,974,793,478,235,638,567,483*10(23,000,000,000,000,000) and all its successors. The ladder's apex is only reached when we conceive of an absolute infinity, and this, Cantor thought, was divine.​

Carl Jung appears to have thought that Gnostics were ancient practitioners of depth psychology. Jung's theory of archetypes suggests that Gnostic mystical awareness of the truth of the Aeons' infinity might've been a mythologized rendering of spontaneous realization that the aleph numbers exist and can be ordered in the way that they are.

Now many mathematicians look on the source of their knowledge as engagement with literally another world or plane of existence. They really widely accept Platonic metaphysics of a very classical kind. So whatever rational support these mathematicians may avail themselves of to defend such a theory about their theories will therefore suggest that there is a mystically intuited dimension, or hierarchy of dimensional structures, leading to a divine finality, proven to exist by very basic mathematical reasoning. And this is just what the Aeons are supposed to be.* But even if we interpret mathematical objects as less--objective, I guess--we might still credit Gnostic reflection with having metaphorically, if unself-consciously, arrived at a simple but profound truth about the metaphysical architectonic of reality.

*Consider also the debate over the duration of hell, which debate is predicated greatly on what words like aion mean in a New Testament context. Now one translation of a relevant passage talks of "forever and ever" or "everlasting." Another translation asserts "ages of ages." The very word Aeon finds its meaning importantly mirrored in this discussion of whether hell is eternal. And "forever and ever" and "ages of ages" are roughly isomorphic to the neverending, yet in itself an end, story of the ascent up the mountain of the aleph numbers (or the descent into an abyss of transfinite light).

 

[Ishraqiyun]

arrived at a simple but profound truth about the metaphysical architectonic of reality.

y

I'm not sure I understand what he means there. What truth was arrived at and what does "metaphysical architectonic of reality" mean? Can you elaborate with a little more simple language maybe ? I have an inkling what it might mean but I'm not exactly sure I'm properly understanding.

 

[Ishraqiyun]

I found the term "architectonic" in the dictionary. I'll post it because it might help people understand better:

architectonic
Definition
ar·chi·tec·ton·ic
[ rkə tek tónnik ]
To hear the pronunciation, install Silverlight


ADJECTIVE

1.
of architecture or architectural qualities: relating to architecture or the qualities such as design and structure that architecture requires

2.
of classification of knowledge: relating to the classification of knowledge used in metaphysics

 

[Ripheus27]

I just meant that there being more than one infinity, and in fact an infinite number of infinities of infinities, is a fact (assuming it is a fact) that has significant bearing on questions related to the structure of the mathematical world, the capacity for finite human consciousness to engage in concrete reasoning about infinite questions, and so on.

 

[eachallberg]

Deep,

IMO the cosmology is spring board into silence.