A DialogueonDialectics.Excerpt.

Dear Readers,

Reproduced below is an excerpt from the [edited] transcript of a recent dialogue,

with a long time comrade of mine, aboutdialectics.

I have labeled my comrade’s remarks with “I1” for “Interlocutor1”, and my remarks with “I2”.

Enjoy!

Regards,

Miguel

I1:It would seem that as there is empty and full zero, so there is empty and full dialectics?

**: Great insight -- thanks for sharing it!**

__I2__As I see it, yes -- drawing from slightly different connotations of "empty" and "full" from the connotations drawn on in

**F**.

__.__

*E*__.’s ‘empty zero’ versus ‘full zero’ distinction -- there are also "empty dialectics", versus "full dialectics".__

*D*To my mind, two examples of ‘‘‘empty dialectics’’’ are the following --

**1**. The Peano

**uccessor function,**

__s__**s**, which resides at the core of the first four, first-order Peano Postulates, which axiomatize the first-order, ordinal arithmetic of the "

**N**atural" Numbers,

**N**

**= {**

**1**

**,**

**2**

**,**

**3**

**, ... }**, propagates an

*"*, but that

**empty dialectic**"*"*is the

**empty dialectic**"

*intuitive***of what we call the 'Seldonian First Dialectical Arithmetic', of the ' "purely"-**

*seed*__ualitative ordinals', i.e., of the__

**q****N**

**'**

__Q__**meta**-

**N**atural meta-Numbers', which, if still only abstractly and generically so, can be interpreted to model

*"*, as the

**full dialectics**"**, or «**

*seed***», of all of the other, later,**

*arché**Seldonian dialectical arithmetics as well, that follow, beyond*

**ever more**"__-__**full****"**__dialectic__al**N**

**, in the Seldonian**

__Q__*method of presentation*of those dialectical arithmetics.

Here's why I call the operation of the Peano

**uccessor operator an**

__s__*"*.

**empty dialectic**"The definition of the Peano

**uccessor operator is ultra-simple:**

__s__**s(**

**n**

**) =**

**n**

**+**

**1**, for any "

**N**atural" Number

**n**in

**N**. The Peano

**uccessor function,**

__s__**s**, operating upon any "

**N**atural" Number, outputs the

**uccessor "**

__s__**N**atural" Number to any "

**N**atural" Number upon which

**s**operates.

This operation

**definition comports to the fundamental, «**

*/***» character of all dialectics: its "output" or result combines**

*aufheben**"*

__conservation__*"*[the

*of*

**n****s(**

**n****)**is still

**"in"**

__preserved__

**n****+**

**1**], transformation

*/**"*

*determinate*

__negation__*"*[

**n**

**+**

**1**is

__NOT__

**n**, and is not so in a

**sense:**

__determinate__**s(**

**n**

**)**is greater than

**n**by exactly one "

**N**atural Numbers"

**], and**

*unit**"*

__elevation__*"*

**advancement [**

*/***n**is increased

**lifted**

*/***advanced**

*/***superseded, in**

*/***s(**

**n**

**)**, into

**n**

**+**

**1**, by a gain in value of

**1**"

**N**atural Numbers", "purely"-quantitative-ordinal

**].**

*unit*But this is merely a “purely”-quantitative

*of «*

__shadow__**» “dialectic” -- the FORM of «**

*aufheben***» dialectic-in-general, but**

*aufheben***of any of the qualitative, ontological, ontology-expansion, ontologically revolutionizing CONTENT of even the generic stage of «**

__EMPTY__**» dialectic represented by the**

*aufheben***N**

**, the first stage, of the Seldonian meta-systematic dialectic of the dialectical arithmetics, for which the**

__Q__**N**alone constitute the

**0**th stage. It is therefore, to my mind,

*"*.

**empty dialectic**"**2**. When an equation modeling physical actuality, such as -- to begin at the psychohistorical beginning of such -- the Newton gravity equation, as a "purely"-quantitative equation, arrives at a division by "empty zero",

**0**, signifying, in this specific case, a collision of, e.g., two mutually-gravitating planets, planet

**1**and planet

**2**, via the disappearance of any distance,

**r**

**12**

**(t)**, between their centers of mass, for a finite value of its

**ime parameter,**

__t__**t**-- call that moment of collision

**t* --**so that

**r**

**12**

**(t*) = 0**, the result is, apparently --

**F**

**12**

**(t*) = GM**

**1**

**M**

**2**

**/r**

**12**

**(t*)^2 = GM**

**1**

**M**

**2**

**/0^2 = GM**

**1**

**M**

**2**

**/0 "=" "**

**oo**

**"**

-- signifying a Newtonian gravitational force of

*infinite***. However, what actually happens, in physical fact, is that the gravitic force between the two planets 'dis-existentiates', along with the two planets themselves. This "**

*magnitude***oo**" answer is

__INFINITELY__**-- departs**

*WRONG***from empirical actuality -- because everything that actually happens remains**

__INFINITELY__**throughout, and because**

__finite__*"*

*model error**"*["residual"] is the difference between the

**inite value actually observed**

__f__**measured, say**

*/***f**, and the model-predicted value.

__ANY__

__f__*inite value*, minus

*"*

**I**

__nfinity__*"*, is "still"

*"*

*infinite**"*, thus yielding an

*infinite***, or "[**

*residual**negative-*]

*; an*

*infinity***"***residual*

*infinite*

*model error**--*

**f**

**-**

**oo**

**=**

**-**

**oo**.

Note that "

**oo**" is

**[even] a "**

__NOT__**R**eal" Number, so that, at the moment of planetary collision

**singularity, the Newton Equation becomes, in effect a "Goedel-Incompleteness-Asserting Formula deformalizing**

*/***solvable diophantine equation" for "**

__un__**R**eal" Numbers arithmetic: its solution is not possible within the "

**R**eal" Numbers; its solution takes us outside

*beyond the set*

**/****R**.

This Newtonian

*"*

**solvable diophantine equation" becomes a**

__un__*"*

**diophantine equation" when re-expressed within the**

__solvable__*'*

*seventh**Seldonian dialectical arithmetic', the*

**R**-subsuming

**R**

*arithmetic, when this "purely"-quantitative equation is 're-qualified', by multiplying it by the appropriate combinations of the 'metrical qualifiers' for the metrological units of*

__mu__**.,**

__sec__**.,**

__gm__**&**

**., and by 'ontological qualifiers' qualifying/distinguishing Planet**

__cm__**1**versus Planet

**2**,

**&**via a new kind of number -- via a new element of number 'ideo-ontology' -- in the form of what we call the

*'*

**meta-number' -- a 'qualo-quantitative, existential zero', for more about which, see --**

*full zero*http://feddialectics-miguel.blogspot.com/2015/04/an-arithmetic-in-which-division-by-zero.html

Moreover, the value "

**oo**" is a mere FORM, a FORM that is EMPTY of any of the real, qualitative, ontological, ontology-expanding, ontologically revolutionizing CONTENT of this gravitic dialectical process of collision that it attempts to model.

What really occurs is that the

**"opposing"**

*two***colliding planets produce a**

*/**"*

*complex unity**"*of mutual fragmentation

**mutual dis-integration, and mutual coalescence**

*/***mutual re-integration, producing, in combination, new planetary and sub-planetary ontology, qualitatively, ontologically different from the ontology -- consisting of Planet**

*/***1**and

*versus Planet*

**/****2**-- whose existence was implicit in the model

*before*

**t***.

This kind of Newtonian, gravitic, collisional dialectic is precisely how stellar

**planetary systems, such as our Solar System,**

*/***.**

*BUILD THEMSELVES*Such systems are a natural-historical

**of countless Newtonian collisional singularities -- of planetessimals colliding with planetessimals, yielding planetessimals**

__cumulum__**PLANETOIDS, of planetoids colliding with planetoids, yielding planetoids**

__PLUS__**'''DWARF PLANETS''', of '''dwarf planets''' colliding with '''dwarf planets''', yielding '''dwarf planets'''**

__PLUS__**PROTO-PLANETS, and of proto-planets colliding with proto-planets, yielding proto-planets**

__PLUS__**PLANETS... all instances of the Seldonian '''Fundamental Law''', which is the 'strong contrary' of the Boolean "Fundamental Law".**

__PLUS__Each planetoid unit is a meta-planetessimal unit, «

**» made up out of a heterogeneous multiplicity of planetessimal units.**

*aufheben*Each '''dwarf planet''' unit is a meta-planetoid unit, «

**» made up out of a heterogeneous multiplicity of planetoid units.**

*aufheben*Each ''proto-planet'' unit is a meta-'''dwarf planet''' unit, «

**» made up out of a heterogeneous multiplicity of '''dwarf planet''' units.**

*aufheben*Each planet unit is a meta-''proto-planet'' unit, «

**» made up out of a heterogeneous multiplicity of ''proto-planet'' units.**

*aufheben*Each such collision corresponds to yet another Newtonian "division-by-zero" singularity; each one produces a "qualitative, ontological change", an "ontological" revolution, changing the ontology of the "solar system"-in-formation.

Each such qualitative, ontological change "singularity" in the course of the 'qualo-quantitative self-

__meta__*-*evolution' of a "solar system"-in-formation, if described by Newtonian, "purely"-quantitative gravitic equations, is described by the

**informative,**

__un__**leading,**

__mis__

__itatively__**quant**

__infinitely__**value "**

*erroneous***oo**".

That is why the Newtonian, "purely"-quantitative description of this gravitic, collisional, solar-system 'self-building'/'self-«

**» dialectic is an example of an**

*bildung**"*: all of the qualitative, ontological, ontology-expansion, ontologically revolutionizing CONTENT of this process of "solar system" 'qualo-quantitative self-

**empty dialectic**"

__meta__*-*evolution' is missing from this Newtonian description. ...

... Apparently, the only way that the "purely"-quantitative mathematical models of the -- still present -- epoch of the "exchange-value" «

**» can describe**

*mentalité*__, but qualitative, ontological change__

**FINITE***revolution, is as an*

**/***"*

**IN**

*finite**"*quantitative change

**...**

*!*...

*"*

__In__finite*"*quantitative change is the quantitative '''shadow''' of ontological change, of qualitative change, of ontological

__-- of__

**gain**

**ontological**

**r***...*

**evolution**
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