A Dialogue on Dialectics. Excerpt -- The Dialectical 'Meta-Number' Signifying Singularity [Ontological Revolution].

A Dialogue on Dialectics.  

Excerpt -- The Dialectical 'Meta-Number' Signifying Singularity [Ontological Revolution].

Dear Reader,

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

with a long time comrade of mine, about dialectics.  

I have labeled my comrade’s remarks with “I1” for “Interlocutor 1”, 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?

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 successor function, s, which resides at the core of the first four, first-order Peano Postulates, which axiomatize the first-order, ordinal arithmetic of the "Natural" 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"-qualitative ordinals', i.e., of the NQ 'meta-Natural 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-dialectical" Seldonian dialectical arithmetics as well, that follow, beyond NQ, in the Seldonian method of presentation of those dialectical arithmetics. 

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

The definition of the Peano successor operator is ultra-simple:  s(n)  =  n + 1, for any "Natural" Number n in N.  The Peano successor function, s, operating upon any "Natural" Number, outputs the successor "Natural" Number to any "Natural" 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 "Natural Numbers" unit], and "elevation"/advancement [n is increased/lifted/advanced/superseded, in s(n), into n + 1, by a gain in value of 1 "Natural 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 NQ, the first stage, of the Seldonian meta-systematic dialectic of the dialectical arithmetics, for which the N alone constitute the 0th 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, r12(t), between their centers of mass, for a finite value of its time parameter, t -- call that moment of collision t* -- so that r12(t*)  =  0, the result is, apparently --

F12(t*)  =  GM1M2/r12(t*)^2  =  GM1M2/0^2  =  GM1M2/0  "="  "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 finite value actually observed/measured, say f, and the model-predicted value.  ANY finite value, minus"Infinity", 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 "Real" Number, so that, at the moment of planetary collision/singularity, the Newton Equation becomes, in effect a "Goedel-Incompleteness-Asserting Formula deformalizing unsolvable diophantine equation" for "Real" Numbers arithmetic:  its solution is not possible within the "Real" Numbers; its solution takes us outside/beyond the set R.

This Newtonian "unsolvable diophantine equation" becomes a "solvable diophantine equation" when re-expressed within the 'seventh Seldonian dialectical arithmetic', the R-subsuming Rmu 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 uninformative, misleading, quantitatively 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 "INfinite" quantitative change! ...

... "Infinite" quantitative change is the quantitative '''shadow''' of ontological change, of qualitative change, of ontological gain -- of ontological revolution ...