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*A Dialogue** on *__Dialectics__`. `**Excerpt**`.`

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`Dear Readers,`

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

`with a long time comrade of mine, about `__dialectics__`. `

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`I have labeled my comrade’s remarks with “`__I1__`” for “`__I__`nterlocutor `__1__`”, and my remarks with “`**I2**`”.`

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`Enjoy!`

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`Regards,`

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`Miguel`

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__I1__`: `It would seem that as there is empty and full zero, so there is empty and full dialectics?

__I2__: Great insight -- thanks
for sharing it!

As I see it, yes -- drawing from slightly different connotations of
"empty" and "full" from the connotations drawn on in **F**.*E*.*D*.’s ‘empty zero’ versus
‘full zero’ distinction -- there are also "empty dialectics", versus
"full dialectics".

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

**1**. The Peano __s__uccessor function, **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 *"***empty dialectic**", but
that *"***empty dialectic**" is the *intuitive **seed* of what we call the
'Seldonian First Dialectical Arithmetic', of the ' "purely"-**q**ualitative ordinals', i.e., of the **N**__Q__ '**meta**-**N**atural meta-Numbers', which, if still only
abstractly and generically so, can be interpreted to model *"***full dialectics**", as the *seed*, or «*arché*», of all of the other, later, **ever more **"**full**-__dialectic__al"**
**Seldonian dialectical arithmetics as well, that follow, beyond **N**__Q__, in the Seldonian *method of presentation* of those dialectical arithmetics.

Here's why I call the operation of the Peano __s__uccessor operator an *"***empty dialectic**".

The definition of the Peano __s__uccessor operator is ultra-simple: **s(****n****) = ****n**** +**** ****1**, for any "**N**atural" Number **n** in **N**. The Peano __s__uccessor function, **s**, operating upon any "**N**atural" Number, outputs the __s__uccessor "**N**atural" Number to any "**N**atural" Number upon which **s** operates.

This operation*/*definition comports to
the fundamental, «*aufheben*» character of all dialectics: its "output" or
result combines *"*__conservation__*"* [the **n**
of **s(****n****)** is still __preserved__ "in" **n**** + ****1**], transformation*/**"**determinate*** **__negation__*"* [ **n**** + ****1** is __NOT__* ***n**, and is not so in a __determinate__ sense: **s(****n****)** is greater than **n**
by exactly one "**N**atural Numbers" *unit*], and *"*__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 __shadow__ of «*aufheben*» “dialectic” -- the FORM of «*aufheben*» dialectic-in-general, but __EMPTY__ of
any of the qualitative, ontological, ontology-expansion, ontologically
revolutionizing CONTENT of even the generic stage of «*aufheben*» dialectic represented by the **N**__Q__, the first stage, of the Seldonian meta-systematic dialectic of the dialectical arithmetics, for which the **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

__t__ime
parameter,

**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** magnitude*. 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 "

**oo**"
answer is

__INFINITELY__* WRONG* -- departs

__INFINITELY__
from empirical actuality -- because everything that actually happens remains

__finite__
throughout, and because

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

__f__inite value
actually observed

*/*measured, say

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

* *__ANY__* *__f__*inite value*, minus

*"***I**__nfinity__*"*, is "still"

*"**infinite**"*, thus
yielding an

*infinite** residual*, or "[

*negative-*]

*infinity** residual*"; an

*infinite** model error ** *--

**f ****-**** ****oo**** =
****-****oo**.

Note that "

**oo**" is

__NOT__ [even]
a "

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

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

__un__solvable
diophantine equation" for "

**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

* "*__un__solvable diophantine equation"
becomes a

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

*'**seventh** *Seldonian
dialectical arithmetic', the

**R**-subsuming

**R**__mu__ 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

__sec__.,

__gm__.,

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

**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

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

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

*two* "opposing"

*/*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

__cumulum __of countless Newtonian collisional
singularities -- of planetessimals colliding with planetessimals, yielding
planetessimals

__PLUS__
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".

Each planetoid unit is a meta-planetessimal unit, «

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

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

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

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

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

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

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

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

__un__informative,

__mis__leading,

**quant**itatively
__infinitely__* erroneous*
value "

**oo**".

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

*bildung*» dialectic is an example of an

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

__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" «

*mentalité*»
can describe

**FINITE**, but qualitative, ontological change

**/**revolution, is as an

* "***IN***finite**"
*quantitative change

*!* ...

...

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

**gain** -- of

**ontological** **r****evolution** ...