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A Supplementary Opposition, NOT a “Radical Dualism” --The Subordinated ‘Quantitativity’ of the N Q   “Purely”-Qualitative Seldonian Arithmetic/Algebra for Dialectic.
 
Dear Guest of this web site,



I have incorporated herein, below, a blog-entry authored by my colleague, Miguel Detonacciones, and posted, earlier, to his ‘F.E.D. Dialectics’ blog.  

The version pasted-in below has incorporated some further edits suggested by the E.D. Editors of the F.E.D. Special Council for Encyclopedia Dialectica [E.D.], beyond those that were included in the original blog-entry.

Enjoy!
 


Dialogically yours,



Aoristos Dyosphainthos,

Voting Member, F.E.D. General Council,
Participant, F.E.D. Special Council for Public Liaison, 
Chief, F.E.D. Office of Public Liaison.











A Supplementary Opposition, NOT a “Radical Dualism” --The Subordinated ‘Quantitativity’ of the N Q   “Purely”-Qualitative Seldonian Arithmetic/Algebra for Dialectic.







Dear Reader,



In the Seldonian ‘Dialectical, Immanent Critique of the “First Order”, “Natural” Arithmetic System’, notated, in the language of the N Q   dialectical arithmetic itself, as -- 
N   ---)  N  N     =   q N + q NN    |-=     N  ~+~ N Q  
--  the ‘quantitativity’ of the, “first order”, “Natural Numbers” arithmetic system is not “abstractly negated”, and, therefore, is not “absolutely absent” in the “pure” ‘qualitativity’ of the N Q   arithmetical axioms-system as the positive fruition of that immanent critique.

On the contrary, that ‘quantitativity’ is merely “demoted” 
[cf. Hegel] -- is ‘subordinated yet still present in’ that N Q   successor system of arithmetic; still present in that “purely” qualitative arithmetical fruition, by way of its subscript[ed] ordinal numbers, and even of the subscript cardinal arithmetic, that goes on in the N Q   axioms-system, e.g., per its main ‘‘‘multiplication’’’ axiom:  qy x qx   |-=  qx + qy+x.

That is, even the subscript-level -- ‘‘‘subordinated’’’ -- ‘quantitativity’ of the N  ordinal/cardinal numbers, is leveraged, crucially, in all variants of the N Q   product-rule axiom, so as to incorporate their cardinal aspect, e.g., in the form of subscript[ed] cardinal addition, to regain, to restore, and to maintain, after each N Q   ‘‘‘multiplication’’’ operation, the ordinal ‘consecutivity’ of the generic N Q   ‘meta-numerals’, in each ‘self-iteration’ of the generic Dyadic and Triadic Seldon Functions.

Therefore, the opposition between N  and N Q   in --
N 2  |-=  N  ~+~ N Q  
-- is not a “radical dualism”, but a dialectical ‘supplementary opposition’, with N Q   «aufheben»-conserving as well as «aufheben»-elevating and «aufheben»-determinately-negating N, and thereby ‘‘‘supplementing’’’ N. 

This ‘‘‘supplementation’’’ arises, conceptually, so as to overcome an internal deficiency discovered within N  itself, e.g., by means of the “first order” conjunction of the Goedel Completeness and Incompleteness Theorems, implying the existence of “Non-Standard Models” of the “Natural Numbers” if the Standard Model is to be posited as existing.







For more information regarding these Seldonian insights, please see --
http://www.dialectics.org/dialectics.org/

and

www.dialectics.info

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ -- see:
https://www.etsy.com/shop/DialecticsMATH?ref=search_shop_redirect




¡ENJOY!



Regards,



Miguel Detonacciones

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.











JPG.











http://www.dialectics.org/dialectics.org/http://www.dialectics.infohttps://www.etsy.com/shop/DialecticsMATH?ref=search_shop_redirect19_Entry_1_files/F.E.D._,_Depiction_,_%27Derivation%20of%20the%20Sub-N-Q_Dialectical_Arithmetic_from_the_Standard_%27%27Natural%27%27_Arithmetic%27_,_Last_Updated_01JAN2020.jpgshapeimage_3_link_0shapeimage_3_link_1shapeimage_3_link_2shapeimage_3_link_3

September 19, 2019 9:19 PM

 
 
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