**[My] **__Full Title__: ‘**Seldon*** in
Session**’*** ***Series*,
blog-entry** ****#3** --

‘**Seldon ***Functions*,
__Dy__adic **&**** **__Tri__*adic**’*.
Dear Readers,

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This blog-entry continues a
new series, here, of excerpts from Karl Seldon’s “introduction to __dialectics__*”* sessions, for new recruits.

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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.

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I have entered, below, an
excerpt of Karl Seldon’s remarks from the edited transcript of a recent such
session.

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Regards,

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Miguel Detonacciones,

Member, **Foundation**** **__Encyclopedia
Dialectica__ [**F**.__E__.__D__.],

Officer, **F**.__E__.__D__. Office of Public Liaison.

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[Karl Seldon] --

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**“**Note that, in this __present__*ation*, by a *“**category**”* we also *mean*, like the *ancients*, the *representation* of an «*arithmos*», of an *assemblage* of __qual__*itative **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 __h__*uman* *agents**/**subjects*] -- of a *concrete* *‘‘‘*__number__*’’’* of *concrete* «*monads*».**”**

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**“**Our _{N}__Q___-based *family* of __dialectical__ functions -- *principally* the __dy__adic __dialectic__*-***function**
and the __tri__adic __dialectic__*-***function**
-- are, __gene__rically, *functions* of an _{N}__Q___ __CONSTANT__: they are *functions*, namely, of the *known* *value* __q___{1}.**”**

However, __speci__fically,
with __q___{1} *“***interpreted**”, i.e., *“***assigned**” [‘**<(---]**’]
to a __speci__fic «__a__*rché*» *category* --

__q___{1} **<(---]**
__a__
__=__ __q___{a}

-- so as to form a __speci__fic
*‘*__dialectical__
**meta**-**model**’,
our __dialectical__ functions
become *functions*
of an _{N}__Q___ __VARIABLE__.

This __variable__
-- e.g., __a__
-- is also a *“*__partial__”
*algebraic* __un__known.

It is so in the sense that the *total* __im__plicit*/potential*
*content* of
that *“*__in__tension”, of that* ‘*__connot__ogram’, __a__, is never *fully* *known*,
and becomes __partially__ known only gradually, with the __ex__tension*/divulgence*
of its __dialectical__ categor__ies__*-***progression**,
as the *hidden*
*‘***intra**-__multi__ality’
of that «__a__*rché*» is *progressively *__reveal__ed*/**-‘*__ex__plicitized’*/actualized*
in the *expanding*
*‘***cumulum**’ of that
*categor*__ies__*-***progression**,
that issues forth from that «__a__*rché*»,
as __gene__rated, in *terms* of its __ideo__graphic*-***symbolic representation**, by the *escalation* in the “__N__atural”
Number *value*
of the ‘self-iteration parameter’ independent variable of these __dialectic__*-***functions**.**”**

**“**For our __dy__adic __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 *‘*__syn__chronic __dialectics__’], or **t = 1 **[for *‘*__dia__chronic __dialectics__’] -- it is the *most recent* *‘*__contra__-**thesis**’
*category* [--
the *category* that
had just *reconciled*
with all of the __pre__ceding categories, that it *‘***op**-**poses**’, in the *form* of the *most recent* *“*__syn__thesis” *category*, the *category* that had just *superseded* that *‘*__contra__-**thesis**’
*category* --] that,
*next*, *supersedes* that *“*__syn__thesis” *in turn*, “turning the flank” of that *“*__syn__thesis” *category*, making an end-run around, and
thereby escaping, that *“*__syn__thesis” *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 *“*__syn__thesis” *category*, *higher* in *‘*__qual__o-fractal’
**scale**, and in *complexity**/determinateness*, than that *“*__syn__thesis” *category*.**”**

**“**The *“*__internal__
contradiction” -- the *‘*__intra__-__du__ality’ or *‘*__in__tra-__multi__ality’
-- of the «__a__*rché*»
*category*,
which resides at the *root*
of the *entire*
__dialectical__ categorial* ***progression**,
*recurringly *re-asserts *itself*, bursts forth
again, each time at a __speci__fically new, *higher* *level**/scale*, from out of the *‘***intra**-__du__ality’, or of the *‘***intra**-__multi__ality’, of each *most recent* *‘*__contra__-**thesis**’
*category*,
when that *‘*__contra__-**thesis**’
*category* *operates upon itself*,
as a __speci__fic «*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 *‘*__qual__itatively,
*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____-__**thesis**^{2}* = *__old contra____-__**thesis**** ****+*** *__new contra____-__**thesis**,
e.g., __gene__rically --

__q___{2}* *x __q___{2}* = *__q___{2}^{2}* = *__q___{2}* *+ __q___{2+2 }*= *__q___{2}* *+ __q___{4}.**”**

**“**Each *new* *‘***contra**-**thesis**’,
*born*[*e*] of that *‘***intra**-__du__ality’, *irrupts* into __ex__plicitude,
or into *actuality*,
through the *self**-***refl**__e__xion,
the *self**-***refl**__e__xive
*action*, or
the *‘‘‘***self**-**activity**’’’
[cf. Marx], i.e., through the *ontological* *‘‘‘*__self__-__multi__plication’’’ [*‘“***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 __D__*omain* being *‘***meta**-**modeled**’, and of its «__a__*rché*», __a__ __=__ __q___{a} **[---)>** __q___{1},

breaks
out *again*, *anew*, but at a yet *higher level*, at a *higher **‘*__qual__o-fractal’ **scale**, than that of *its* __pre__ceding, *ancestor* *‘***contra**-**category**’.**”**

**“**For our __tri__adic __dialectic__*-***function** *‘***meta**-**equation** **meta**-**models**’ of __dialectical__ process*/progression*, it is the *most recent* *past* *‘*__uni__-**thesis**’,*
*or *“*__syn__thesis”, *category*, that is the *source* of the *next*, *new*, *higher* *‘*__contra__-**thesis**’
*category*, due
to the __speci__fic *new* *‘***intra**-__du__ality’ of that *most recent* *past* *“*__syn__thesis” *category* *itself*, that is, of the *very* *category* that *resolved in itself* the __pre__ceding __speci__fic
*‘***intra**-__du__ality’.**”**

**“**Each *“*__syn__thesis”
*category*, by *its*
*self**-***refl**__e__xion,
by *its* *self**-***refl**__e__xive *action*, by *its*
*‘‘‘***self**-**activity**’’’,
i.e., by *its* *ontological* *‘‘‘*__self__-__multi__plication’’’ [*‘“***self**-**squaring**”’], *amplifies* *its* *own*
__speci__fic *‘*__end__o-__du__ality’, until that *‘*__end__o-__du__ality’ bursts forth into a *new* *‘*__ex__o-__du__**ality**’, in the *form* of a *new*, *higher* *‘*__qual__o-fractal’
**scale** *‘*__contra__-**category**’ --

__old
uni____-__**thesis**** ****x*** *__old uni____-__**thesis**** = **__old uni____-__**thesis**^{2}* = *__old uni____-__**thesis**** ****+*** *__new contra____-__**thesis**,
e.g., __gene__rically --

__q___{3}* *x __q___{3}* = *__q___{3}^{2}* = *__q___{3}* *+ __q___{3+3 }*= *__q___{3}* *+ __q___{6}.”

**“**In the light of the foregoing *considerations* on *‘*__tri__adicity’
and *‘*__dy__adicity’ 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 *“*__tri__plicity”, __and__ __on__*
‘*__tetra__dicity’, in the __gene__ric *‘***num**__b__erology’ of __dialectic__ --

“...Kant did not apply* the infinitely important form*
of __tri__plicity -- with him it
manifested itself at first only as a *formal* spark of light -- to the *genera* of his *categories* (__quant__ity, __qual__ity,
etc.), but only to their *species*
which, too, alone he called *categories*. Consequently he was unable to hit on the *third* to __qual__ity and __quant__ity.”
[__Note__:
Per Hegel’s «__Logik__», that *“***third**” is* “***measure**”, an «*arithmos*» of __quant__ifiable __qual__itative «*monads*», or *units*, of *measurement*; of *‘*__quant__ifiable dimensional __qual__ifiers’ -- **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, __tri__partite; and then, because particularity
presents itself as *doubled*,
the __division__
moves on to __four__foldness as well. In the sphere of *spirit* __tri__chotomy 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__.]. ... .**”**