**.**

*Seldonian*__Dialectical__*Algebra**Simplified*
Dear Readers,

One of my internet interlocutors recently wrote: “. .
. I can't make heads or tails out of the algebra”.

**Here’s hoping that the simplified summary below will reveal for you here both the “heads” and the “tails” of Seldon’s sensational discovery**

*¡*

*!*
Regards,

Miguel

**. Suppose ‘**

__Preliminaries__**~**’ stands for the operation of

__dialectical__*negation*

**rically, and that this**

__gene__**ric ‘**

__gene__**~**’ comes in many

**fic,**

__speci__

*determinat***varieties, ‘**

*e***~**

**’, where the subscript category-variable,**

_{x}**x**, is the

*"*of the dialectical negation operation, i.e., where

**determination**"**x**

**fies the variety of the negation ‘categorially’ -- as opposed to ‘**

__speci__**¬**’, standing for

*formal-logical negation*,

**rically**

__gene__**.**

__only__If so, by the rules of the Seldonian dialectical algebra of the

_{N}**dialectical arithmetic,**

__Q__**fically, with**

__speci__**and**

__a__**representing qualitatively distinct “ontological” categories --**

__b__*“*of thing” categories -- then:

**kind**

__a__**x**

**=**

__b__**~**

**[**

_{a}**], and, in particular:**

__b__

__a__**x**

**=**

__a__**~**

**[**

_{a}**].**

__a__
That
is, the “times” operation, or ontological-categorial “multiplication”
operation, is interpreted, in Seldonian dialectical algebra, as representing

**,**__dialectical__**determinate***negation*, of the multiplicand --**, in our first example -- by its multiplier,**__b__**, and, also, thereby, the “time” operation as well -- as ‘time**__a__**ration’, the**__gene__**ration of historical order-of-progression, or of the time/order-of-presentation of a step in the systematic presentation of the content of a “synchronic slice”, or “snapshot”, representing an historical present.**__gene__
In
the presentation(s) / narratives below, the names of

__dialectical__**-- of***categories***eric categories of the**__gen__**-- are indicated by underscoring those names.***Marxian*__dialectic__
The
arrow symbol, ‘

Exponentiation is signified via the '

**--->**’, indicates the process of historical becoming, or of a systematic shift in presentational focus, and the direction of the arrow indicates that direction of becoming / shifting.Exponentiation is signified via the '

**^**' sign, e.g.,**3^2****=****3**"squared"**= 9**.
Two
different,

**ric dialectical interpretations of the Seldonian arithmetic/algebra are presented below, the first,**__gene__*‘*__dyad__*-*ic’, the second,*‘*__triad__*-*ic’.**A**.

__Seldonian Dialectical Algebra____,__

*‘*

__Dyad__

__-__

__ic____’__

**.**

__Interpretation__**: The initial, ‘**

__Given__**Stage**

**0**’ category, designated as the

**ric dialectical “**

*gene***” category, including the shared, implicit “connotations” of that category, assigned [‘**

__thesis__**[---]**’] to the

**ric Seldonian ‘**

*gene***1**st dialectical meta-number’,

**--**

__q___{1}

__q___{1}**[---]**

**.**

__thesis__

__Stage____:__

**0**

__thesis__**=**

__thesis__**^1**.

__Stage____: “Square” the__

**1****, the result of**

__thesis__**Stage**

**0**, with itself --

__thesis__**^2**

**=**

__thesis__**^1**

**x**

__thesis__**^1**

**=**

__thesis__**^1[**

__thesis__**^1**

**]**

**=**

__thesis__**[**

__thesis__**]**

**=**

**~**

**[**

_{thesis}**]**

__thesis__**=**

__thesis__

*"*

*of*

*"*

__thesis__**=**

__thesis__

**+**

**;**

__antithesis__this qualitatively hetero

**ous categories-sum of two ontological categories, here described only**

*gene***rically, as “**

*gene***” and/versus as “**

__thesis__**”, does not “simplify” to any single category, precisely because these two categories are mutually**

__antithesis__**homo**

__in__**ous; qualitatively different, like the proverbial “**

*gene***”**

__apples__**+**“

**”.**

__oranges__Overall, we can describe this operation, of ‘ontological multiplication’, connoting also one of 'ontological [self-]proliferation' -- of the ‘dialectical [self-]multiplication’ --

**the category**

__of__**[**

__thesis__**]**

*as*operand/argument/multiplicand,

**itself,**

__by__**that category**

__by__

__thesis__**[ ... ]**, again, this time

*as*operator/function/multiplier, as a «

**»**

*aufheben*

__double__*-*conservation of the operand,

**[**

__thesis__**]**, including by adding that operand back in the result/function-value/product, as well as by the conservation/

*“*of the

**containment**-**negation**”**in the**

__t__hesis

__a__nti**thesis**:

__t__**x**

__t__**=**

__t__[__t__]**=**

**~**

_{t}**[**

__t__]**=**

__t__+

__delta__**[**

__t__]**=**

**.**

__t__+__a__

__Stage____: “Square” the result of__

**2****Stage 1**with itself --

**[**

__thesis__+__antithesis__]^**2**

**= [**

__thesis__+__antithesis__]

**x**

**[**

__thesis__+__antithesis__] =

**[**

__thesis__+__antithesis__]

**+**

**[ [**

__thesis__**x**

__thesis__] + [__thesis__**x**

__antithesis__] + [__antithesis__**x**

__thesis__] + [__antithesis__**x**

__antithesis__] ] =

**[**

__thesis__+__antithesis__]

**+**

**[ [**

__thesis__+__antithesis__] + [__thesis__+__synthesis__] + [__antithesis__+__synthesis__] +

**[**

__antithesis__+__second antithesis__] ] =

__thesis__+__antithesis__+__+__~~thesis~~__+__~~antithesis~~__+__~~thesis~~__synthesis__+__+__~~antithesis~~__+__~~synthesis~~__+__~~antithesis~~**;**

__second antithesis__

The

**category occurs**

__thesis__**3**times in the foregoing heterogeneous sum of categories, the

**category**

__antithesis__**4**times, and the

**category occurs twice.**

__synthesis__But just a single occurrence of each unique, qualitatively distinct ontological category is sufficient; more than that is redundant.

So that sum, after we apply to it of the rule of single occurrence sufficiency just articulated, simplifies to just four terms:

**.**

__thesis__+__antithesis__+__synthesis__+__second antithesis__‘Retro-renaming’ the first

**3**terms to cohere with the naming of the

**4**th term yields:

**.**

__first thesis__+__first antithesis__+__first synthesis__+__second antithesis__Using the symbol ‘

**--->**’

**to stand for the phrase “goes to”, or for the word “becomes”, we obtain the following re-rendition of the whole story of this section --**

__Re____-__

__Rendered in__

*‘*

__Phono__

*-*

__Ideo__

*-*

__gram____-____ical__

*’***:**

__Shorthand__

__t1__=__t1__**^1**,

**--->**

__t1__**^2**

**=**

__t1__+__a1__= [__t1__+__a1__]**^1**,

**--->**

**[**

__t1__+__a1__]**^2**

**=**.

__t1__+__a1__+__s1__+__a2__**:**

__Summary__**ic Seldon Function,**

__Dyad__

_{2}

__|-|-|__

_{h}**= [**

__t1__]**^(2^h)**,

for

**h**=

**0**,

**1**,

**2**.

**: Stage**

__Next Stage__**3**,

**h = 3**--

_{2}

__|-|-|__

_{3}**= [**

__t1__]**^(2^3)**

**=**

**[**

__t1__]**^(8)**

**=**,

__t1__+__a1__+__s1__+__a2__+__ps1__+__ps2__+__s2__+__a3__
in which “

**” stands for “**__ps__**artial**__p__**ynthesis”.**__s__

**If the examples above have “given you the gist” of how the Seldonian rules work, then “do the math yourself” for**

*¡***Stage**(s)

**3**(

**+**), and see what you get

*!*

B. ., Seldonian Dialectical Algebra‘Triad-ic’ InterpretationGiven: The initial, ‘Stage 0’ category, designated as the generic dialectical “thesis” category, including the shared, implicit “connotations” of that category, assigned [ ‘[---]’ ] to the generic Seldonian ‘first dialectical meta-number’, --q1q1[---] .thesisA “cool” thing about Seldon’s algebra -- , q1^n = q1 + ... + qn
-- with '
', as opposed to mere '+ ... ++ ... +', meaning the sum of of the allq
numbers, with
“every consecutiveatrual” number subscript between n1 and n [inclusive].: Stage 0.thesis = thesis^1: Stage 1dialectical self- of the negationdialectical self- of the negation, thesis
the result of
Stage 0:thesis^3 =thesis^1 × thesis^1 × thesis^1 =thesis^1[ thesis^1[ thesis^1 ] ] =thesis[ thesis[ ] ] =thesisthesis "of" [ thesis "of" thesis ] = ~thesis [ ~thesis[ thesis ] ] = ,thesis × thesis × thesiswhich involves two distinct ‘associativities’, or orders of multiplicative operation, ,thesis × [ thesis × thesis ]versus[ ,thesis × thesis ] × thesisaddressed below in (1.a.) and (1.b.), respectively,to show that both converge to the same result. (1.a.) , thesis^3 = thesis × [ thesis × thesis ]=, thesis × [ thesis + antithesis ]=[ , thesis + antithesis ] + [ thesis × thesis ] + [ thesis × antithesis ]=[, thesis + antithesis ] + [ thesis + antithesis ] + [ antithesis + synthesis ]=,thesis + antithesis + thesis + antithesis + antithesis + synthesiswhich, after removing “redundant” repetitions of categories / terms, simplifies to: .thesis + antithesis + synthesis:Re-Rendered in ‘Phono-Ideo-gram-ical’ Shorthand.t1 = t1^1, → t1^3 =t1 × [ t1 × t1 ] =t1 × [ t1 + a1 ] =[ t1 + a1 ] + [ t1 × t1 ] + [ t1 × a1 ] =[ t1 + a1 ] + [ t1 + a1 ] + [ a1 + s1 ] =t1 + a1 + t1 + a1 + a1 + s1 =t1 + a1 + s1(1.b.) , thesis^3 = [ thesis × thesis ] × thesis= [ , thesis + antithesis ] × thesis=[ , thesis ] + [ thesis × thesis ] + [ antithesis × thesis ]=[ , thesis ] + [ thesis + antithesis ] + [ thesis + synthesis ]=thesis+ + antithesis+ + ,synthesiswhich, after removing “redundant” repetitions of categories / terms, simplifies to: .thesis + antithesis + synthesis:Re-Rendered in ‘Phono-Ideo-gram-ical’ Shorthand.t1 = t1^1, → t1^3 =[ t1 × t1 ] × t1 =[ t1 + a1 ] × t1 =t1 + [ t1 × t1 ] + [ a1 × t1 ] =t1 + [ t1 + a1 ] + [ t1 + s1 ] =t1 + t1 + a1 + t1 + s1 =t1 + a1 + s1: SummaryTriadic Seldon Function, 3, for |-|-|h = [ t1 ]^(3^h)h = 0, 1.: Next StageStage 2, h = 2 -- 3|-|-|2 = [ t1 ]^(3^2) = [ t1 ]^(9) = , t1 + a1 + s1 + pa1 + pa2 + a2 + ps1 + ps2 + s2
in which “
” stands for “paartial pntithesis”.aIf the examples above have “given you the gist” of how the Seldonian rules work, then “do the math yourself” for ¡Stage(s) 2(+), and see what you get! |

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