These comments are intended to help you to "get a handle" on "

**F**.

__.__

**E**__.__

**D****Dialectics**", by sharing some things that, over a long period of study, I've come to notice about the "

**F**.

__.__

**E**__.__

**D****Dialectical Method**" -- their

*"*.

**Organonic Algebraic Method**"__Note__: This exposition will be continued in the immediately-subsequent blog entry.

The

**F**.

**.**

__E__**.**

__D__*First Dialectical Algebra's "*is best understood, I think, as a

**Organonic Algebraic Method**"**-- as a**

*heuristic***,**

__heuristic__

*intensional**-*[<<

**intuitional tool****>>] for**

*organon**"*constructing" the mysteries of the deep-past-to-present, of

**-**__re__

*natural systems**"*[including of

*"*nature-al"

**human**-**, external-physical and/or "ideative"], and of**

*systems**"*constructing" [

**-**__pre__*"*dict-ing"] their futures.

**-**__pre__This Method is

*"*, because it deals with

**tensional"**__in__**.**

*connotations*It deals with deciphering the algorithmically-generated [ideographical] symbols of an

**N**

**dialectical meta-model for the**

__Q__**of**

*new qualities***-- of both new**

*new*__ontology__*"*and of new

**-**__ideo__**ontology**"*"*-- that they represent; in short, for the "meanings" -- or "in-tensions" -- of those symbols.

**-**__physio__**ontology**"Therefore, this Method is

**an "exact science".**

__not__Its being

*"*is also what makes it

**intensional**"*"*and

**heuristic**"*"*.

**intuitional**"What precisely does

*"*mean in this -- "symbolic logics" -- context?

**"**__in__tensionIt means the opposite of

*"*.

**"**__ex__tension[One will also find that, for

**F**.

**.**

__E__**.,**

__D__*"*tension" has connotations of

**-**__in__*"*ternal

__in__

*tension**"*, i.e., of "dialectical

*internal contradiction"*,

*"intra-*duality", or

*"self-*duality", while

*"*tension" has connotations of

**-**__ex__*"*, i.e., of

**ternal**__ex__**tension**"**ternal differences / conflicts / "self-bifurcations" / "singularities", e.g., the stellar "self-**

__ex__**plosion**

__im__**#**self-

**plosion" internal tension, or**

__ex__*physio-self-duality*, that "extends" stars' existential [contribution to] time as the [diverse stages of the] life-histories of stars, or the

*ideo-self-duality*of the

*"*

__card__inality**#**

__ord__inality*"*[in]tension "inside" the concept of the "

**N**atural Numbers" system of arithmetic, that "extends" as the

**N**

**"meta-**

__Q__**N**atural meta-Numbers" system of arithmetic, and in the forms of all of the other, subsequent systems of dialectical arithmetic in the system

**-progression of the**

__s__**F**.

**.**

__E__**.**

__D__*"*

**Meta**-**System-atic**__Dialectic__*of the*.]

__Dialectical__**Arithmetics**"For example, the

*"*of the concept named

**"**__ex__tension*"celestial*[spheroidal]

*orbs of the stellar/planetary system of the star Sol"*is and explicit

**, by name, of all of those objects which fit this concept, e.g., the**

*list**"*containing the names of all of those objects --

**set**"**{Sol, Earth, Moon, Mercury, Venus, Mars, Jupiter, Europa, Ganymede, Callisto, . . ., Saturn, Enceladus, Titan, . . ., Neptune, Triton, . . ., Pluto, Charon, . . .}**

-- whereas the

*"*of that

**"**__in__tension*"*is just the

**"**__ex__tension**that encompasses precisely that**

*concept**"*-- no more and no less -- as re-called to mind by its name, or by its words/phrase-definition:

**set**"*"celestial orbs of the stellar/planetary system of the star Sol"*-- i.e., is the

**, or "unified connotations-cluster", of that "phrasal predicate".**

*meaning*Here's what Leibniz had to say about what

**F**.

**.**

__E__**. characterizes as the**

__D__*"*

**tension**__in__

*#**internal duality dialectic within [symbolic] logics --*

**tension"**__ex__"The common manner of statement concerns individuals, whereas Aristotle's refers rather to ideas or universals [Aristotle's version of Plato's <<

**>> --**

*Eide***M.D.**].

For when I say

*Every man is an animal*I mean that all men are included amongst all the animals; but at the same time I mean that the idea of animal is included in the idea of man.

[cf. George Boole's

*"*equation --

**deductive**-**logical ideography**"**h = r**x

**a**,

-- or --

"

**h**umans are

**r**ational

**a**nimals",

-- and --

Karl Seldon's

*"*equation --

**dialectical-logical ideography**"

__l__**(**,

__l__) =__l__+__h__-- or --

'''the self-intra-action of the populations of proto-

**anguage-based anima**

__l__**-societies**

__l__**[o-**

__quant__**]**

__qual__

__itatively__**-**

*expandedly***those populations of proto-**

*reproduces***anguage-based anima**

__l__**-societies, and also[, at**

__l__**&**after they achieve their critical density, ]

**[o-**

__qual__**]**

__quant__

__itatively__expandedly*-*those populations by each irrupting a new, unprecedented population of

**reproduces****uman[oid] meta-societies'''].**

__h__'Animal' comprises more individuals than 'man' does, but 'man' comprises more ideas or attributes [more

**, more "**

*predicates*

__speci__*-*fications", i.e., more

*"*[key

**de**"__term__inations**used by both Hegel and Marx] --**

__term__**M.D.**]:

one has more instances, the other more

**;**

*degrees of reality*one has the

**greater**

**, the other the**

*extension***greater**

**."**

*intension*[Wolfgang Lenzen, "Leibniz's Logic", in Dov M. Gabbay and John Woods, eds.,

**, volume**

__Handbook of the History of Logic__**3**,

**The Rise of Modern Logic**:

**From Leibniz to Frege**, Elsevier B. V., [San Francisco:

**2004**], p.

**11**,

**emphases**

**].**

*added*Now, other than

**itself, the axiomatic system of arithmetic of the "**

__N__**atural" Numbers ['**

__N__**' signifies "is equal to**

__=__*] --*

__by____definition__"

**N**

__=__**{ 1, 2, 3, 4, . . .}**

-- itself, the

**"dialectical" arithmetic in the**

__first__**F**.

**.**

__E__**. "meta-system", or "dialectical system**

__D__**-progression", of dialectical arithmetics, which can only**

__s__*"*or

**quantify**"*"*[and quantitatively order or "

**"**__card__inize**[al]**

__ord__in

*ize**"*], the second axiomatic system of "dialectical arithmetic" in that "meta-system", or system

**-progression", that of the**

__s__**N**

__Q__*"*

**meta**-**atural**

__N__

__meta__*-*Numbers" --

**N**

__Q__

__=__**{**

__q__/1,__q__/2,__q__/3,__q__/4, . . .}-- is the

*most**"*tensional" -- the

__in__

*least**"*tensional" -- of all of the

__ex__**F**.

**.**

__E__**. axiomatic systems of dialectical arithmetic in that dialectical system**

__D__

__s__*-*progression.

This is because the

**N**

**system of dialectical arithmetic is less rich -- less complex and less "thought-concrete"; less "determinate" -- in its syntax, and in its semantics -- than are all of its subsequent, successor systems of dialectical arithmetic in that**

__Q__**F**.

**.**

__E__**. dialectical progression of dialectical systems of arithmetic, and, therefore, the**

__D__**N**

**system has less descriptive power as an [ideographical] language for systems-modeling than do all of its subsequent, successor systems in that dialectical systems-progression.**

__Q__Such gradients of growing "determinateness" [Hegel, Marx], complexity, and "thought-concreteness" are of the essence of [e.g.,

**]**

*Systematic***ontological-categorial progressions in general.**

*Dialectical*Thus, dialectical

*"meta-*models" [ideographical representations which encompass both the other-induced / self-induced "evolution" [mere "

__model__" aspect],

*and the "self-induced*[

**volution"**__re__

__meta__*-*model aspect], of the systems they re-construct/pre-construct], if written in those

**N**

**-subsequent systems of dialectical ideography, can be expected to be no longer so "heuristic", so "intuitional", so "intensional" as the versions of those "meta-models" expressed in**

__Q__**N**or in

**N**

**.**

__Q__Many of those

**N**

**-subsequent systems of**

__Q__**, i.e., of dialectical arithmetic, are capable of being used to represent the detailed "determinations", or**

*dialectical ideography**"*[

__speci__*es*]

*-*, of the dialectical, [meta-]evolutionary, [meta-]

**fications**"**[**

*dynamical*

*meta**-*

__super__**^**

**z**-]

**of**

*systems**"*, in exact, precise,

**dialectical systems theory**"*"*, state-space trajectory / control-parameter-space path detail [in the cases of the axioms-systems of dialectical arithmetic that correspond to generic

**o-**__quant__**itative"**__qual__**N**

**"meta-numerals" with subscripts of the form**

__Q__**2^n - 1**, for

**n**

**> 3**, i.e., that correspond to

**N**

**"generic meta-numerals" of the form**

__Q__

__q__**/(2^n - 1)**, , for

**n**

**> 3**, in the

**N**

**"meta-model" of that "meta-system-atic" dialectical progression of axioms-systems of dialectical arithmetic], or in the form of explicit, trans-Platonian, Human-Phenomic <<**

__Q__**>> content-structures of, e.g.,**

*arithmoi eidetikoi***Super-**<<

**>>**

*Genos***/**<<

**Gene**>>

**/**<<

**Species**>>

**/ Sub-**<<

**Species**>>

**/ . . .**

*"*[in the cases of the axioms-systems of dialectical arithmetic that correspond to generic

**o-fractals"**__qual__**N**

**"meta-numerals" with subscripts of the form**

__Q__**8xn**, for

**n**

**> 2**, i.e., that correspond to

**N**

**"generic meta-numerals" of the form**

__Q__

__q__**/(8xn)**, for

**n**

**> 2**, in the

**N**

**"meta-model" of that "meta-system-atic" dialectical progression of axioms-systems of dialectical arithmetic].**

__Q__The

**N**-based "

**atural Numbers" axioms-system is the <<**

__N__**>> axioms-system in the**

*arche'***F**.

**.**

__E__**. 'ideo-meta-system' generated by the Seldon-Function formula for the**

__D__*"*-- for the dialectical system

**Meta**-**Systematic****"**__Dialectic__**-progression -- of the**

__s__**F**.

**.**

__E__**. axioms-systems of dialectical arithmetic.**

__D__That

**N**-based arithmetic is "dialectical" only in the "pre-vestigial" form of the

*purely-*, vestigial <<

**itative**__quant__**>> content of the Peano**

*aufheben***uccessor function,**

__s__**s**, per the second axiom of that axiomatic system of arithmetic, "

**P**eano

**P**ostulate

**2**", or

**PP2**for short:

**PP2**. If

**n**is in set

**N**, then

**s(n)**is also in set

__=__n + 1**N**.

The

**uccessor function, or**

__s__**uccession**

__s__*operator*,

**s**, operating upon any "

**atural" Number,**

__N__**n**, concurrently (

**a**.) <<

**>>-**

*aufheben*

*conserves***n**, in the sense that

**n**

*reappears in*and is

*"contained"*in

**n**

**+ 1**, (

**b**.) <<

**>>**

*aufheben*

*-elevates***n**, by adding to it a single

**of**

*unit***itative increment,**

__quant__**+ 1**, and also (

**c**.) <<

**>>-determinately**

*aufheben*

*negates***n**, by changing

**n**into its "next", into

*"*

**-**__not__**n**", in the specific, determinate form of

**n**

**+ 1**

**--**

**n**

**~= n + 1**;

**n < n + 1**;

**n + 1**

**is [a**

**fic case of]**

*speci*

*-*__not__**n**.

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