Thursday, September 19, 2019

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 Readers,




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 notabsolutely absent” in the purequalitativity’ 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 --

and

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of dialectical art -- see:




¡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.























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