Dear Hegel-Hegelians Group Members,

Note that the self-movement of the "Set of All Objects" is, precisely, a
DIALECTIC, an <<AUFHEBEN>> <<auto-kinesis>>; a set self-progression; a
self-propelled "categorial progression", with sets as its "categories":

If we use the shorthand symbols --

'A ---C B'

-- to stand as shorthand for the phrase --

'set A is wholly contained within set B'

-- then we have the <<aufheben>> condition that --

Osub0 ---C Osub1 ---C Osub2 ---C Osub3 ---C Osub4 ---C Osub5 ---C...

-- and, in general, for every T in the set of Natural Numbers --

N = { 1, 2, 3, . . . }

-- we have --

OsubT ---C Osub(T+1).


Notice that the self-propelled movement --

OsubT ---> Osub(T+1) = [OsubT]^2

-- wherein --

Osub(T+1) = [OsubT] union [Power-Set of OsubT]

-- is an <<aufheben>>, determinate self-negation of OsubT.



When OsubT "reflects/reflexes/refluxes" upon itself --

OsubT x OsubT = OsubT "of" OsubT = [OsubT]^2

-- the resulting process --

OsubT union 2^OsubT

-- exhibits all of the moments of the <<aufheben>> operation:

(1) "conserving" 'OsubT' inside 'Osub(T+1)', since 'OsubT ---C Osub(T+1)';

(2) "elevating" 'OsubT' to a one unit higher Russellian "logical type" level,
qualitatively changing 'OsubT' into a qualitatively different/higher
'Osub(T+1)', and;

(3) "determinately [self-]negating" 'OsubT', converting it[self] into
'Osub(T+1)', because 'Osub(T+1)' is a DETERMINATE case of a 'NOT-OsubT'.



Thus --

[OsubT]^2 = OsubT x OsubT = OsubT <<AUFHEBEN>> OsubT.



The drive behind --

OsubT ---> Osub(T+1)

-- is INTERNAL, IMMANENT to 'OsubT' itself.

It is not an EXTERNALly-caused/imposed transition.


The symbol '--->' within the symbol-complex --

OsubT ---> Osub(T+1)

Means NOT so much that 'OsubT' "IMPLIES" 'Osub(T+1)', as would the statement --

OsubT ===> Osub(T+1)

-- but that 'OsubT' "BECOMES" 'Osub(T+1)'; "TRANSFORMS ITSELF INTO" 'Osub(T+1)',
"CAUSES ITSELF TO CHANGE INTO" 'Osub(T+1)', due to its own, INTERNAL, IMMANENT
causes/reasons.



The self-movement expressible as --

Osub0 ---> Osub1 ---> Osub2 ---> Osub3 ---> Osub4 ---> Osub5 ---> ...

is a "self-necessary", "neccessitarian" one.

Since 'OsubT' is an idea of a mental object, of an idea-object, rather than an
idea of a physical, <<physis>>-object, the necessity of its self-movement is a
mental, ideative, conceptual, semantic necessity, rather than a physical
necessity.


The set 'Osub0', or 'U', may start out as representing a collection of physical
objects, of <<physis>> objects.

However, from 'Osub1' on, the expanded universe set includes set-theroetical,
extensional representations of Predicates of
various orders, of Qualities, of "Intensions" or "Connotations" such as are
perceived/constructed by human subjects, by human cultures, by human
"meme-pools", by human "Phenomes" -- by human inter-subjectivities.

Thus, this model captures something which is of the essence of Marx's
world-historical breakthrough in human cognition, in human science, in human
knowing, evident already in his "Theses On Feuerbach"; of Marx's
negation/transcendance/synthesis/complex-unification of both one-sided
mechanical materialism and 'other-sided' dialectical idealism; his founding of
what F.E.D. terms "PSYCHO-Historical Materialism", in which the human Phenome
and its Meme-Pool -- in which human ideology and human science -- are not
denied; are not declared non-existent, or outside of the "material" universe,
but in which they are seen as "matter" too; as also "material"; as part of a
<<Genos>> of matter which comes in two primary <<species>> --

<<species #1>>: <<physis>>-matter; "physical" matter;

<<species #2>>: idea-matter.



The formula for "the Set of All Objects" --

OsubT = [Osub0]^(2^T) = U^(2^T)

-- is NOT that of an [EXO-]"Iteration", as is --

XsubT = (F^T) "of" (Xsub0), as the value of T escalates.

In the case of 'OsubT', the 'F' is replaced by 'OsubT' itself.

Therefore, F.E.D. calls --

OsubT = [Osub0]^(2^T)

-- a "SELF-Iteration"; an "ENDO-iteration"; an "INTRO-Iteration", or; an
"INTRA-Iteration".



In the symbol complexes --

[OsubT]^2 = OsubT "times" OsubT = OsubT "of" OsubT = Osub(T+1)

-- we express, ideographically, a "Subject/Object Identical", and a higher form
of mathematical "NONLINEARITY" even than that of those inherently
singularity-prone [zero-division-prone], and STILL-UNSOLVED nonlinear partial
differential equations that formulate the "Laws", or the presently prevailing
"habits" [Peirce], of Nature, to the extent that they are presently known to
humanity, when those nonlinear equations are presented in their "standard form"
-- i.e., in their "unqualified", purely-quantitative form, without the explicit
presence in them of [F.E.D.] "ontological qualifier meta-numbers", and/or of
[F.E.D.] "metrical qualifier meta-numbers".

That is, we express a "Self-[Reflexive ]Function", or "Self-Reflexion" -- a
Bending ["Flex"] Back ["Re"] Upon "Self" -- of 'OsubT', and also a "Self-
Refluxive Function", or "Self-Refluxion" -- a Flowing ["Flux"] Back ["Re"]
upon/to "Self" -- of 'OsubT', in which 'OsubT' semantically, as meaning, as
definition -- and also as sentential SUBJECT, in this context -- confronts
itself as sentential
OBJECT, and, finding that its 'OBJECT-ive' existence in its 'Tth' stage falls
short of its meaning/nature/definition, expands itself by the set-ontological
increment denoted by '2^OsubT', that is, by the generation, and by the inclusion
within itself, of all of its sub-sets, thus transforming its own self/identity,
into that of a NEW
set, a new "self", a new "identity", with a DIFFERENT power-set, although a new
self/identity which is <<aufheben>>-related to its old self/identity, as a
"conservative extension" of itself, of that old self/identity.

It finds that its 'Tth' self, as sentential OBJECT, contradicts its self as
sentential SUBJECT, and it responds by expanding itself set-qualitatively;
set-ontologically, creating, thereby, its '(T+1)st' self.



When one mentally simulates the "Set Of All Objects", when one mentally behaves
AS IT; constructs it in one's own mind, one sees that this Set is "forced" to
expand itself -- by adding its own sub-sets to itself; is forced to do so by its
own nature; by its own essence; by its own definition -- in fact, by its own
NAME.

It always, inherently, has left itself and its proper subsets out of itself,
and, when it therefore moves to bring them in to itself, thereby changes itself,
and, along with that self change, it changes also its subsets.


This process of its continuing qualitative self-expansion potentially never
ends, because each time it changes itself, changes what it contains, its
power-set also therefore changes; its "new" self means that its "new" power-set
is unprecedented, qualitatively different from all of the previous power-sets of
all of its previous selves -- containing NEW "LOGICAL [META-]INDIVIDUALS", NEW
PREDICATES, and NEW RELATIONS -- new 'ideo-ontology, never before extant or
explicit in its series/sequence/succession/progression of likewise
ever-SELF-inadequate "it selfs".

Regards,

Miguel