**01 May 2012**--

Dear Readers,

The

**F**.

__.__

**E**__. generic model of dialectical progressions in general, holds as follows --__

**D**Suppose that we have a "sum" of mutually qualitatively different qualitative determinations, collectively denoted by

**, characterizing a given system, as of step**

__H__h**h**in the dialectical presentation / systematic dialectic of that

*theoretical*system, or as of epoch

**h**in the

*self-*presentation / historical dialectic of that

*natural*system, where

**h**is a discrete variable ranging over the "Whole" Numbers,

**{ 0, 1, 2, 3, . . . }**.

If that "sum" of characteristics is a qualitative, heterogeneous [or inhomogeneous], irreducible, and non-amalgamating, or <<

*>> [Plato: unaddible] sum, then stage*

**asumbletoi****h+1**will exhibit the following, expanded non-amalgamative sum, with additional possible determinations/characteristics describable as follows --

__H__h**--->**

__H__h+1**=**

__H__h

*"of"*

__H__h**=**

__H__h**(**

__H__h**) = ~**

**(**

__H__h**)**

**=**

__H__h**x**

__H__h**=**

__H__h

__H__h**=**

__H__h

*"squared"*

**=**

__H__h**^2**

**=**

__H__h**+**

__Delta__(

__H__h**)**

-- such that the term

__Delta__(

__H__h**)**"contains" all of the revolutionary, new "ontology" -- all of the newest possible determinations / characteristics -- all computed from the old determinations / characteristics of stage

**h**.

For example, if

**h = 1**, and if the possible features of the maximal natural system known as the cosmos, as of that epoch, epoch

**1**, are --

**(**

__n__+__s__)__=__(__sub-nuclears__+__sub-atomics__**)**

__=__(__bosons & non-composite fermions__+__hadrons__**)**

-- such that the underscores indicate the "contra-Boolean" computational logic exhibited by these terms as [dialectical] logic elements, or as [dialectical] logic symbols [i.e.,

**], then, as of the next discretely representable epoch, epoch**

__x__^2 ~=__x__**h + 1 = 1 + 1 = 2**, the possible features of the cosmos are "predicted" by the

**F**.

__.__

**E**__. "Dialectical "Theory of Everything" Equation" to be --__

**D**

__H__1

**=****(**

__n__+__s__)**--->**

__H__2

**=****(**

__q__n +__q__s**+**

__q__sn**+**

__q__ss**)**

**=**

__H__1

*"of"*

__H__1**=**

**(**

__n__+__s__)

*"of"*

**(**

__n__+__s__)**=**

__H__h**(**

__H__h**) =**

**(**

__n__+__s__)**((**

__n__+__s__))**=**

**~**

**(**

__H__1**)**

**=**

**~**

**(**

__n__+__s__)**=**

__H__1**x**

__H__1**=**

**(**

__n__+__s__)**x**

**(**

__n__+__s__)

**=**

__H__1

__H__1**=**

**(**

__n__+__s__)**(**

__n__+__s__)

**=**

__H__1

*"squared"*

**=**

**(**

__n__+__s__)

*"squared"*

**=**

__H__1**^2**

**=**

**(**

__n__+__s__)**^2**

**=**

__H__1**+**

__Delta__(

__H__1**)**

**=**

**(**

__n__+__s__)**+**

__Delta__**(**.

__n__+__s__)**=**

**(**

__n__+__s__**)**

**+**

**(**

__q__sn**+**

__a__**)**

**=**

**(**

__n__+__s__**+**

__q__sn**+**

__a__**)**

**=**

__H__2

__=__(__sub-nuclears__+__sub-atomics__**+**

__real subsumption of sub-nuclears by sub-atomics__**+**

__atomics__

**)**

__=__**(**

__sub-nuclears__+__sub-atomics__**+**

__sub-atomic / sub-nuclear hybrids__**+**

__atomics__

**)**.

Note especially the "sub-equation" extracted from the original serial equation above --

__H__h**(**

__H__h**) = ~**

**(**

__H__h**)**.

Its Left-Hand-Side [LHS] expression, read off as "

**of**__H__h**", denotes the "self-function[ing]" of**__H__h**, that is, the**__H__h*"*of__-movement"__**self****-- the**__H__h*"*__kinesis" [Plato] of__**auto****.**__H__h
Its Right-Hand-Side [RHS] expression, read off as "[dialectical] negation of

**", or as "[determinate] not**__H__h**", denotes the dialectical, determinate negation of**__H__h**, that is, the <<**__H__h*>> negation of***aufheben****.**__H__h
So, the sub-equation --

__H__h**(**

__H__h**) = ~**

**(**

__H__h**)**

-- asserts that the dialectical, determinate, <<

*>>***aufheben***symbol, for a given system-characterization symbol, generically denoted by*__negation____operation__**, itself formulated as a function / operation / action / activity, is, precisely,**__H__h__--__**itself****~**

**=**

__H__h**[**

*for*

**]. What more**

__H__h*determinate*,

*specific*,

**could there be, for**

*negator***, than**

__H__h**itself?**

__H__h

That is, the effect of the inherent, immanent, "intra-duality", or "self-duality", of such a system, as of stage

**h**in its [self-]development, denoted**-- the "internal dialectical contradiction" or "dialectical self-contradiction" of / immanent to that system -- can be expressed as a dialectical, determinate, <<**__H__h*>> self-negation of that system-stage --***aufheben**

__H__h**--->**

**~**

**(**

__H__h**)**

**=**

__H__h**(**

__H__h**) =**

__H__h**x**

__H__h**=**

__H__h

__H__h

**=**

__H__h**^2**

**=**

__H__h**+**

__Delta__(

__H__h**)**

**=**

**.**

__H__h+1

[Note that

**~**

**(**

__H__h**)**

**=**

__H__h**(**

__H__h**)**, so

**~**

**(**

**~**

**(**

__H__h**)**

**)**

**=**

**~**

**(**

__H__h+1**)**

**=**

__H__h+1**(**

__H__h+1**) =**

__H__h**^2**

**(**

__H__h**^2**

**) =**

__H__h**^4**,

**not****~**

**(**

**~**

**(**

__H__h**)**

**)**

**=**

__H__h**(**

__H__h**(**

__H__h**)**

**)**

**=**

__H__h**(**

__H__h**^2**

**) =**

__H__h**^3**.

That is, the "tilde" symbol, '

**~**', acts like a pair of "horizontalized" ditto marks].

The series of equations --

__H__h**--->**

**~**

**(**

__H__h**)**

**=**

__H__h**(**

__H__h**) =**

__H__h**x**

__H__h**=**

__H__h

__H__h

**=**

__H__h**^2**

**=**

__H__h**+**

__Delta__(

__H__h**)**

**=**

__H__h+1-- expresses the core breakthrough discovery of

**F**.

__.__

**E**__. in achieving the first algebraic representation of dialectical processes in general,__

**D***--*

**the first algebraic**__dialectical__logichttp://www.dialectics.org/dialectics/Dialectic_Ideography_files/5_Dialectics-Part1b-WhyDI_OCR.pdf

-- [

**F**.

__.__

**E**__.,__

**D**__,__

**Dialectical Ideography***, Part*

**Prolegomena****I**.

**b**., pages

**I**-

**73**through

**I**-

**75**].

**F**.

__.__

**E**__. thus achieved, in 1999 [or even as early as 1996, judging from the day-counter in their document version-numbers], for__

**D***, the counterpart and <<*

**algebraic**__dialectical__logic*>> of what Leibniz, from 1666 [though he did not publish his algebra of logic], and Boole, from 1847 [who published, in that year, his booklet entitled*

**surpassement**__:__

**The Mathematical Analysis of Logic***], achieved for*

**Being an Essay towards a Calculus of Deductive Reasoning**

**algebraic formal logic****--**

Leibniz / Boole:

**x^2 = x**, i.e.,

**0^2 = 0**, and

**1^2 = 1**.

**F**.

__.__

**E**__.:__

**D****, i.e., for every**

__x__---> ~__x__=__xx__=__x__^2 =__x__+__delta_____x__**n**in

**N**

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

__q__n ---> ~__q__**n**

**=**

__q__**n**

**x**

__q__**n**

**=**

__q__**n**

**^2 =**

__q__**n**

**+**

__delta_____q__**n**

**=**

__q__**n**

**+**

__q__**n+n**

**=**

__q__**n**

**+**

__q__**2n**.

*--*

__dialectical__negation

__H__h**--->**

**~**

**(**

__H__h**)**

**--->**

**~**

**(**

**~**

**(**

__H__h**))**

**--->**

**~**

**(**

**~**

**(**

**~**

**(**

__H__h**)))**

**--->**. . .

-- which is equivalent to the following

*iteration of dialectical*__-__**self***negation --*__-__**self**

__H__h**^1**

**--->**

__H__h**^1**

**(**

__H__h**^1**

**)**

**=**

__H__h**^2**

**--->**

__H__h**^2**

**(**

__H__h**^2**

**)**

**=**

__H__h**^4**

**--->**

__H__h**^4**

**(**

__H__h**^4**

**)**

**=**

__H__h**^8**

**--->**. . .

-- is the process that

**F**.

__.__

**E**__. names__

**D***"*, which can be succinctly summarized as --

**The Dyadic Seldon Function**"

__H__h**=**

__H__0**^(2^h)**.

Regards,

Miguel

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