Aoristos
’
s Blog
September 19, 2019 9:19 PM
![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.
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