**The F**.

__.__

**E**__. '__

**D****Meta-Pythagorean Proposition**' --

Dear Readers,

As I see it, the

**F**.

__.__

**E**__. <<__

**D***>> rises upon the foundation of a series of*

**oeuvre***of a seminal succession of previous*

**immanent critiques****mythopoeic**,

**religious**,

**philosophical**,

**scientific**, mathematical, and

**psychohistorical**contributions to human civilization -- to

*"*.

**The Human Phenome**"I plan to summarize these

*here in a series of posts, mostly in the chronological order of the contributions critiqued, and stating with an*

**immanent critiques***that*

**immanent critique****F**.

__.__

**E**__. explicitly posits, in module__

**D****# 136**of their book

*A*__, which is quoted in its entirety below, with commentary, by yours truly, interspersed.__

*Dialectical**"***Theory of Everything**"It summarizes their

*of the ideology of the ancient Pythagorean brotherhood-sisterhood, circa*

**immanent critique****570**to

**500**

**B**.

**C**.

**E**.

__Note__:

**F**.

__.__

**E**__. describes__

**D***, in module*

**themselves****# 231**of

__, as "a__

*A**Dialectical**"***Theory of Everything**"*'*sisterhood-brotherhood".

**Meta**-**Pythagorean**'The

**F**.

__.__

**E**__.__

**D***of the ideology of*

**immanent critique***can be grasped heuristically, using the*

**Pythagoreanism**

__Q__*, and using the*

__dialectical__ideography__tep__

**s****s = 1**

*Seldon Function, as follows --*

__Tri__adic

__)-|-(__0 =

(

(

__Pythagoreanism__)^(3^0)**=**

**(**

__Pythagoreanism__)^(1)**=**

**;**

__Pythagoreanism__

__)-|-(__1 =

(

(

__Pythagoreanism__)^(3^1)**=**

(

(

__Pythagoreanism__)^3**=**

((

((

__Pythagoreanism__)**(**

__Pythagoreanism__))**(**

__Pythagoreanism__)**=**

(

(

__Pythagoreanism__)**((**

__Pythagoreanism__)**(**

__Pythagoreanism__)) =

__Pythagoreanism__**+**

__Contra__

__-__

__Pythagoreanism__**+**

__Trans__

__-__

__Pythagoreanism__**=**

__P__+__C__+__q__/CP**=**

__+__

PP

__C__+__T__

[---)

[---)

__/1 +__

qq

__q__/2 +__q__/(2+1)**-- in which the "ideo-ontological category"**

**, or**

__P__**, functions as specific**

__Pythagoreanism__*"*<<

__-__**ideo***>>", or*

**arche'***"*, and in which the "ideo-ontological category"

**thesis**"**, or**

__C__

__Contra__

__-__**, functions as**

__Pythagoreanism__*"*, or immanent-/self-negation of

**-**__contra__**thesis**"**, or**

__P__**, and in which the "ideo-ontological category"**

__Pythagoreanism__**, or**

__q__/CP

__Trans__

__-__**, functions as**

__Pythagoreanism__*"*, i.e., as the reconciliation of, or

**-**__uni__**thesis**"*"*of,

**complex unity**"**and**

__Pythagoreanism__

__Contra__

__-__**, or of**

__Pythagoreanism__**, and**

__C__**.**

__P__The progression of propositions extracted below -- "

**Pythagorean**" followed by "

**trans**-

**Pythagorean**", "critically-corrected" propositions -- from their module

**# 136**, constitutes, to my reading, a kind of abbreviated

*presentation of the fruits of their immanent critique of Pythagoreanism, as if*

**Systematic**-__Dialectical__*a succession of "*, or of

**"**__syn__theses*"*, with the usual

__-__**uni****theses**"*gradient: from simple/abstract to more and more complex/thought-concrete, sequentially "explicitizing" the formerly implicit network of meanings inherent in the Pythagorean <<*

**Systematic**-__Dialectical__*>> --*

**arche'***"*<<

**All is***>>".*

**arithmos**-- or --

'''<<

*>>*

**Arithmoi***<<*

**constitute the***>>'''.*

**Kosmos**-- usually,

*, translated into modern English as --*

**and misleadingly***"*

**All is number**".-- or as --

*'''*.

**Numbers constitute the cosmos**'''**F**.

__.__

**E**__. holds that <<__

**D***>>, in ancient Greek, meant*

**arithmos***"*<<

__assemblage__of__qual__itative**>>"**

*monads**, i.e., "*

**number**

**of****".**__qual____itative____units__This is

__at all the same meaning as that of the more abstract and__

*not**meaning of, e.g., the English word*

**purely**-__quant__**itative***"*, ever since the end of the Dark Ages that separate the "modern" human phenome from the ancient Mediterranean one.

**number**"Realizing this "gulf of meaning-difference" helps us to hear the ancient Pythagoreans' <<

*>> claim in a less mystical, more concrete way --*

**arche'***'''*of

**Populations****of various kinds constitute the**

*individual units*

**cosmos***'''*.

-- that is, "things", "

**units**", do not come as absolute "singletons", but arise in "multiplicities of similars", forming various

*"*or <<

**kinds**"*>>.*

**gene**This realization helps us to no longer see so much mystery as to why, to our ancient Mediterranean human-phenomic progenitors, "

**one**" was

__[a]__

**not***"*--

**number**"__an <<__

**not***>>;*

**arithmos**

**not***"*-- but was just a single,

**"**__quant__itative*<<*

__qual__itative*>>; why, for them, the domain of*

**monad***"*, of

**number**"*"*, began with

**the**"__quant__itative**two**,

**with**

__not__**one**, and why "

**zero**" was

**an <<**

__not__*>>-concept for them.*

**arithmos**It helps us to understand the "mysteries" cited by the following authoritative, "definitionary" source on the word <<

*>> --*

**arithmos**"

**:**

*arithmos***;**

*number*

*arithm*

*ê*

*tik***; the science of**

*ê***.**

*number**Zero was unknown as a*

**and**

*number**one also was not counted as a*

**, the**

*number**first*

*number**being the*

*duas*

*– two*. From

*the Pythagoreans*,

*ton*

*arithm**on nomizontes arkh*

*ê*

*n einai*– who

*consider*

*number**to be*

*the first principle*(

**Ar**.

**.**

*Met***986a15**) –

**played a great part in metaphysics, especially in**

*number**Plato’s*

*unwritten doctrines*, involving

*obscure*distinctions of e.g.

*sumbl*

*ê***and**

*toi*

__a__

*sumbl*

*ê***–**

*toi***and**

*addible*

__non__*-*

**." [J. O. Urmson,**

*addible number***, Gerald Duckworth & Co., Ltd. [London:**

__The Greek Philosophical Vocabulary__**1990**], pp.

**31**-

**32**, [

__emphasis__**]].**

*added*This veritable contradiction between ancient and modern Occidental theories of number, and of arithmetic, were glaringly evident in perhaps the last great work of ancient science to survive, the work that laid the foundation for modern algebra, and, in many ways, for modern ideographical mathematics entire -- the <<

*>>, by Diophantus of Alexandria.*

**Arithmetike'**In that work, the "abstraction of number" from ordinary-language discourse was made in a crucially-different way from the way in which we and our ancestors have made it ever since the Dark Ages gave way to the present "Dim Ages".

From "

**two apples plus two apples makes four apples**"., we moderns abstract

*:*

__only__the**generic**__quant__ifiers**.**

2 + 2 = 4

2 + 2 = 4

Diophantus abstracted, in

*form, the*

**generic***["kind-of-thing"]*

**ontological***as well as the*

__qual__ifiers

**ontological***.*

__quant__ifiersHe abstracted

*<<*

**a generic**

**Mo****-**

*>>[-ic*

**nad***], denoted by the "syncopated" abbreviation "letter-*

__qual__ifier**o**micron-atop-letter-

**M**u", or

**M^o**, as well as its

*, also using, by way of "gematria", the primed second Greek letter,*

__quant__ifiers*"*eta-

**b***, to denote what we take to be "*

**prime**"**2**", and the primed fourth Greek letter,

*"*elta-

**d***, to denote what we take to be "*

**prime**"**4**":

**2M^o + 2M^o = 4M^o**,

or, with considerably greater faithfulness -- within standard typographical limitations -- to the actual Diophantine

*"*extant in the portions of Diophantus's manuscripts that survived the last

**syncopated**-**algebraic**" handwritten**notation***:*

**Dark Ages****M^o**<<

*b'b'**>>*

**aequalis****M^o**.

*d'*Diophantus's mathematical, arithmetical <<

*>>, or*

**monad***,*

**unit****M^o**, is, in fact, a forerunner, or "pre-vestige", of

**F**.

__.__

**E**__.'s__

**D***, like*

**dialectical-arithmetical**__qual__itative**units****[for any**

__q__/n**n**in the space of "

__atural" Numbers,__

**N****N**].

More exactingly, with the two English characters,

__, denoting the single-character__

**Mu****12**th Greek letter <<

*>>, Diophantus's*

**mu****M^o**is a "pre-vestige" of the value

**, or**

__Mu__/(u/0)**-subscript-**

__Mu__**(u**-subscript-

**0)**,

**, in**

__Mu__u0**F**.

__.__

**E**__.'s__

**D***dialectical-arithmetical axiomatic system, the subscript-*

**second full**__uni__-system**w**"subscript-

__q__/7 (---]**W**" axiomatic system of dialectical arithmetic, which "internalizes" the "subscript-

__Mu_______**W**

__"__

**U****_***dialectical-arithmetical axioms-system, both being based upon the*

**first full**__uni__-system*axioms-system of the "Standard" arithmetic of the "*

**zero**-including__hole Numbers",__

**W**__, whose space is__

**W****W**

**,**

__=__{ 0**1**,

**2**,

**3**,

**4**,

**5**,

**6**,

**7 . . . }**, and wherein

**functions as a**

__Mu__/(u/0)*"*

**dimension-less**"*, or*

**unit****%**-like

*, similar to*

**unit****M^o**, e.g., --

**1%**

**+**

**1%**

**=**

**2%**

*a'*M^o +*a'*M^o =*b'*M^o**1**

__Mu__u0**+ 1**

__Mu__u0**=**

**(**

**1**

**+ 1**

**)**

__Mu__u0**= 2**

__Mu__u0-- or --

**1**

__Mu__/(u/0) + 1

__Mu__/(u/0)**=**

**(**

**1**

**+ 1**

**)**

__Mu__/(u/0)**= 2**

__Mu__/(u/0)-- and --

*M^o x*

a'a'

*a'*M^o =*a'*M^o**1**

__Mu__/(u/0) x**1**

__Mu__/(u/0) =**1**

__Mu__/( u/0**+**

**u/0**

**)**

**=**

__Mu__/(u/0)-- or --

**1**

__Mu__u0**x**

**1**

__Mu__u0**=**

**1**

__Mu__**u0**

**+**

**u0**

**=**

__Mu__u**0**

The marked discrepancy between the ancient and the modern Occidental meanings, and scientific theories, of the concept of

*"*/ <<

**number**"*>> represents a major fount and foundation for the*

**arithmos****F**.

__.__

**E**__.__

**D***"*of

__-__**meta****science**"*'''*, and for their

**psychohistory**'''*"*, as well as for their Marxian paradigm as a whole, which they name

**psychohistorical**"__dialectics__*"*

**Psycho****historical***.*

__"__**Materialism****F**.

__.__

**E**__. accounts for this discrepancy in__

**D***"*

**number**"*-- in the concept of the*

**theory***"*and in the intrinsically-related concept of the

**",**__quant__itative*"*-- in terms of the less-permeating molding of the ancients experience by their emerging,

**"**__qual__itative*"*law of value, and in terms of the ever-more-pervasively-permeating, unconscious molding of the modern <<

**protoic**"*>>, by the Capital-relation's*

**mentalite'***.*

**law of value**Marx's "

**elementary value form**" -- the single, <<

*>> socio-ontological category from which all of the rest of the categorial progression of*

**arche'****dialectically flows -- shows how, in our normal ignorance of "the socially-necessary abstract human labor-time presently required to**

*Capital*__produce a commodity" as core determinant of a commodity's prevailing monetary value/price central tendency, and, therefore, in our ignorance of the core, qualitative meaning of the monetary__

**re***-- e.g., of*

**unit****$**-- our incessant commodity purchase [and sale] activities in our modern

**=**capital-centered society unconsciously inculcate in us a fallacious sense of the

*exchange-equating of*

**purely**-__quant__itative*commodities, thus continually reinforcing a mentality of*

__qual__itatively heterogeneous**, of which**

*the abstraction of pure*__quant__ity*become the deeply-addicting paradigm, permeating the collective,*

**money-value**__quant__ities*"*of humanity -- the

**social**-__un__conscious**mind**"*conscious ideology-forming domain of the human phenome -- to its deepest reaches, and*

**un**__consciously__

**un***even the most conscious summits of the capital epoch's ideological sciences with a profound*

**deforming***of*

**fetishism***,*

**-**__hetero__geneity**denying***"*

**"-**__qual__itativity**denying***"*.

**"**__quant__ism**F**.

__.__

**E**__. wrote, in their module__

**D****#136**--

**1**. «

**»**

*Arithmoi***constitute the**«

**».**

*Kosmos*[To hold that <<

*>> of <<*

**arithmoi***>> constitute the <<*

**monads***>> is, as already pointed out above, merely to emphasize a commonplace empirical observation: "individuals" of all kinds come in populations -- M.D.].*

**kosmos****2**. «

**»**

*Arithmoi***constitute the**«

**»,**

*Kosmos***via**[

__self__*-*]«

**»**

*aufheben**‘*

*meta**-*

*monadization**’*.

[In this

**second**step,

**F**.

__.__

**E**__. adds their noticing of the process of '[self-]-meta-__

**D***ization', breaking with the tendencies toward a Parmenidean stasis view of the <<*

**unit**-*>>, by naming/describing the mechanism [or '''organism'''] in the universe that generates new <<*

**kosmos***>>, new*

**arithmoi***"*, new

**numbers**"*"*/<<

**kinds**-**of**-**being**"*>>:*

**gene**

__new____.__

**ontology****F**.

__.__

**E**__. also, in the process, notes that this generator is an <<__

**D***>> one, i.e., a*

**aufheben**__, one -- M.D.].__

**dialectical****3**. «

**»**

*Arithmoi***constitute the**«

**»,**

*Kosmos***via**

__self__*-*

**,**

*reflexive***,**

*nonlinear**‘*

__self__*-*

*iterated**’*[

__self__*-*]«

**» [**

*aufheben*

__self__*-*]

*‘*

*meta**-*

*monadization**’*.

[In this step

**three**,

**F**.

__.__

**E**__. adds notice of the interconnexions that they see, among__

**D***'''*,

**dialecticity**'''*"*, and mathematical, differential equation

**self**-**refl**"__e__xivity*"*-- M.D.].

**nonlinearity**"**4**. «

**»**

*Arithmoi***constitute the**«

**»,**

*Kosmos***via tau**-

**,**

__Epochal__

__self__*-*

**,**

*reflexive**‘*

__self__*-*

*refl*

__u__

*xive**’*,

*‘‘‘*

*karmic**’’’*,

**,**

*nonlinear**‘*

__self__*-*

*iterated**’*[

__self__*-*]«

**» [**

*aufheben*

__self__*-*]

*‘*

*meta**-*

*monadization**’*.

[In this

**fourth**step,

**F**.

__.__

**E**__. adds notice of the interconnexions that they see, among__

**D***'''*, and

**dialecticity**'''*"*, as

**self**-**refl**"__u__xivity*'''*, the latter as a fruition, I think, of their immanent critique of ancient Oriental religious and mystical ideologies. The self-iterated "epochality" of the posited

**karmicity**'''*"*-meta-<<

**self***>>-izations" is also explicitly noted here for the first time in this sequence of propositions.*

**monad***"*as used in above means essentially "suitable to be modeled, mathematically, via a

**Self**-**iterated**"*"*, such as one of the

**-**__self__**reflexive function**"*"*-- M.D.].

**Seldon Functions**"**5**. «

**»**

*Arithmoi***constitute the**«

**»,**

*Kosmos***via**

**tau**-

**,**

__Epochal__

__self__*-*

*refl*

__e__**,**

*xive**‘*

__self__*-*

*refl*

__u__

*xive**’*,

*‘‘‘*

*karmic**’’’*,

**,**

*nonlinear**‘*

__self__*-*

*iterated**’*[

__self__*-*]«

**» [**

*aufheben*

__self__*-*]

*‘*

*meta**-*

*monadization**’*,

**producing natural**-

**historical**

*time***as an**

*accelerating*

__progress__*ion*

**of**«

**»,**

*aufheben***or**

*‘‘‘*

*evolute**’’’*,

**,**

*evolutions***each**

**characterized by a**

__quant__*itatively*

*expanding*

__self__*-*

*reproduction***of the then**-

**leading**

*‘*

*Arithmic**’*,

*Monadic***,**

*population***which**,

**upon**

**reaching**

**,**

*critical population densities*

*punctuate***those**

*natural evolutions***with**

*‘‘‘*

__meta__*-*

*evolutions**’’’*--

*‘*

__self__*-*

*revolutions**’*

*in***--**

*Nature***manifesting**

**as**

*‘*

*meta**-*

__finite__*’*,

*‘*

__self__*-*

*bifurcation**’*,

*‘‘‘*

*resonant**’’’*,

*‘*

*meta**-*

*monadizing**’*

**,**

__singularities__**superseding each**

**current leading**«

**»**

*Arithmos***with a new one**,

**of**

*new**‘*

__qualo__*-*

*fractal**’*

*scale*

*/level**;*

*a*

*new***/**

*Quality***/«**

__Kind__**»,**

__Genos__**of**

**,**

__universal__*‘*

*Arithmic**’,*‘[

*Meta**-*]

*Monadic**’*

**.**

*ontology*[In this

**fifth**/

**final**step for this module,

**F**.

__.__

**E**__. irrupts a whole cascade of "explicitization" of former "implicitudes" of their "Trans-Pythagorean" account of the <<__

**D***>>.*

**kosmos**They connect

*"*--

**"**__quant__itative change*and "[self-]densification" of*

**-**__quant__itatively**expanding****self**-**reproduction****monadic**populations -- with

*"*-- with

**"**__qual__itative change*of*

**-**__qual__itatively**expanding self**-**reproduction****monadic**populations in the form of the

*"*irruption

*"*of new,

__-__**meta****monadic**populations -- new

*"*, new <<

**kinds**"*>>,*

**gene***-- which they identify as the fruits of "*

**new ontology***self-*, or

__-evolutions"__**meta***"self-*, in

**re****volutions**"*, and which they also connect with the construction, by*

**Nature***, of new*

**Nature***"*scales/levels of being, and with

**-**__qual__o__"__**fractal***"*in

**singularities**"*, which they further characterize as "meta-finite", and "resonant", and as*

**Nature***"*.

__-__**self****bifurcations**"They thus relate their new paradigm, in an

*"*fashion -- to

**immanently critical**"*"*, or to so-called "chaos theory", as the theory of [especially

**dynamical systems theory**"*, and therefore*

**nonlinear***]*

__-prone__**singularity***"*

**total**"

*differential equations**-*

**, or**

*systems**"ordinary"*

*differential equations-systems*, as applied to the modeling of, e.g., "natural", "physical" dynamical systems [systems that are typically, for

**F**.

__.__

**E**__., both__

**D***"*dynamical", or

**-**__self__*"*dynamizing", as well as

**-**__self__*"*dynamized"], using the language of

__-systems-__**other***"*differential equations", i.e., of

**total**__eal numbers or__

**R**__omplex numbers algebra, supplemented, or "extended", to incorporate two additional, mutually-inverse, '''[hyper-]arithmetical''' operations, operations__

**C****#7**and

**#8**, in addition to the traditional, paired, six: addition/subtraction, multiplication/division, raising to the

**r**th power/taking the

**r**th

**r**oot -- namely

*/*

**integration***, and using only*

**differentiation***"*, as opposed to

**total**"*"*,

**partial**"*.*

**differentiation operations**They also critique the modern,

*concept of*

**abstract***, by re-defining*

**time***in terms of its continual [re-]production process in the*

**time***processes of*

**concrete***and, especially, of*

**universal**__e__volution

**universal***"*, or of

__-__**meta****"**__e__volution*"*

**universal**

**self**-**re****volution**" -- M.D.].

Regards,

Miguel

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