A 'Supplementary Opposition', NOT a “Radical DUALism”.

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_   |-=   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_ arithmetic axioms-system as positive fruition of that immanent critique.

On the contrary, that ‘quantitativity’ is merely “demoted” [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 the subscript[ed] ordinal numbers, and even of the subscript[ed] cardinal arithmetic, that goes on in the _N_Q_ axioms-system, e.g., per its ‘‘‘multiplication’’’ axiom.

That is, even the subscript-level -- ‘‘‘subordinated’’’ -- ‘quantitativity’ of the N_ ordinal/cardinal numbers, is crucially leveraged, 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_ 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 posited as existing.

For more information regarding these Seldonian insights, please see --

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.