Dear Readers,

A new, second version of

**F**.__.__**E**__. Vignette__**D****#12**, was posted, earlier today, to the www.dialectics.org website.
The URLs for that version are the following --

http://www.dialectics.org/dialectics/Vignettes.htmlhttp://www.dialectics.org/dialectics/Vignettes.html

-- and I have also rendered this second version, below, using the typography local to this blog.

Enjoy!

Regards,

Miguel

**F**.

**.**

__E__**.**

__D__

__Vignette__

**--**

__#12__**[**

*The***]**

*Psycho*

*Historical*

__Dialectic__

*of*

*Ancient Mediterranean Philosophy*

*through***’**

*Plato*

*s Philosophical Developments**by*

*Aoristos Dyosphainthos*

__Author__*. The purpose of*

__’__**s Preface****.**

__F__**.**

__E__**.**

__D__**Vignette**

**#12**

**is to present an abbreviated**

**.**

__E__**.**

__D__*‘*for the [

__Dialectical__**Meta**-**Model****Meta**-**Equation**’**]**

*psycho***-- and for the [**

*history***]**

*psycho*

*historical***-- of the progression of Ancient Mediterranean philosophies through the two philosophies espoused by Plato, his “early” and his “final” philosophies.**

__dialectic__
This

*‘*can also serve as a worked, “cook-book” example, and sample, of the application of the__Dialectical__**Meta**-**Model****Meta**-**Equation**’_{N}__Q__**to summarize interconnections of, and to “solve for”, the**__dialectical__algebra*psychohistorical**-*of key episodes in the [**‘**__dialectical__**ideo**-**meta**-**dynamics**’**]***psycho**historical***of***progress**‘*.**The Human Phenome**’

__A Note about the On__

__-__

__Line Availability of Definitions of__

__F____.__

__E____.__

__D____.__

**. Definitions of**

__Key Technical Terms__**technical terms, including**

__Encyclopedia Dialectica__**.**

__E__**. ‘neologia’, are available on-line via the following URLs --**

__D__
-- by clicking on the links associated with each
such term, listed, alphabetically, on the web-pages of the links above.

Definitions of the

**special terms most fundamental to this vignette are linked-to below --**__Encyclopedia Dialectica__
«

**»***arché*
«

**» and «***arithmos***»***arithmoi*
«

**»***aufheben*

*Historical*

__Dialectics__

_{N}

__Q__

__dialectical__

*arithmetic*

*/*

*algebra*

*Psycho*

*historical*

__Dialectics__

-- and we plan to expand these definitions resources
as the

__Encyclopedia Dialectica__*Dictionary***unfolds.***Project*
[

__Note__:__‘‘‘Arithmetical Quantifiers’’’ vs. ‘Arithmetical Qualifiers’__. In the phrase “**3**apples”, we term “**3**” the “arithmetical [“pure”-]quantifier”, and “apples” the*‘‘‘**ontological**’’’*-- or**of thing -- ‘‘‘qualifier’’’. In the phrase “**__kind__**3**pounds of apples”, we term “pounds” the*‘***[-unit] qualifier’ -- or ‘‘‘unit of measure qualifier’’’ -- quantified by the***metrical***3**, which, together,*‘*__quant__*o**-*__qual__*ify**’*the*‘**ontological***qualifier’, “apples”. A key use-value of the**__dialectical__**is to provide algorithmic, ideographical-symbolic systems for the various kinds of ‘arithmetical***arithmetics***ifiers’, both with and without the co-presence of ‘‘‘arithmetical**__qual__**ifiers’’’.].**__quant__

__I____.__

**Introduction****. The historical expanse of “Ancient Mediterranean [“Occidental”] Philosophy”, up to and including both of the two major stages of the philosophies of Plato, offers a stunningly rich diversity of ‘human memetic content’ -- of**

__to the__*Psychohistorical Dialectic*of*Ancient Mediterranean Philosophy**‘*

*psycho*

*historical*

*material**’*.

The task of framing a
unified model, let alone a

*‘*__dialectical__*-**mathematical meta**-**model**’*, to encompass all or most of the history of this vast human-phenomic proliferation, as an*‘**ideo**-**meta**-**genealogy**’*, all following from a single philosophy as «**», or starting point, via the iterated***arché**‘**self**-*, and**reflexion**’*‘**self**-*, of that «**refluxion**’**», and of the***arché**‘*spawned by that**ideo**-**cumula**’*‘*, would seem to be a daunting assignment, to say the least.**self**-**iteration**’
Many difficult choices face
the

*‘‘‘**psychohistorian**’’’*, the*‘*__dialectical__*meta**-**modeler**’*who pursues such a task, not least of which is the choice of «**» philosophy, of the***arché**ultimate**‘*, of all that follows it in the**ideo**-**ancestor**’*‘**psychoalgebraic**’***of the***representations**‘**meta**-*of multi-category [multi-philosophy]**model**-**generated**’**progression***‘**ideo**-*.**cumula**’
One might want to consider,
as candidates

*this «*__for__**» philosophy -- i.e., for the***arché**‘‘‘**kernel**’’’*or*‘‘‘**seed**’’’*of the*‘**meta**-***model**’**-- the early philosophies***Seldon Function**the «*__of__**» of the «***arché***» -- e.g., the philosophy of Anaximander [moisture as «***kosmos***»], the philosophy of Anaximenes [air/breath-of-life as «***arché***»], and the philosophy of Pythagoras [the origin of the number sequence as «***arché***»], etc.***arché*
For the purposes of the guided

*‘**meta**-**model**’*construction exercise exposited in this vignette, we have chosen the philosophy of Herakleitos as «**», and have sought thereby to encompass, by the***arché**‘*of its**connotative entailments**’*‘‘‘***Triadic Seldon Function**’’’*‘*, and via two successive such**self**-**iterata**’*‘*, or**self**-**iterations**’*‘‘‘*, of our Herakleitean «**negations of negations**’’’**», both the philosophy of Parmenides, and, then, also Plato’s early philosophy of the supremacy of***arché**“*, and, finally, Plato’s final recorded philosophy, of the supremacy of «**The Forms**”**».**__auto__kinesis
The

__dialectical__*-***that we will employ in constructing this***algebraic language**‘*__dialectical__*meta**-**model**’*is that of the_{N}__Q____dialectical__**, the first and simplest***arithmetic*__explicitly____dialectical__**in the***arithmetic*__dialectical__*progression of*__dialectical__**discovered by our co-founder, Karl Seldon.***arithmetics*

__II____.__

__E____.__

__D____.__

__Standard Interpretations for the__*Initial*

__Generic Ordinal Qualifiers__

__of the__

_{N}

__Q__**. The first four, first-order-logic, Dedekind-Peano Postulates for the “**

__Arithmetic__**N**atural” Numbers focus on

**,**

*ordinality*

__not__**, viz. --**

*cardinality***1**.

**1**is a “Natural Number”.

**2**. The

**of any “Natural Number” is also a “Natural Number”.**

*successor***3**. No two, distinct “Natural Numbers” have the same

**.**

*successor***4**.

**1**is

**the**

__not__**of any “**

*successor***N**atural Number”, i.e.,

**1**has

__no__**within the “Natural Numbers”.**

*ancestor*
-- defining the essence of the
“

In keeping with this focus on

The

**N**atural Numbers” explicitly in terms of [apparently purely-]__quant__*itative***.***ordinality*In keeping with this focus on

**, Seldon defines the system of the***the ordinal*_{N}__Q____dialectical__**-- the first***arithmetic**‘*__anti__*thesis**-**system**’*, or*‘*__contra__*-**system**’*, to the “**N**atural Numbers”**-- in terms of***system*__qual__*itative***.***ordinality*The

_{N}**, which he also calls the**__Q__*‘**meta**-***N***atural**meta**-**Numbers**’*, are, in their simplest, least-interpreted essence, a consecutive sequence of ‘meta-numeral’ ideograms representing the successive__qual__*ities*,__not____quant__*ities*, of**-- the***ordinality*__qual__*ity*of*‘**first**-*ness’, followed by the__qual__*ity*of*‘**second**-*ness’, followed by the__qual__*ity*of*‘**third**-*ness’, and so on... -- satisfying the four first-order-logic*‘*__contra__*-**Peanic**’*,*‘*__Qual__*o**-Peanic**’*axioms:**1'**. The

*ordinal*

__qual__*ifier*for the

__qual__*ity*of

*‘*

*first**-*ness’ is an element of the

*‘*

*consecuum**’*of generic

*ordinal*

__qual__*ifiers*.

**2**

**'**. The

**of any element of the**

*successor**‘*

*consecuum**’*of generic

*ordinal*

__qual__*ifiers*is also an element of same.

**3**

**'**. Any two, distinct

*ordinal*

__qual__*ifiers*have

__qual__*itatively*

*equal*

__un__**.**

*successors***4**

**'**. The

*ordinal*

__qual__*ifier*for the

__qual__*ity*of

*‘*

*first**-*ness’ is «

**»:**

*arché***the**

__not__**of any element of its**

*successor**‘*

*consecuum**’*.

The symbols, or

That process is the positive fruition of the

This involves the turning of

The conceptual

That

*‘**meta**-**numerals**’*, that stand for the*‘**meta**-**numbers**’*of the_{N}__Q__*‘*__arche__*onic**consecuum**’*are derived,*syntactically*, in a way which represents the*semantic**‘**self**-**subsumption**’*,*‘**self**-**subordination**’*, or*‘**self**-**demotion**’*[**,**__dialectical__*self**-*«**»***aufheben**self**-*] of the “**negation****N**atural Numbers”.That process is the positive fruition of the

**,**__dialectical__*immanent*__self__*-***of the “***critique***N**atural Numbers”, which divulges the_{N}**as the implicit, most extreme known opposite,**__Q__*“*Standard Model” of the “Standard”, Peano “__Non__-**N**atural Numbers”.This involves the turning of

*‘generic**ordinal*__quant__*ifiers**’*of the “**N**atural Numbers” into the*‘generic**ordinal*__qual__*ifiers**’*of the_{N}__Q__*‘**meta**-***N***atural**meta**-**Numbers**’*.The conceptual

*‘**self**-**subsumption**’*of the__quant__**intended by the Dedekind-Peano Postulates surfaces the***itative ordinality*_{N}**as their hitherto hidden, implicit**__Q__*‘**intra**-**dual**’*, based upon the__generic____qual__*ity of***, a***ordinality**‘‘‘**generic**ity’’’*which we represent by the*‘**meta**-**numeral**ic**’*ideogram ‘**’.**__q__That

*‘**meta**-**numeral**component**’*represents*‘*__qual__*itative***’, or***ordinality**‘**ordinal*__qual__*ity**’*,__in__**: just ‘**__general__**’, or, more fully expressed, just**__q____q__**.**_{N}
To fully express,

*‘**meta**-**numeral**-**y**’*, or ideographically, the*‘**consecuum**’*of__specific__*ordinal***, namely --**__qual__ities

_{N}

__Q__

**=**

**{**

*‘*

__first__*-*ness’;

*‘*

__second__*-*ness’;

*‘*

__third__*-*ness’, etc.

**}**

-- we must add a second

*‘**meta**-**numeral**component**’*, via*‘‘‘*__sub__*ordinating**’’’***“**__specific__**N**atural Numbers”, as__specific__*‘**ordinal*__quant__*ifiers**’*, to the__generic__*ordinal*__qual__*ifier*symbol ‘**’, by**__q__*‘*__sub__*scripting**’*those**“**__specific__**N**atural Numbers” to a ‘script-level’ ‘**’ above them, yielding --**__q__

_{N}

__Q__

**=****{**

__q__**,**

_{1}

__q__**,**

_{2}

__q__**,**

_{3}**... }**[in which each

*‘*

*meta**-*

*number**’*is an «

**»],**

*arithmos eidetikos*
vs.

**N****=****{ 1**,**2**,**3**,**... }**.
Note that this

This

The

That is,

**of an arithmetical system of***opposition**purely**-*__quant__*itative***, based upon the***ordinality***N**,**an arithmetical system of**__versus__*purely**-*__qual__*itative***, based on the***ordinality*_{N}**, is not a**__Q__**, imagined as an***radical dualism***,***absolute***between an***irreconcilable diremption**absolute*__quant__*itative*and an*absolute*__qual__*itative*.This

**is, on the contrary, a***opposition*__dialectical__*anti**thesis**-***.***sum*The

**N**__quant__*ifiers*are still there -- still present -- in, or ‘‘‘under’’’, the_{N}__Q____qual__*ifiers*, though**sumed,**__sub__**ordinated,**__sub__**moted -- as their**__de__**scripts or denominators: The**__sub__**N**__quant__*ifiers*are still*“**contained**”*in[side] the_{N}__Q____qual__*ifiers*.That is,

_{N}__Q____qual__*ifiers*are «**» determinate***aufheben***/***negations***/***conservations***of***elevations***N**__quant__*ifiers*.
For this first layer of
interpretation of these

*“purely-*__qual__*itative**”*_{N}__Q__*‘**meta**-**numbers**’*-- which does not yet make explicit their universal interpretability for the modeling of__dialectical__**-- this is all that they represent:***progressions***; [***abstract temporality**abstract chronological*]**;***order**generic**‘**order**ed**-ness**’*; the consecutive succession of*‘*__qual__*itative**ordinality**’*; the*‘**consecuum**’*of*order*__qual__*ity*or of*order*__qual__*ities*.
But even here, at this
minimally-interpreted stage of the construction of the

True, it is but a shadow, and but a ‘pre-vestigial’ harbinger, of the richness of the kind of particularity of

A case in point is exemplified in the very

_{N}__Q____dialectical__**, there is already a kind of***arithmetic**generic**‘**connotative entailment**’*at work.True, it is but a shadow, and but a ‘pre-vestigial’ harbinger, of the richness of the kind of particularity of

**that drives forward, intuitively, the***categorial followership***,**__dialectical__*purely**-**qual**itative***of the more concrete, more specific***logic*__dialectical__*-***interpretations thereof.***algebraic*A case in point is exemplified in the very

*‘**meta**-**model**’*of*the*__dialectic__*of***, constructed herein.***the Ancient Mediterranean Philosophies*
This

*generic**‘**connotative entailment**’*can be formulated as follows:*‘**second**-*ness’ follows -- and even follows**--**__from__*‘**first**-*ness’;*‘**third**-*ness’ follows [**]**__from__*‘**second**-*ness’, and so on.
In the next section, the
construction, by iterated interpretations layering, of the Seldonian

*first*__dialectical__**will advance from this harbinger of***arithmetic**‘**connotative entailment**’*to the following, still**, but at last also explicitly**__generic__**, form of**__dialectical__*‘**connotative entailment**’***:***ordinality**first**full**anti***follows from the***thesis*__self__*-***of [«***interaction***»***arché**-*]**;***thesis**first***follows from the***full synthesis***of***mutual interaction***and***first full thesis***, and so on.***first full antithesis*

__III____.__

__Triad__

__ic Seldon Function__

__Interpretation of the__*Initial*

__Generic__

_{N}

__Q__

**.**

__Ontological Category Qualifiers__
The generic form for the functions-family
of the Seldon Functions is that of a generic

**symbol [**__cumulum__**] on the LHS [**__|-|-|____L__eft-__H__and__S__ide] of the*‘*__dialectical__*meta**-**equation**’*, equated to an RHS expression representing*‘**self**-**reflexive operation**’*of an [«**»,***arché**‘‘‘**seed**’’’*,*‘‘‘**cell**-*, or**form**’’’*‘**ultimate ancestor**’*ontological category symbol [__q__**1**] -- indicating its recurring*‘**self**-**reflexion**’*via a ‘meta-exponentiated’,*monotonically increasing*whole-number-valued ‘‘‘independent variable’’’ [**h**] -- on the RHS of the generic**, viz. [with ‘generic-ness’ connoted by the “rectangular”***Seldon Function equation**motif*of the symbols-set]:

__|-|-|__

_{h}**=**

**[**

__q__**1**

**]v**

**, for**

^{h}**h**in

**{**

**0**,

**1**,

**2**,

**3**,

**.**

**.**

**.**

**}**.

If

**v =****2**, the Generic Seldon Function above is said to belong to the**sub-family.**__Dyad__ic Seldon Function
If

**v =****3**, the Generic Seldon Function above is said to belong to the**sub-family.**__Triad__ic Seldon Function
Our remarks herein are
concentrated on the

**, as the**__Triad__ic Seldon Functions*‘*modeling the**-**__dialectical__**mathematical meta**-**equation**’,*of the*__dialectical__progression**, exposited herein, is of the***Ancient Mediterranean Philosophies***v =****3**variety.
With

**v =****3**, and selecting that special generic__Triad__*ic**Seldon Function**that we reserve for an*__form__**, or for a**__historical____dialectic__**, the***psycho*__historical____dialectic__*of the*__form__*‘**meta**-**model meta**-**equation**’*to be constructed herein becomes, more specifically --

__>____-|-____<__**t**

****

**=**

**<**

__q__**a**

**>**

**3**

^{t }****,

for

**t**in

**{**

**0**,

**1**,

**2**,

**3**,

**.**

**.**

**.**

**}**.

-- wherein the symbol

**t**, replacing the more generic symbol**h**, takes on ‘**emporal’ connotations, representing successive**__t__**periods, or “epochs”, and wherein, in general, the “angular”**__historical__*motif*of the entire symbols-set used is to connote the [**]***psycho***domain of**__historical__*‘*.__dialectical__**meta**-**modeling**’
The

**bring with them a further,***Seldon Functions***layer of interpretation of the***second*_{N}__Q____q__*ual**ifiers*,**{**

__q__**,**

_{1}

__q__**,**

_{2}

__q__**,**

_{3}**... }**,

by which they are interpreted as

__q__*ual**ifiers*that symbolize__gene__*ric*__dialectical__**, e.g., as***ontological categories**‘‘‘*__thesis__*’’’*categories, or as full or partial*‘*__contra__*-**thesis**’*categories, or as full or partial*‘*__uni__*-**thesis**’*categories.
If we

**[ ‘***assign***[--->**’ ] the «__a__**»***rché**-*category,**thesis**__q__**a**, to the generic_{N}__Q____q__*ual**ifier**‘*,**meta**-**number**’__q__**, as signed by ‘**_{1}__q__**a**_{ }**[--->**__q__**’, and if we can discern that**_{1}__q__**a**, and all of its successor-categories, and their**, as generated by its successive,***cumula***, ‘Seldon-functional self-operations’, connote «***cumulative***»***aufheben***, that is,***operators***, then the**__dialectical____negation__operators**is seen to signify, under the axioms of the system of arithmetic of the**__Triad__ic Seldon Function_{N}__Q__*‘*[ http://www.dialectics.org/dialectics/Correspondence_files/Letter17-06JUN2009.pdf ], a**meta**-**numbers**’*‘*,**-**__self__**iterated**’**recurrence of***cumulative*__dialectical__*“*[**negation**__s__of**]***the**negation*__s__*”*.
With every [unit] increase in

Only for

**t**, the**‘formulaic recipe’ calls for the**__Triad__ic Seldon Function*triadic**self**-*of the result of the previous**operation***triadic**self**-*, i.e., for a**operation****of the result of the previous***negation of the negation***.***negation of the negation*Only for

**t****=****0**-- only for the case in which__no__*self**-*occurs -- is the “result” a singleton [ideo-] ontological category symbol, the symbol for the «**operation**__a__**» [ideo-]ontological category alone, instead of that “result” taking the form of a***rché***of***cumulum***or more such symbols, i.e., a “non-amalgamative sum” [cf. Musès], or «***three*__a__*-*» sum [cf. Plato], of ‘[ideo-]ontological category’ symbols, since__sum__bletoi**3**^{0}**=****1**:

__|__

__-|-__

__|__**0**

**=**

**[**

__q__**a**

**]**

**3**

^{0}**=**

**[**

__q__**a**

**]**

**1**

**=**

**[**

__q__**a**

**]**

**=**

__q__**a**.

For example, if we take epoch

**t****=****1**, and denote the «__a__**» ontological category simply by***rché***, for syntactical convenience, then the**__a__**calls for the following, as per the**__Triad__ic Seldon Function_{N}**axioms, because**__Q__**3**^{1}**=****3**--

__|__

__-|-__

__|__**1**

**=**

**[**

__a__**]**

**3**

^{1}**=**

**[**

__a__**]**

**3**

**=**

**[**

__a__**]**

**x**

**[**

__a__**]**

**x**

**[**

__a__**]**

**=**

__a__

**+**

__b__

**+**

**.**

__c__
-- wherein

__a__**[--->****denotes the «**__q__1__a__**»***rché***or***category**‘‘‘*,**thesis**’’’__b__**[--->**__q__**the**_{2}*first**‘*or**contra**-**category**’*‘‘‘*, and**antithesis**’’’__c__**[--->**__q__**the**_{3}*first**‘*or**uni**-**category**’*‘‘‘*, with ‘**synthesis**’’’**+**’ standing for a generalized addition operation, that covers the addition of__q__*ual**itatively*distinct terms, and with ‘**x**’ standing for a generalized multiplication operation, that covers multiplication of_{N}__Q____q__*ual**ifiers*.
If, now interpreting

‘

as connoting the associative grouping

**as the «**__a____a__**» of a [***rché**]***psycho****historical**__, we take__**dialectic**‘

**<**__a__**>****x****<**__a__**>****x****<**__a__**>**’as connoting the associative grouping

‘

**< <**__a__**>****x****< <**__a__**>****x****<**__a__**>****>****>**’,
with

**<**

__a__**>**

denoting the category to be

**, and then**__dialectically__negated**again, and with**__dialectically__negated
‘

**< <**__a__**>****x****<**__a__**>****>**’
denoting the

**of that category, and with**__first__negation
‘

**< <**__a__**>****x****<****<**__a__**>**^{2}**>****>**’
as the

**,***next***, then we have**__second__negation
‘

**< <**__a__**>****x****< <**__a__**>****x****<**__a__**>****>****>**’,
as a whole, connoting the

**, yielding the***first*__dialectical__negation of the negation

*first***of ‘‘‘**

*triad*

__thesis__

**+**

__antithesis__

**+**

**’’’, viz. --**

__synthesis__**< <**

__a__**>**

**x**

**<**

__a__**>**

**>**

**=**

__q__**a**

**x**

__q__**aa**

**=**

__q__**a**

**x**

__q__**b**

__=__

__a__**+**

__b__

-- and --

**<**

__a__**>**

**x**

**<**

__a__**>**

**x**

**<**

__a__**>**

**=**

**<**

__a__**>**

**x**

**< <**

__a__**>**

**x**

**<**

__a__**>**

**>**

**=**

**<**

__a__**>**

**x**

**<**

__a__**+**

__b__**>**

**=**

__a__**+**

__b__**+**

__q__**b**

**a**

**=**

__a__**+**

__b__**+**

__c__

-- which, in terms of the
generic, minimally-interpreted

_{N}__Q__**, is a***arithmetics*__dialectical__**of the generic --***interpretation*

__|-|-|__**1**

**=**

**[**

__q__**1**

**]**

**3**

^{1}**=**

**[**

__q__**1**

**]**

**3**

**=**

**[**

__q__**1**

**]**

**x**

**[**

__q__**1**

**]**

**x**

**[**

__q__**1**

**]**

**=**

**[**

__q__**1**

**]**

**x**

**[**

**[**

__q__**1**

**]**

**x**

**[**

__q__**1**

**]**

**]**

**=**

**[**

__q__**1**

**]**

**x**

**[**

__q__**1**

**+**

__q__**1**

**+**

**1**

**]**

**=**

**[**

__q__**1**

**]**

**x**

**[**

__q__

**1****+**

__q__**2**

**]**

**=**

**[**

**[**

**[**

__q__**1**

**]**

**x**

**[**

__q__**1**

**]**

**]**

**+**

**[**

**[**

__q__**1**

**]**

**x**

**[**

__q__**2**

**]**

**]**

**]**

**=**

**[**

**[**

__q__

**1****+**

__q__**1**

**+**

**1**

**]**

**+**

**[**

__q__**2**

**+**

__q__**1**

**+**

**2**

**]**

**]**

**=**

__q__**1**

**+**

__q__**2**

**+**

__q__**3**,

given that

__q__**2**

**+**

__q__**2**

**=**

__q__**2**.

The

**iteration of this***second***, corresponding to the consecutively**__dialectical__negation of the negation**value of***next***t**, namely,**t****=****2**, yields the following, ontologically-expanded**of***cumulum***-- a***ontological categories**‘*, consisting of**triad of triads**’**9**consecutive**:***ontological categories*

__|__

__-|-__

__|__**2**

**=**

**[**

__a__**]**

**3**

^{2}**=**

**[**

__a__**]**

**9**

**=**

**[**

**[**

__a__**]**

**3**

**]**

**3**

**=**

**[**

__a__**+**

__b__**+**

__c__**]**

**3**

**=**

**[**

__a__**+**

__b__**+**

__c__**]**

**x**

**[**

__a__**+**

__b__**+**

__c__**]**

**x**

**[**

__a__**+**

__b__**+**

__c__**]**

**=**

**[**

__a__**+**

__b__**+**

__c__**]**

**x**

**[**

**[**

__a__**+**

__b__**+**

__c__**]**

**x**

**[**

__a__**+**

__b__**+**

__c__**]**

**]**

**=**

__a__

**+**

__b__

**+**

__c__

**+**

__d__

**+**

__e__

**+**

__f__

**+**

__g__

**+**

__h__

**+**

**.**

__i__
The additional

**6**ontological category-symbols above are**, per the**__dialectically__interpreted**.**__E__**. standard, as follows, in terms of their generic**__D____interpretation:__**dialectical**

__d__

**=**

*four***,**

*th ontological category*

*first*

__partial__

*contra**-*

**;**

*category*

__e__

**=**

*fifth***,**

*ontological category*

*second*

__partial__

*contra**-*

**;**

*category*

__f__

**=**

*six***,**

*th ontological category*

*second*

__full__

*contra**-*

**;**

*category*

__g__

**=**

*seven***,**

*th ontological category*

*first*

__partial__

*uni**-*

**;**

*category*

__h__

**=**

*eighth***,**

*ontological category*

*second*

__partial__

*uni**-*

**;**

*category*

__i__**=**

*ninth***,**

*ontological category*

*second*

__full__

*uni**-*

**.**

*category*

We will not here pursue this

**.**__E__**. standard**__D__**of the**__dialectical__interpretation**generated by the generic***ontological categories***beyond**__Triad__ic Seldon Function**t****=****2**, because the ‘‘‘solution’’’ -- or*‘*-- of the category-terms generated by the**semantification**’*‘*constructed in this vignette [whose terms are generated, initially, as**-**__dialectical__**mathematical meta**-**model meta**-**equation**’**, terms of**__algebraic____un__knowns**meaning], as presented herein, does not extend beyond that**__un__known*second**‘*for that**self**-**iteration**’*‘*.**meta**-**model**’
The

*‘*illustrated above describe our expectations for this**purely**-**qual**itative**calculations**’*‘*in terms of**meta**-**model**’__gene__*ric*characterizations of the successive, consecutive**.**__dialectical__categories
The next section addresses the heart of this

*‘*-- the**meta**-**model**’__speci__*fic*meanings of the*gene**ric*as applied to the__dialectical__categories__speci__*al**case*of**.***the psychohistorical*__dialectic__of the Ancient Mediterranean Philosophies

__IV____.__

__E____.__

__D____.__

__Solution for the__

__‘__

__Meta__

__-__

__Model__

__Meta__

__-__

__Equation__

__’__**. We have selected, as the «**

__of our__*Dialectic of Ancient Philosophy***» of the universe of discourse of**

*arché***, the philosophy of Herakleitos [**

*Ancient Mediterranean Philosophy**circa*

**540**-

**475**B.C.E.], and we denote that philosophy, in the

*‘*

*meta**-*

*model**’*thereof, constructed in this section, by the symbol

**, or**

__H__

__q__**H**,

**[--->**

__q__**.**

_{1}
The few fragments of
Herakleitos’s writings that survived the last Dark Ages indicate that he held a
view of reality as a flowing continuum/universal flux, characterized by

**, a***constant change**‘**uni**-**category**’*of*“**constancy**”***&**/vs.*“**change**”*:**Everything changes and nothing remains still ... and ... you cannot step twice into the same stream.**

*“***”**;

**We both step and do not step in the same rivers. We are and are not.**

*“***”**;

**All things are an interchange for fire, and fire for all things, just like goods for gold and gold for goods.**

*“***”**;

**We must know that war is common to all and strife is justice, and that all things come into being through strife necessarily.**

*“***”**;

[Diogenes Laërtius interpreting]:

**All things come into being by***“***conflict of opposites**, and the sum of things flows like a stream.**”**;**There is a harmony in**

*“***the bending back**as in the case of the bow and the lyre.

**”**[

**by A.D.]**

*Emphasis added**“*serves as metaphor, in Herakleitos’s philosophy, for the

**Fire**”**, or «**

*primal substance***», of the «**

*arché***»; the**

*kosmos***of all other things.**

*ultimate origin*
Our

**step, then, is to***next***this**__dialectically__negate**, using**__H__**itself as the**__H__**for itself --**__dialectical__negation operation**< <**

__H__**>**

**x**

**<**

__H__**>**

**>**

**=**

__q__**H**

**+**

__q__**HH**

**=**

__q__**H**

**+**

__q__**?**

**=**

__H__

**+**

__?__

-- and to inquire, then, as
to what might be an apt historical,

as to what might have been the new, historical, philosophical,

I.e., our next task is to

**meaning, for the algorithmically-generated new symbol***Ancient Mediterranean*__q__**HH**,as to what might have been the new, historical, philosophical,

*‘*__ideo__*-**ontological category**’*; the**of philosophical ideas, of philosophical***new*__kind__*‘**psycho**historical*__material__*’*-- that irrupted from out of this**,***immanent*__self__*-***-- this***confrontation*__self__*-***--***critique*__of__**or**__H____q__**H**,__by__**or**__H____q__**H**.I.e., our next task is to

*“*for”__solve____q__**HH**.What we find, as our best candidate for the historical/philosophical meaning of our

*‘‘‘*

*algebraic unknown**’’’*,

__q__**HH**,

is the later emerged

*‘*

*contra**-*

*philosophy**’*--

*‘*

*contra**-*

__Herakleitean__*philosophy’*-- of

**armenides, denoted herein by**

__P__**or**

__P__**.**

__q__P
The philosophy of Parmenides
[

**515**-**450**B.C.E.], as determined from surviving accounts of his views, is one of a claimed eternal changelessness of reality -- a “reality” in which change is only a human delusion:**There is one story left, one road: that**

*“***it is**. And on this road there are very many

**signs**that

**being**is

**and**

__un__created**perishable, whole, unique,**

__i__*m***, and complete.**

__un__wavering**”**[

**by A.D.]**

*Emphasis*__added__**is a kind of**

*Parmenideanism*

*absolutist**‘*of

**meta**-**monad**-**ization**’**diversity and flux: a single «**

*Heraclitean***» of**

*monad**“*

*being**”*posited

**as the «**

__not__**» of the vast multiplicity of «**

*aufheben***» of**

*monads*

*diversity*

*/***, but claimed to be their**

*flux***, as**

*absolute obliteration**“*

*falsity**”*, in a singular

*“*

*truth**”*of

*absolute**“*

**.**

*being*
Our solution to the

part of

**< <**__H__**>****x****<**__H__**>****>**part of

__H__**3**

**=**

**<**

**<**

__H__**>**

**x**

**< <**

__H__**>**

**x**

**<**

__H__**>**

**>**

**>**

is thus

__q__**HH**

**=**

__q__P

**=****,**

__P__**[--->**

__q__**.**

_{2}
But what of the rest of

**<****<**__H__**>****x****< <**__H__**>****x****<**__H__**>****>****>**;
what of

**<**

**<**

__H__**>**

**x**

**<**

__q__**H**

**+**

__q__**HH**

**>**

**>**

**=**

__H__**x**

**<**

__H__**+**

__P__**>**?

What historic

**of the***meme**Ancient Occidental**‘**Human Phenome**’*corresponds to__q__P**H**,**[--->**__q__**?**_{3}
What we find, as our best
candidate for the historical/philosophical meaning of our

is the later emerged

*‘‘‘**algebraic unknown**’’’*,__q__**P****H**,is the later emerged

*‘*__uni__*-**philosophy**’*of Plato, the philosophy of the transcendental «__E__**», also denoted herein by***ide***or**__E____q__**E**.
The earlier philosophy of
Plato, as determined from his extensive written remains, is one combining the opposing
philosophies of Parmenides and Herakleitos into a Parmenidean-dominant

*“**complex unity**”*[cf. Hegel], or*‘‘‘*__dialectical__*synthesis**’’’*, positing a ruling, transcendental, eternally changeless and “true” reality -- the reality of the «__E__**» or «***ide***» --***Idea**“**above**”*, and controlling, a subordinate, truth-falsifying, illusional realm of human sensuous experience*“**below**”*.
This Platonian

is

Their

*“**complex unity**”*,**PH,**__q__is

**a simple welding-together of a Parmenidean realm,**__not__**P**, “atop” a Herakleitean one,**H**.Their

*‘**unifying complex**’*features a**, mediating and bridging the Parmenidean realm***middle realm**“**above**”*this*‘‘‘**median**’’’*, and/with the Herakleitean realm*“**below**”*that*‘‘‘**median**’’’*.
Magisterial Plato scholar Jacob Klein describes this
Platonian

*‘*in the following terms --**unifying complex**’**“**...While the

**[«**

*numbers***»; assemblages of**

*arithmoi***— A.D.] with which the arithmetician deals, the**

*units*

*arithmoi*

__mathema__*tikoi*or

__monad__*ikoi*[

*abstract*,

*generic*, idealized,

*,*

__qualitatively-identical__*“monads” or [ideal[ized], abstract*

__homogeneous__*qualitative units*— A.D.] are capable of being counted up, i.e.,

**, so that, for instance, eight**

*added***[eight**

*monads**‘ideo-*; eight

**monads**’*abstract*ideal[ized]-

**,**

*units***, or idea-**

*unities*

__a__*-*— A.D.] and ten

**toms****make precisely eighteen**

*monads***together, the**

*monads*

*assemblages**of*

**[of ‘mental**

__eide__*seeings’*or mental

*visions*; of

*ultimate ancestor*

*“*«

**»**

*ideas**”*— A.D.], the

*“*[

**arithmoi**”__eide__tikoi*assemblages*,

*ensembles*, ‘‘‘sets’’’, or [

*sub**-*]

**of**

*totalities***, or**

*qualitatively different*

__heterogeneous__*,*or «

**ideas****» — A.D.], cannot enter into any “community” with one another [i.e., are**

*eide**‘*,

**-**__non__**’**__reductive__*‘‘‘*,

**’’’**__nonlinear__*“*,

**-superpositioning”**__non__*“*,

**-**__non__**additive**”*‘*, or

**-**__non__**addable**’*“*/ «

**-**__non__**amalgamative**”**» — A.D.].”**

__a__sumbletoi*“Their*

**monads**are all__of____different__**[i.e., are**

__kind__*‘*,

**categorially**’**,**

*ontologically***— A.D.] and can be brought “together” only “partially”, namely only insofar as they happen to**

__qualitatively____unequal__**to one and the same**

*belong***, whereas insofar as they are “entirely bounded off” from one another...they are incapable of being thrown together,**

*assemblage*

*in**-*[incapable of being

**comparable***counted*as replications of the same quality of

**[y], of the same**

__unit__**, or ‹‹**

*qualitative*__unit__**››; incomparable**

__monad__*quantitatively*— A.D.] ... .”

“The

**which constitute an***monads**“*, i.e.,**”**__eide__tic number**, are nothing but a conjunction of***an assemblage of ideas**eide*which**.”***belong together*
“They

**because they belong to one and the same***belong together**eidos*[singular form of «**»:***eide**one particular ‘internal / interior*, or «**seeing**’,**vision****» — A.D.]***ιδεα**of a*, namely a “class” or__higher____order__*genos*[akin to, and ancestor to, the grouping of multiple**under a single***species***in classical biological ‘‘‘taxonomics’’’ or ‘‘‘systematics’’’ — A.D.].”***genus*
“But all will together be able to “partake” in this

**(as for instance, “***genos***human being**”, “**horse**”, “**dog**”, etc., partake in “**animal**”)*without “partitioning” it among the (*[singular form of «**finitely**) many**eide**and without losing their indivisible unity only if the genos itself exhibits the mode of being of an**arithmos****»: a single***arithmoi***, or***assemblage**“*, of**multitude**”**/ «**__units__**» — A.D.].”**__monads__
“Only the

**structure with its special***arithmos**koinon*[“community” or “commonality” — A.D.] character is able to guarantee the essential traits of the community of*eide*demanded by**; the indivisibility [**__dialectic____a__*-tom-*icity or*‘*ability’ — A.D.] of the single**-cut-**__un__*“*which form the**monads**”*arithmos**assemblage*, the limitedness of this**as expressed in the joining of many***assemblage of monads***into one assemblage, i.e., into one***monads***, and the***idea**untouchable*. What the single**integrity**of this**as well**__higher____idea__*eide*have “in common” is theirs only*in their community*and is not something which is to be found “beside” and “outside”...them. ... .”
“The unity and determinacy of the

*arithmos**assemblage*is here rooted in the**of the**__content__**..., that***idea***which the**__content__*logos*[*word; rational speech; ratio*— A.D.] reaches in its characteristic activity of uncovering foundations*“*.**analytically**”
“A special kind of [

*all-of-*— A.D.]**-**__one__**kind**, generic-units-based**of a particular nature is not needed in***number***, as it was among***this realm***[the «***the dianoetic numbers***» — A.D.]..., to provide a foundation for this***arithmoi*__monad__ikoi**. In fact, it is impossible that any kinds of**__unity__**[«***number***» — A.D.] corresponding to those of***arithmoi***[***the dianoetic realm**the realm of ‘dia-noesis’ or of*‘«*dianoia*»’,*i.e., of ‘*— A.D.] should exist**-/**__pre__**-**__sub__**’ thinking**__dialectical__**, since each***here*__eide__tic number*is*, by virtue of its**[«**__eide__tic character**»***eide**-character*or «**»***idea**-nature*— A.D.],**[i.e.,**__unique__in kind*qualitatively*unique / distinct /**in comparison to other «**__heterogeneous__**» — A.D.], just as each of its***eide**“*has not only**monads**”**but also***unity***. For each**__uniqueness__**is characterized by being always the same and simply***idea***[**__singular__**\***additively*, and__idempotent__**\**also*‘*, as per the axioms of the**quantifiable’**__un___{N}**«**__Q__**» — A.D.] in contrast to the unlimitedly many***arithmêtikê**of the*__homogeneous__**monads****of***realm***, which can be rearranged as often as desired into***mathematical number***. ... .”***definite numbers*
“The “pure”
mathematical

**are, to be sure, differentiated from the single objects of sense by being outside of change and time, but they are not different in this sense — that they occur in***monads***(Aristotle,**__multitudes__and are of the__same____kind____Metaphysics__B 6, 1002 b 15*f.*: [Mathematical objects] differ not at all in being**and of the**__many__**...), whereas each**__same__kind*eidos*is, by contrast,**[***unreproducible**hence modelable by idempotent addition, or ‘*— A.D.] and truly**-addability’, and ‘**__non__**-quantifiability’**__non__*one*(__Metaphysics__A 6, 987 b 15*ff.*:*“*differ from__Mathematical____objects__**in being everlasting and unchanged, from**__objects____of____sense__**, on the other hand, in being many and alike, while**__the____eide__*an**eidos is*...).”**each by itself one only**”
“In consequence, as Aristotle reports (e.g.,

__Metaphysics__A 6, 9876 b 14*ff.*and N 3, 1090 b 35*f*.), there are**: (1) the***three kinds of arithmoi***—**__arithmos____eidetikos____idea__*-*, (2) the__number__**—***arithmos aisthetos***, (3) and “between”...these, the***sensible number**arithmos**mathematikos*or*monad**ikos*— mathematical and**, which shares with the**__monad__ic number**first**its “purity” and “changelessness” [here Aristotle reflects only the early, more ‘**armenidean’, Plato, not the later, «**__P____A__**» Plato — A.D.] and with the***utokinesis***second**[the**in hierarchical order] its manyness and reproducibility.**__third__
“Here the

*“*[**aisthetic**”*“sensible”*, i.e., ‘sense-able’, or**— A.D.]***sensuous***represents nothing but***number***which happen to be present for***the things themselves***[for***aisthesis**sense perception*— A.D.] in this number.”
“The

**form***mathematical numbers**an independent domain of objects**of study*[an**«***independent***» in their own right**__mathesis__*— A.D.] which the***[***dianoia**the faculty of ‘*— A.D.] reaches by noting that its own activity finds its exemplary fulfillment in**-/**__pre__**-**__sub__**thinking’**__dialectical__*“*[i.e.,**reckoning***ac*__count__*-*] and**giving***counting**”*... .”
“The

**, finally, indicates the**__eidetic____number__*mode of being of the*[that which exists__noeton__*“***for**”*thought*;*that which thought “beholds”; the object of thought*; the**[***idea***]***l**-*— A.D.]**object***as such*—*it defines the*eidos__ontologically__*as a being which has***multiple relations**to other*eide***[i.e.,***in accordance with their particular*__nature__*in accord with their*— A.D.]__content__*and which is nevertheless in itself altogether*.”**indivisible***“*of the

**The**__Platonic__theory**is**

__arithmoi____eidetikoi__

*known**to us in these terms*(

**only from the Aristotelian polemic against it***cf*., above all,

__Metaphysics__M 6-9)...

**”**

[Jacob Klein,

**, Dover [NY:**__Greek Mathematical Thought and the Origin of Algebra__**1968**], pp.**89**-**91**,*italic,***bold**,__underline__, and**color****added by A.D.]**__emphasis__William Riese describes the

**of Plato’s two systems of**

__final__known phase**philosophy as follows, whose bifurcation is signaled in Platonic dialogue known as**

__dialectical__*The Parmenides*:

**“**The dialogues of the Socratic period provide that view of the world usually associated with Plato.”

*“The period of transition and criticism, and the final synthesis, are*...”

**little noted***“*can be taken as signaling the change. In this dialogue Socrates is unable to defend his Doctrine of

**The Parmenides****[i.e., of the «**

*Ideas*

__E__**», herein denoted by**

*ide***-- A.D.]. ...”**

__E__
“Where the

In this dialogue, the

The difference now between

*Republic*and*Phaedo*stressed the unchanging nature of the soul, the emphasis in the*Phaedrus*is exactly reversed.In this dialogue, the

**is the principle of***soul*__self__*-*[in Greek, «**motion**__A__*uto**-***» -- A.D.], and we are told that the***kinesis***is always in***soul***, and what is always in***motion***is***motion***.***immortal*The difference now between

**and***spirit***is***matter*__not__*changelessness*in contrast with*change*, but__self__*-*, the essence of the**motion****, in contrast with***soul**derived**.”***motion**
“The emphasis on

__self__*-*is continued even in the**motion***Laws*, Plato's**dialogue.**__final__**”**
[William L.
Riese,

**, Humanities Press, Inc. [New Jersey:**__Dictionary of Religion and Philosophy: Eastern and Western Thought__**1980**], pp.**442**-**443**[*italic*,**,***bold*__underline__, and**color***emphasis**added***A.D.]**__by__
By a

Herein, by the term-phrase ‘[

By a

__dynamical__*mathematical**“**model**”*is usually meant an ideographical, ‘‘‘algebraic’’’, analytical analogue of a target reality, one that describes the__quant__*itative*variation, through time, of some metrics of the**constituents, within a***model***universe of such constituents, a**__fixed____fixed__*“**ontology**”*, with such constituents constituting the presumptive “ontological commitments” of that**.***model*Herein, by the term-phrase ‘[

__meta__*-***]***dynamical*__meta__*-**model**’*, we mean an ‘*ontologically**-**dynamical**’*,__multi__*-ontological-**epochs**-spanning and -bridging,**equational**analogue of a target reality which, relative to a**epoch of the*__given__*self**-***of that reality, treated as being its***development**epoch,*__present__**the***reconstructs***of its***ontology**epochs, and also*__past__*‘*__pre__*-*constructs’, or “predicts”, the**of its***ontology**epochs.*__future__By a

*‘*__meta__*-**equation**’*we mean a*‘**super**-**equation**’*, i.e., an**‘of***equation***degree’, made up out of a heterogeneous multiplicity of***second***‘of***equations***degree’; a***first**‘**super**-**equation**’*«**» or***monad***which is a***unit**‘*__meta__*-*«**»’, or***monad**‘*__meta__*-*, made up out of a multiplicity, a**unit**’__sub__*-*«**», of***arithmos**equation**-*«**», or of “mere”***monads**equation**-*, as its**units****[***internalized**sub-*]«**».***monads*
Thus,

*‘**the generic*__dialectical__*meta**-**equation**’*, or*‘**equation of the*__second__*qualo**-**fractal scale**’*--

__|__

__-|-__

__|__**t**

**=**

**[**

__q__**a**

**]**

**3**

^{t }
-- is made up out of
the following multiplicity/sequence of “mere”

**,***equations**‘*, one**equations of the**-__first__qualo**fractal scale**’__qual__*itatively-*[ive]**distinct****for each distinct value of***equation***t**:

__|__

__-|-__

__|__**0**

**=**

**;**

__a__

__|__

__-|-__

__|__**1**

**=**

__a__

**+**

__b__

**+**

**;**

__c__

__|__

__-|-__

__|__**2**

**=**

__a__

**+**

__b__

**+**

__c__

**+**

__d__

**+**

__e__

**+**

__f__

**+**

__g__

**+**

__h__

**+**

**, etc.**

__i__
Our

*‘*for the**psychohistorical**-**-**__dialectical__meta**equation meta**-**model**’*psychohistorical domain*of**[***Ancient*__M__*editerranean Philosophy***M**] can thus be expressed compactly, in a*‘*form, ‘‘‘located’’’**-**__dialectical__**ideographical**’**3**levels of*‘meta-**fractal**’ scale*down from the level**1**scale of**h**, the**umanities «**__h__**», in the***arithmos***.**__E__**.**__D__**, as --***Universal Taxonomy*

__|__

__-|-__

__|__**2**

**=**

**[**

__H__**]**

**3**

^{2}

^{ }

**=**

__H__**+**

__P__**+**

__E__**+**

__q__**E**

**H**

**+**

__q__**E**

**P**

**+**

__A__

**+**

__q__**A**

**H**

**+**

__q__**A**

**P**

**+**

__q__**A**

**E**

-- for which we have ‘‘‘solved’’’ explicitly the first

connoting

as --

**3**categories, and the**6**th category, of the**9**categories total, and, in a*‘*form, for**-**__dialectical__**pictographical**’__q___{6}**<---]**__A__**=**__q__**EE****=**__q__**P****H****<****P****H****>**,connoting

**,***immanent*__self__*-*of**critique**__E__**=**__q__**P****H**,as --

__V____.__

**. The following further explorations of the**

__Suggestions for Reader Exploration__*‘*

*psycho*

*historical**-*

__dialectical__

*domain**’*addressed in this vignette -- the domain of

**-- via the tools of the**

*Ancient Occidental Philosophies*

_{N}

__Q__

__dialectical__**, are recommended to our readers:**

*ideography***1**. Try your hand at “solving for” the five terms, generated by the

*‘*herein presented, that we left “unsolved” in our explication of that

**meta**-**model**’*‘*, viz.,

**meta**-**model**’

__q__**E**

**H**,

**[--->**

__q__**,**

_{4}and

__q__**EP**,

**[--->**

__q__**,**

_{5}as well as

__q__**A**

**H**,

**[--->**

__q__**,**

_{7}and

__q__**AP**,

**[--->**

__q__**,**

_{8}and

__q__**APH**

**=**

__q__**A**

**E**,

**[--->**

__q__**.**

_{9}__Hint__: ‘Categorograms’ of the form, e.g., ‘

__q__**Y**

**X**’ are standardly interpreted, per the

__Encyclopedia__**canon, as connoting the process/‘processor’ that produces the**

__Dialectica__**of some**

*conversion***«**

__X__**» into**

*monads***«**

__Y__**» -- or into «**

*monads***» which are**

*monads***of the**

*hybrids***and the**

__X__**«**

__Y__**»; of the**

*monads***of some of the**

*assimilation***s by**

__X__**s; of the**

__Y__**of some**

*appropriation***s by**

__X__**s; of the**

__Y__**of the existence of the**

*adjustment***s to the existence of the**

__X__**s, or of the critique of**

__Y__**by the**

__X__**, the**

__Y__**and**

*critical review***of the merits and demerits of the**

*evaluation***kind of ideas from the perspective of the**

__X__**kind of ideas, the**

__Y__**of the**

*correction***kind of ideas by means of the**

__X__**kind, and the**

__Y__**of the**

*theory of error***kind of ideas from the point-of-view of the**

__X__**kind.**

__Y__In particular --

*

__q__**E****H**connotes the result of critique of__H__**eraclitean**philosophy in light of the “Socratic” philosophy of the «__E__**»;***ide*
*

__q__**EP**connotes the result of critique of__P__**armenidean**philosophy in light of the “Socratic” philosophy of the «__E__**»;***ide*
*

__q__**A****H**connotes the result of critique of__H__**eraclitean**philosophy in light of the Platonic philosophy of «__A__**»;***utokinesis*
*

__q__**AP**connotes the result of critique of__P__**armenidean**philosophy in light of the Platonic philosophy of «__A__**»;***utokinesis*
*

__q__**A****E**connotes the result of critique of “Socratic” «__E__**» philosophy by the Platonic philosophy of «***ide*__A__**».***utokinesis*
With the help of the hints
above, can you identify specific, named or described doctrines of Plato,
together with citations of passages in Plato’s Dialogues, which correspond with
some or all of these five terms?

For example, Plato criticizes the philosophy of Herakleitos, from the perspective of the “Socratic” philosophy of the «

For example, Plato criticizes the philosophy of Herakleitos, from the perspective of the “Socratic” philosophy of the «

__E__**», in the following terms: “...how can that be a real thing which is never in the same state? ... for at the moment that the observer approaches, then they become other and of another nature, so that you cannot get any further in knowing their nature or state .... but if that which knows and that which is known exist ever ... then I do not think they can resemble a process or flux ....”, in the dialogue***ide**Cratylus*, in its paragraph**439**, section**e**through paragraph**440**, sections**a**-**b**. [E. Hamilton, H. Cairns, editors,__The Collected Dialogues of Plato____,__**, Princeton University Press [Princeton:**__including the Letters__**1989**]. pp.**473**-**474**].**2**. See if, by exploring other candidate «

**» for a**

*arché*

__Triad__ic Seldon Function*‘*of this domain, you can construct a

**meta**-**model**’

*‘*which encompasses, e.g., the earlier philosophies of Thales [

**meta**-**model**’**640**-

**546**B.C.E.], and of Anaximander [

**610**-

**547**B.C.E.], Anaximenes [

**588**-

**524**B.C.E.], and/or Pythagoras [

**570**-

**500**B.C.E.], as well as later philosophies, of Herakleitos [

**540**-

**475**B.C.E.], Parmenides [

**515**-

**450**B.C.E.], Democritus [

**460**-

**370**B.C.E.], Plato [

**428**-

**348**B.C.E.], and even of Aristotle [

**384**-

**322**B.C.E.], in a single

__Triad__ic Seldon Function*‘*.

**-**__dialectical__meta**model meta**-**equation**’**3**. Determine whether or not you do better with a

__Dyad__ic Seldon Function*‘*,

**meta**-**model**’*in covering a fuller range of the [psycho]history of*

**, than with the**

*Ancient Mediterranean Philosophy*

__Triad__ic Seldon Function*‘*that you constructed for/in step

**meta**-**model**’**2**above.

Links to definitions of additional

__Encyclopedia Dialectica__**special terms deployed in the discourse above --**
«

**»***arithmos aisthetos*
«

**»***arithmos eidetikos*
«

**»***arithmos monadikos*
«

**»***autokinesis*

*categorial*

*category**‘*

**cumulum**’

__dialectical__

*categorial progression*

*dynamics**‘‘‘*

**eventity**’’’

*The Human Phenome*

*immanent*

*immanent critique*

*meta**-*

**dynamics**

*meta**-*

**genealogy**
«

**»***monad*

*ontological category*

*ontology*

*ontology**-*

**dynamics**

*psychohistory*

__qual__

*o**-*

*fractal*

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/QualoFractal/QualoFractal.htm

__qual__

*o**-*

*Peanic*

*Seldon Functions**‘*or

**self**-**meta**-**monad**-**ization**’*‘*or

**self**-**meta**-**individual**-**ization**’*‘*

**self**-**meta**-**holon**-**ization**’
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