[My] Full Title: ‘Seldon in
Session’ Series,
blog-entry #3 --
‘Seldon Functions,
Dyadic & Triadic’.
Dear
Reader,
This blog-entry continues a
new series, here, of excerpts from Karl Seldon’s “introduction to dialectics” sessions, for new recruits.
In this new series, I
will share with you some of the delectable morsels of creative mentation that
fly forth from these sessions, once their transcripts have been edited, by the E. D. editors, and cleared, by the Foundation’s General Council, for public
sharing.
I have entered, below, an
excerpt of Karl Seldon’s remarks from the edited transcript of a recent such
session.
Regards,
Miguel Detonacciones,
Member, Foundation Encyclopedia
Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.
[Karl Seldon] --
“Note that, in this presentation, by a “category” we also mean, like the ancients, the representation of an «arithmos», of an assemblage of qualitative units, e.g., of a “population” of individuals [individuals which/who may be active agents of evolutionary, and of ‘meta-evolutionary’, change, though not
necessarily being human agents/subjects] -- of a concrete ‘‘‘number’’’ of concrete «monads».”
“Our NQ_-based family of dialectical functions -- principally the dyadic dialectic-function
and the triadic dialectic-function
-- are, generically, functions of an NQ_ CONSTANT: they are functions, namely, of the known value q1.”
However, specifically,
with q1 “interpreted”, i.e., “assigned” [‘<(---]’]
to a specific «arché» category --
q1 <(---]
a
= qa
-- so as to form a specific
‘dialectical
meta-model’,
our dialectical functions
become functions
of an NQ_ VARIABLE.
This variable
-- e.g., a
-- is also a “partial”
algebraic unknown.
It is so in the sense that the total implicit/potential
content of
that “intension”, of that ‘connotogram’, a, is never fully known,
and becomes partially known only gradually, with the extension/divulgence
of its dialectical categories-progression,
as the hidden
‘intra-multiality’
of that «arché» is progressively revealed/-‘explicitized’/actualized
in the expanding
‘cumulum’ of that
categories-progression,
that issues forth from that «arché»,
as generated, in terms of its ideographic-symbolic representation, by the escalation in the “Natural”
Number value
of the ‘self-iteration parameter’ independent variable of these dialectic-functions.”
“For our dyadic dialectic-function ‘meta-equation meta-models’ of dialectical process/progression, it is the most recent past ‘contra-thesis’
category that
is the source
of the next, new, higher ‘contra-thesis’
category.”
“For any stage of such a progression -- for any value of the
‘self-iteration parameter’ beyond s = 1 [for ‘synchronic dialectics’], or t = 1 [for ‘diachronic dialectics’] -- it is the most recent ‘contra-thesis’
category [--
the category that
had just reconciled
with all of the preceding categories, that it ‘op-poses’, in the form of the most recent “synthesis” category, the category that had just superseded that ‘contra-thesis’
category --] that,
next, supersedes that “synthesis” in turn, “turning the flank” of that “synthesis” category, making an end-run around, and
thereby escaping, that “synthesis” category, thus placing the
‘self-hybrid’
category of
that ‘contra-thesis’
category, i.e.,
its new ‘contra-thesis’ category, ahead of, in advance of, that “synthesis” category, higher in ‘qualo-fractal’
scale, and in complexity/determinateness, than that “synthesis” category.”
“The “internal
contradiction” -- the ‘intra-duality’ or ‘intra-multiality’
-- of the «arché»
category,
which resides at the root
of the entire
dialectical categorial progression,
recurringly re-asserts itself, bursts forth
again, each time at a specifically new, higher level/scale, from out of the ‘intra-duality’, or of the ‘intra-multiality’, of each most recent ‘contra-thesis’
category,
when that ‘contra-thesis’
category operates upon itself,
as a specific «aufheben» operation, e.g., as an «arithmos»-‘self-meta-«monad»-izing’ operation, yielding itself
again, its own “simple reproduction” [cf. Marx], but together with
the new ‘contra-thesis’ category/«arithmos» [ net result of a ‘qualitatively,
ontologically expanded self-reproduction of and by
that «arithmos»-of-«monads»], which was born[e] by/from/out of the old --
old
contra-thesis x old contra-thesis = old contra-thesis2 = old contra-thesis + new contra-thesis,
e.g., generically --
q2 x q2 = q22 = q2 + q2+2 = q2 + q4.”
“Each new ‘contra-thesis’,
born[e] of that ‘intra-duality’, irrupts into explicitude,
or into actuality,
through the self-reflexion,
the self-reflexive
action, or
the ‘‘‘self-activity’’’
[cf. Marx], i.e., through the ontological ‘‘‘self-multiplication’’’ [‘“self-squaring”’, cf. Mandelbrot], of that formerly
most recent
‘contra-thesis’
category.”
“That ‘‘‘self-squaring’’’ of the old ‘contra-thesis’
category net-yields
a new ‘contra-thesis’ category, in which the
essential ‘‘‘dialectical
[self-]contradiction’’’ of the Domain being ‘meta-modeled’, and of its «arché», a = qa [---)> q1,
breaks
out again, anew, but at a yet higher level, at a higher ‘qualo-fractal’ scale, than that of its preceding, ancestor ‘contra-category’.”
“For our triadic dialectic-function ‘meta-equation meta-models’ of dialectical process/progression, it is the most recent past ‘uni-thesis’,
or “synthesis”, category, that is the source of the next, new, higher ‘contra-thesis’
category, due
to the specific new ‘intra-duality’ of that most recent past “synthesis” category itself, that is, of the very category that resolved in itself the preceding specific
‘intra-duality’.”
“Each “synthesis”
category, by its
self-reflexion,
by its self-reflexive action, by its
‘‘‘self-activity’’’,
i.e., by its ontological ‘‘‘self-multiplication’’’ [‘“self-squaring”’], amplifies its own
specific ‘endo-duality’, until that ‘endo-duality’ bursts forth into a new ‘exo-duality’, in the form of a new, higher ‘qualo-fractal’
scale ‘contra-category’ --
old
uni-thesis x old uni-thesis = old uni-thesis2 = old uni-thesis + new contra-thesis,
e.g., generically --
q3 x q3 = q32 = q3 + q3+3 = q3 + q6.”
“In the light of the foregoing considerations on ‘triadicity’
and ‘dyadicity’ in our dialectical-functions-based ‘meta-models’ of dialectical process/progression, it is of value to evaluate the
following two passages from Hegel’s remarks, on “triplicity”, and on
‘tetradicity’, in the generic ‘numberology’ of dialectic --
“...Kant did not apply the infinitely important form
of triplicity -- with him it
manifested itself at first only as a formal spark of light -- to the genera of his categories (quantity, quality,
etc.), but only to their species
which, too, alone he called categories. Consequently he was unable to hit on the third to quality and quantity.”
[Note:
Per Hegel’s «Logik», that “third” is “measure”, an «arithmos» of quantifiable qualitative «monads», or units, of measurement; of ‘quantifiable dimensional qualifiers’ -- F.E.D.]
[Hegel, Science of
Logic, Prometheus [NY: 1969], p. 327, emphases added
by F.E.D.].
“Any division
is to be considered genuine when it is determined by the Concept. So genuine division is, first of all, tripartite; and then, because particularity
presents itself as doubled,
the division
moves on to fourfoldness as well. In the sphere of spirit trichotomy predominates, and it is one of Kant’s
merits to have drawn attention to this.”
[Hegel, The
Encyclopedia Logic, Hacket [NY: 1991], p. 298, emphases added by F.E.D.]. ... .”
